Abstract group data - 972.525

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• gps_groups •

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

  
  {'Agroup': False, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '27.5', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 3, 'aut_exponent': 12, 'aut_gen_orders': [6, 6, 12, 6], 'aut_gens': [[1, 3, 9, 54], [38, 813, 855, 550], [668, 327, 495, 117], [19, 681, 819, 738], [19, 6, 9, 99]], 'aut_group': None, 'aut_hash': 7701181865426587749, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 23328, 'aut_permdeg': 60, 'aut_perms': [1363373940097568734829774090367783710636974871602255140636990074203858192288973668, 7077614723885748809937171602828661606959745700260308333384758562489319522269658716, 7220957735481524442566304972388279109482965861967602833810998886126026556399725683, 7221241390907246963491622583860072529791410581785871959195280028907276925901900948], 'aut_phi_ratio': 72.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 3, 1, 1], [3, 1, 2, 1], [3, 3, 2, 1], [3, 3, 6, 1], [3, 4, 6, 1], [3, 9, 2, 1], [3, 12, 4, 1], [3, 12, 12, 1], [3, 36, 4, 1], [6, 3, 2, 1], [6, 9, 2, 1], [6, 9, 6, 1], [6, 27, 2, 1], [9, 9, 4, 1], [9, 36, 8, 1], [18, 27, 4, 1]], 'aut_supersolvable': False, 'aut_tex': 'C_6^2.C_3^4.C_2^3', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 3, 'autcent_group': '27.5', 'autcent_hash': 5, 'autcent_nilpotent': True, 'autcent_order': 27, 'autcent_solvable': True, 'autcent_split': False, 'autcent_supersolvable': True, 'autcent_tex': 'C_3^3', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 12, 'autcentquo_group': '864.4673', 'autcentquo_hash': 4673, 'autcentquo_nilpotent': False, 'autcentquo_order': 864, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'S_4\\times S_3^2', 'cc_stats': [[1, 1, 1], [2, 3, 1], [3, 1, 2], [3, 3, 8], [3, 4, 6], [3, 9, 2], [3, 12, 16], [3, 36, 4], [6, 3, 2], [6, 9, 8], [6, 27, 2], [9, 9, 4], [9, 36, 8], [18, 27, 4]], 'center_label': '3.1', 'center_order': 3, 'central_product': True, 'central_quotient': '324.130', 'commutator_count': 1, 'commutator_label': '36.14', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '3.1', '3.1', '3.1', '3.1', '3.1'], 'composition_length': 7, 'conjugacy_classes_known': True, 'counter': 525, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [['12.3', 1], ['81.7', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 3, 1, 1], [3, 1, 2, 1], [3, 3, 2, 4], [3, 4, 2, 3], [3, 9, 2, 1], [3, 12, 2, 8], [3, 36, 2, 2], [6, 3, 2, 1], [6, 9, 2, 4], [6, 27, 2, 1], [9, 9, 2, 2], [9, 36, 2, 4], [18, 27, 2, 2]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 21060, 'exponent': 18, 'exponents_of_order': [5, 2], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [[9, 0, 6]], 'familial': False, 'frattini_label': '9.2', 'frattini_quotient': '108.41', 'hash': 525, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 6, 'inner_gen_orders': [3, 3, 6, 6], 'inner_gens': [[1, 3, 333, 396], [1, 3, 522, 81], [649, 516, 9, 702], [37, 30, 333, 54]], 'inner_hash': 130, 'inner_nilpotent': False, 'inner_order': 324, 'inner_split': True, 'inner_tex': 'A_4\\times \\He_3', 'inner_used': [1, 2, 3, 4], 'irrC_degree': 9, 'irrQ_degree': 18, 'irrQ_dim': 18, 'irrR_degree': 18, 'irrep_stats': [[1, 27], [3, 33], [9, 8]], 'label': '972.525', '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': 'C6^2.C3^3', 'ngens': 7, 'nilpotency_class': -1, 'nilpotent': False, 'normal_counts': [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 17, 'number_characteristic_subgroups': 17, 'number_conjugacy_classes': 68, 'number_divisions': 35, 'number_normal_subgroups': 44, 'number_subgroup_autclasses': 106, 'number_subgroup_classes': 272, 'number_subgroups': 1710, 'old_label': None, 'order': 972, 'order_factorization_type': 32, 'order_stats': [[1, 1], [2, 3], [3, 404], [6, 132], [9, 324], [18, 108]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': True, 'outer_exponent': 6, 'outer_gen_orders': [2, 6, 6], 'outer_gen_pows': [0, 0, 0], 'outer_gens': [[649, 6, 45, 605], [325, 6, 9, 81], [668, 651, 693, 379]], 'outer_group': '72.48', 'outer_hash': 48, 'outer_nilpotent': False, 'outer_order': 72, 'outer_permdeg': 10, 'outer_perms': [367920, 145, 806404], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_6\\times D_6', 'pc_rank': 4, 'perfect': False, 'permutation_degree': 13, 'pgroup': 0, 'primary_abelian_invariants': [3, 3, 3], 'quasisimple': False, 'rank': 3, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 1], [2, 13], [3, 1], [6, 16], [18, 4]], 'representations': {'PC': {'code': 24449422340869039611836880317974969067063990891, 'gens': [1, 2, 3, 5], 'pres': [7, 3, 3, 2, 3, 2, 3, 3, 6995, 3663, 58, 18651, 13864, 956, 2748, 760, 102, 6053, 2035, 1790, 166]}, 'GLZN': {'d': 2, 'p': 36, 'gens': [47089, 1182841, 1622293, 909811, 46825, 70633, 607117]}, 'Perm': {'d': 13, 'gens': [566183644, 562474920, 1089851040, 14888280, 566183640, 7, 16]}}, 'schur_multiplier': [3, 3, 6], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [3, 3, 3], 'solvability_type': 8, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': 'C_6^2.C_3^3', '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: 143947918
    {'aut_label': '1A', 'centralizer': '1.a1', 'counter': 1, 'group_counter': 525, 'group_order': 972, 'label': '1A', 'order': 1, 'powers': [1, 1], 'representative': 0, 'size': 1}
  • id: 143947929
    {'aut_label': '2A', 'centralizer': '3.b1', 'counter': 2, 'group_counter': 525, 'group_order': 972, 'label': '2A', 'order': 2, 'powers': [1, 2], 'representative': 27, 'size': 3}
  • id: 143947940
    {'aut_label': '3A1', 'centralizer': '1.a1', 'counter': 3, 'group_counter': 525, 'group_order': 972, 'label': '3A1', 'order': 3, 'powers': [4, 1], 'representative': 324, 'size': 1}
  • id: 143947951
    {'aut_label': '3A1', 'centralizer': '1.a1', 'counter': 4, 'group_counter': 525, 'group_order': 972, 'label': '3A-1', 'order': 3, 'powers': [3, 1], 'representative': 648, 'size': 1}
  • id: 143947962
    {'aut_label': '3B1', 'centralizer': '3.a1', 'counter': 5, 'group_counter': 525, 'group_order': 972, 'label': '3B1', 'order': 3, 'powers': [6, 1], 'representative': 18, 'size': 3}
  • id: 143947973
    {'aut_label': '3B1', 'centralizer': '3.a1', 'counter': 6, 'group_counter': 525, 'group_order': 972, 'label': '3B-1', 'order': 3, 'powers': [5, 1], 'representative': 36, 'size': 3}
  • id: 143947983
    {'aut_label': '3C1', 'centralizer': '3.a1', 'counter': 7, 'group_counter': 525, 'group_order': 972, 'label': '3C1', 'order': 3, 'powers': [8, 1], 'representative': 469, 'size': 3}
  • id: 143947984
    {'aut_label': '3C1', 'centralizer': '3.a1', 'counter': 8, 'group_counter': 525, 'group_order': 972, 'label': '3C-1', 'order': 3, 'powers': [7, 1], 'representative': 542, 'size': 3}
  • id: 143947985
    {'aut_label': '3C1', 'centralizer': '3.a1', 'counter': 9, 'group_counter': 525, 'group_order': 972, 'label': '3D1', 'order': 3, 'powers': [10, 1], 'representative': 866, 'size': 3}
  • id: 143947919
    {'aut_label': '3C1', 'centralizer': '3.a1', 'counter': 10, 'group_counter': 525, 'group_order': 972, 'label': '3D-1', 'order': 3, 'powers': [9, 1], 'representative': 145, 'size': 3}
  • id: 143947920
    {'aut_label': '3C1', 'centralizer': '3.a1', 'counter': 11, 'group_counter': 525, 'group_order': 972, 'label': '3E1', 'order': 3, 'powers': [12, 1], 'representative': 578, 'size': 3}
  • id: 143947921
    {'aut_label': '3C1', 'centralizer': '3.a1', 'counter': 12, 'group_counter': 525, 'group_order': 972, 'label': '3E-1', 'order': 3, 'powers': [11, 1], 'representative': 757, 'size': 3}
  • id: 143947922
    {'aut_label': '3F1', 'centralizer': '4.a1', 'counter': 13, 'group_counter': 525, 'group_order': 972, 'label': '3F1', 'order': 3, 'powers': [14, 1], 'representative': 3, 'size': 4}
  • id: 143947923
    {'aut_label': '3F1', 'centralizer': '4.a1', 'counter': 14, 'group_counter': 525, 'group_order': 972, 'label': '3F-1', 'order': 3, 'powers': [13, 1], 'representative': 6, 'size': 4}
  • id: 143947924
    {'aut_label': '3F1', 'centralizer': '4.a1', 'counter': 15, 'group_counter': 525, 'group_order': 972, 'label': '3G1', 'order': 3, 'powers': [16, 1], 'representative': 327, 'size': 4}
  • id: 143947925
    {'aut_label': '3F1', 'centralizer': '4.a1', 'counter': 16, 'group_counter': 525, 'group_order': 972, 'label': '3G-1', 'order': 3, 'powers': [15, 1], 'representative': 654, 'size': 4}
  • id: 143947926
    {'aut_label': '3F1', 'centralizer': '4.a1', 'counter': 17, 'group_counter': 525, 'group_order': 972, 'label': '3H1', 'order': 3, 'powers': [18, 1], 'representative': 651, 'size': 4}
  • id: 143947927
    {'aut_label': '3F1', 'centralizer': '4.a1', 'counter': 18, 'group_counter': 525, 'group_order': 972, 'label': '3H-1', 'order': 3, 'powers': [17, 1], 'representative': 330, 'size': 4}
  • id: 143947928
    {'aut_label': '3I1', 'centralizer': '9.j1', 'counter': 19, 'group_counter': 525, 'group_order': 972, 'label': '3I1', 'order': 3, 'powers': [20, 1], 'representative': 344, 'size': 9}
  • id: 143947930
    {'aut_label': '3I1', 'centralizer': '9.j1', 'counter': 20, 'group_counter': 525, 'group_order': 972, 'label': '3I-1', 'order': 3, 'powers': [19, 1], 'representative': 37, 'size': 9}
  • id: 143947931
    {'aut_label': '3J1', 'centralizer': '12.b1', 'counter': 21, 'group_counter': 525, 'group_order': 972, 'label': '3J1', 'order': 3, 'powers': [22, 1], 'representative': 21, 'size': 12}
  • id: 143947932
    {'aut_label': '3J1', 'centralizer': '12.b1', 'counter': 22, 'group_counter': 525, 'group_order': 972, 'label': '3J-1', 'order': 3, 'powers': [21, 1], 'representative': 15, 'size': 12}
  • id: 143947933
    {'aut_label': '3J1', 'centralizer': '12.b1', 'counter': 23, 'group_counter': 525, 'group_order': 972, 'label': '3K1', 'order': 3, 'powers': [24, 1], 'representative': 12, 'size': 12}
  • id: 143947934
    {'aut_label': '3J1', 'centralizer': '12.b1', 'counter': 24, 'group_counter': 525, 'group_order': 972, 'label': '3K-1', 'order': 3, 'powers': [23, 1], 'representative': 24, 'size': 12}
  • id: 143947935
    {'aut_label': '3L1', 'centralizer': '12.b1', 'counter': 25, 'group_counter': 525, 'group_order': 972, 'label': '3L1', 'order': 3, 'powers': [26, 1], 'representative': 112, 'size': 12}
  • id: 143947936
    {'aut_label': '3L1', 'centralizer': '12.b1', 'counter': 26, 'group_counter': 525, 'group_order': 972, 'label': '3L-1', 'order': 3, 'powers': [25, 1], 'representative': 386, 'size': 12}
  • id: 143947937
    {'aut_label': '3L1', 'centralizer': '12.b1', 'counter': 27, 'group_counter': 525, 'group_order': 972, 'label': '3M1', 'order': 3, 'powers': [28, 1], 'representative': 115, 'size': 12}
  • id: 143947938
    {'aut_label': '3L1', 'centralizer': '12.b1', 'counter': 28, 'group_counter': 525, 'group_order': 972, 'label': '3M-1', 'order': 3, 'powers': [27, 1], 'representative': 383, 'size': 12}
  • id: 143947939
    {'aut_label': '3L1', 'centralizer': '12.b1', 'counter': 29, 'group_counter': 525, 'group_order': 972, 'label': '3N1', 'order': 3, 'powers': [30, 1], 'representative': 59, 'size': 12}
  • id: 143947941
    {'aut_label': '3L1', 'centralizer': '12.b1', 'counter': 30, 'group_counter': 525, 'group_order': 972, 'label': '3N-1', 'order': 3, 'powers': [29, 1], 'representative': 439, 'size': 12}
  • id: 143947942
    {'aut_label': '3L1', 'centralizer': '12.b1', 'counter': 31, 'group_counter': 525, 'group_order': 972, 'label': '3O1', 'order': 3, 'powers': [32, 1], 'representative': 221, 'size': 12}
  • id: 143947943
    {'aut_label': '3L1', 'centralizer': '12.b1', 'counter': 32, 'group_counter': 525, 'group_order': 972, 'label': '3O-1', 'order': 3, 'powers': [31, 1], 'representative': 133, 'size': 12}
  • id: 143947944
    {'aut_label': '3L1', 'centralizer': '12.b1', 'counter': 33, 'group_counter': 525, 'group_order': 972, 'label': '3P1', 'order': 3, 'powers': [34, 1], 'representative': 62, 'size': 12}
  • id: 143947945
    {'aut_label': '3L1', 'centralizer': '12.b1', 'counter': 34, 'group_counter': 525, 'group_order': 972, 'label': '3P-1', 'order': 3, 'powers': [33, 1], 'representative': 436, 'size': 12}
  • id: 143947946
    {'aut_label': '3L1', 'centralizer': '12.b1', 'counter': 35, 'group_counter': 525, 'group_order': 972, 'label': '3Q1', 'order': 3, 'powers': [36, 1], 'representative': 224, 'size': 12}
  • id: 143947947
    {'aut_label': '3L1', 'centralizer': '12.b1', 'counter': 36, 'group_counter': 525, 'group_order': 972, 'label': '3Q-1', 'order': 3, 'powers': [35, 1], 'representative': 130, 'size': 12}
  • id: 143947948
    {'aut_label': '3R1', 'centralizer': '36.j1', 'counter': 37, 'group_counter': 525, 'group_order': 972, 'label': '3R1', 'order': 3, 'powers': [38, 1], 'representative': 197, 'size': 36}
  • id: 143947949
    {'aut_label': '3R1', 'centralizer': '36.j1', 'counter': 38, 'group_counter': 525, 'group_order': 972, 'label': '3R-1', 'order': 3, 'powers': [37, 1], 'representative': 355, 'size': 36}
  • id: 143947950
    {'aut_label': '3R1', 'centralizer': '36.j1', 'counter': 39, 'group_counter': 525, 'group_order': 972, 'label': '3S1', 'order': 3, 'powers': [40, 1], 'representative': 34, 'size': 36}
  • id: 143947952
    {'aut_label': '3R1', 'centralizer': '36.j1', 'counter': 40, 'group_counter': 525, 'group_order': 972, 'label': '3S-1', 'order': 3, 'powers': [39, 1], 'representative': 491, 'size': 36}
  • id: 143947953
    {'aut_label': '6A1', 'centralizer': '3.b1', 'counter': 41, 'group_counter': 525, 'group_order': 972, 'label': '6A1', 'order': 6, 'powers': [3, 2], 'representative': 162, 'size': 3}
  • id: 143947954
    {'aut_label': '6A1', 'centralizer': '3.b1', 'counter': 42, 'group_counter': 525, 'group_order': 972, 'label': '6A-1', 'order': 6, 'powers': [4, 2], 'representative': 810, 'size': 3}
  • id: 143947955
    {'aut_label': '6B1', 'centralizer': '9.a1', 'counter': 43, 'group_counter': 525, 'group_order': 972, 'label': '6B1', 'order': 6, 'powers': [5, 2], 'representative': 9, 'size': 9}
  • id: 143947956
    {'aut_label': '6B1', 'centralizer': '9.a1', 'counter': 44, 'group_counter': 525, 'group_order': 972, 'label': '6B-1', 'order': 6, 'powers': [6, 2], 'representative': 45, 'size': 9}
  • id: 143947957
    {'aut_label': '6C1', 'centralizer': '9.a1', 'counter': 45, 'group_counter': 525, 'group_order': 972, 'label': '6C1', 'order': 6, 'powers': [7, 2], 'representative': 56, 'size': 9}
  • id: 143947958
    {'aut_label': '6C1', 'centralizer': '9.a1', 'counter': 46, 'group_counter': 525, 'group_order': 972, 'label': '6C-1', 'order': 6, 'powers': [8, 2], 'representative': 442, 'size': 9}
  • id: 143947959
    {'aut_label': '6C1', 'centralizer': '9.a1', 'counter': 47, 'group_counter': 525, 'group_order': 972, 'label': '6D1', 'order': 6, 'powers': [9, 2], 'representative': 118, 'size': 9}
  • id: 143947960
    {'aut_label': '6C1', 'centralizer': '9.a1', 'counter': 48, 'group_counter': 525, 'group_order': 972, 'label': '6D-1', 'order': 6, 'powers': [10, 2], 'representative': 380, 'size': 9}
  • id: 143947961
    {'aut_label': '6C1', 'centralizer': '9.a1', 'counter': 49, 'group_counter': 525, 'group_order': 972, 'label': '6E1', 'order': 6, 'powers': [11, 2], 'representative': 271, 'size': 9}
  • id: 143947963
    {'aut_label': '6C1', 'centralizer': '9.a1', 'counter': 50, 'group_counter': 525, 'group_order': 972, 'label': '6E-1', 'order': 6, 'powers': [12, 2], 'representative': 74, 'size': 9}
  • id: 143947964
    {'aut_label': '6F1', 'centralizer': '27.e1', 'counter': 51, 'group_counter': 525, 'group_order': 972, 'label': '6F1', 'order': 6, 'powers': [19, 2], 'representative': 10, 'size': 27}
  • id: 143947965
    {'aut_label': '6F1', 'centralizer': '27.e1', 'counter': 52, 'group_counter': 525, 'group_order': 972, 'label': '6F-1', 'order': 6, 'powers': [20, 2], 'representative': 11, 'size': 27}
  • id: 143947966
    {'aut_label': '9A1', 'centralizer': '9.k1', 'counter': 53, 'group_counter': 525, 'group_order': 972, 'label': '9A1', 'order': 9, 'powers': [54, 3], 'representative': 108, 'size': 9}
  • id: 143947967
    {'aut_label': '9A1', 'centralizer': '9.k1', 'counter': 54, 'group_counter': 525, 'group_order': 972, 'label': '9A-1', 'order': 9, 'powers': [53, 4], 'representative': 864, 'size': 9}
  • id: 143947968
    {'aut_label': '9A1', 'centralizer': '9.k1', 'counter': 55, 'group_counter': 525, 'group_order': 972, 'label': '9B1', 'order': 9, 'powers': [56, 3], 'representative': 452, 'size': 9}
  • id: 143947969
    {'aut_label': '9A1', 'centralizer': '9.k1', 'counter': 56, 'group_counter': 525, 'group_order': 972, 'label': '9B-1', 'order': 9, 'powers': [55, 4], 'representative': 865, 'size': 9}
  • id: 143947970
    {'aut_label': '9C1', 'centralizer': '36.k1', 'counter': 57, 'group_counter': 525, 'group_order': 972, 'label': '9C1', 'order': 9, 'powers': [58, 3], 'representative': 642, 'size': 36}
  • id: 143947971
    {'aut_label': '9C1', 'centralizer': '36.k1', 'counter': 58, 'group_counter': 525, 'group_order': 972, 'label': '9C-1', 'order': 9, 'powers': [57, 4], 'representative': 96, 'size': 36}
  • id: 143947972
    {'aut_label': '9C1', 'centralizer': '36.k1', 'counter': 59, 'group_counter': 525, 'group_order': 972, 'label': '9D1', 'order': 9, 'powers': [60, 3], 'representative': 456, 'size': 36}
  • id: 143947974
    {'aut_label': '9C1', 'centralizer': '36.k1', 'counter': 60, 'group_counter': 525, 'group_order': 972, 'label': '9D-1', 'order': 9, 'powers': [59, 4], 'representative': 255, 'size': 36}
  • id: 143947975
    {'aut_label': '9C1', 'centralizer': '36.k1', 'counter': 61, 'group_counter': 525, 'group_order': 972, 'label': '9E1', 'order': 9, 'powers': [62, 3], 'representative': 323, 'size': 36}
  • id: 143947976
    {'aut_label': '9C1', 'centralizer': '36.k1', 'counter': 62, 'group_counter': 525, 'group_order': 972, 'label': '9E-1', 'order': 9, 'powers': [61, 4], 'representative': 571, 'size': 36}
  • id: 143947977
    {'aut_label': '9C1', 'centralizer': '36.k1', 'counter': 63, 'group_counter': 525, 'group_order': 972, 'label': '9F1', 'order': 9, 'powers': [64, 3], 'representative': 968, 'size': 36}
  • id: 143947978
    {'aut_label': '9C1', 'centralizer': '36.k1', 'counter': 64, 'group_counter': 525, 'group_order': 972, 'label': '9F-1', 'order': 9, 'powers': [63, 4], 'representative': 385, 'size': 36}
  • id: 143947979
    {'aut_label': '18A1', 'centralizer': '27.h1', 'counter': 65, 'group_counter': 525, 'group_order': 972, 'label': '18A1', 'order': 18, 'powers': [53, 41], 'representative': 54, 'size': 27}
  • id: 143947980
    {'aut_label': '18A1', 'centralizer': '27.h1', 'counter': 66, 'group_counter': 525, 'group_order': 972, 'label': '18A-1', 'order': 18, 'powers': [54, 42], 'representative': 117, 'size': 27}
  • id: 143947981
    {'aut_label': '18A1', 'centralizer': '27.h1', 'counter': 67, 'group_counter': 525, 'group_order': 972, 'label': '18B1', 'order': 18, 'powers': [55, 41], 'representative': 55, 'size': 27}
  • id: 143947982
    {'aut_label': '18A1', 'centralizer': '27.h1', 'counter': 68, 'group_counter': 525, 'group_order': 972, 'label': '18B-1', 'order': 18, 'powers': [56, 42], 'representative': 119, '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: 13974758
    {'cdim': 1, 'counter': 1, 'faithful': False, 'group': '972.525', 'group_order': 972, 'image': None, 'label': '972.525.1a', 'multiplicity': 1, 'nt': [1, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 'schur_index': 1}
  • id: 13974769
    {'cdim': 1, 'counter': 2, 'faithful': False, 'group': '972.525', 'group_order': 972, 'image': None, 'label': '972.525.1b', 'multiplicity': 2, 'nt': [3, 1], 'qdim': 2, 'qvalues': [2, 2, 2, 2, -1, 2, -1, -1, -1, -1, -1, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 2, -1, -1, 2, 2, -1, -1, 2, 2, -1, 2, -1, -1, 2, 2, 2, 2, 2, -1, -1, 2, -1, -1, -1, -1, -1, -1, 2, -1, -1, 2, 2, -1, -1, -1, -1, -1, -1, 2, -1, -1, 2, 2], 'schur_index': 1}
  • id: 13974780
    {'cdim': 1, 'counter': 3, 'faithful': False, 'group': '972.525', 'group_order': 972, 'image': None, 'label': '972.525.1c', 'multiplicity': 2, 'nt': [3, 1], 'qdim': 2, 'qvalues': [2, 2, 2, 2, -1, 2, -1, -1, -1, -1, -1, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 2, -1, -1, 2, 2, -1, -1, 2, 2, -1, 2, 2, 2, -1, -1, 2, 2, 2, -1, -1, 2, -1, -1, -1, -1, -1, -1, -1, 2, 2, -1, -1, 2, -1, -1, 2, -1, -1, -1, 2, 2, -1, -1], 'schur_index': 1}
  • id: 13974787
    {'cdim': 1, 'counter': 4, 'faithful': False, 'group': '972.525', 'group_order': 972, 'image': None, 'label': '972.525.1d', 'multiplicity': 2, 'nt': [3, 1], 'qdim': 2, 'qvalues': [2, 2, 2, 2, -1, 2, -1, -1, -1, -1, -1, 2, -1, -1, -1, -1, -1, -1, -1, -1, 2, -1, -1, -1, 2, -1, 2, 2, -1, -1, 2, -1, -1, -1, 2, -1, -1, -1, 2, 2, 2, 2, 2, -1, -1, 2, -1, -1, -1, -1, -1, -1, -1, 2, 2, -1, -1, -1, 2, -1, -1, -1, 2, -1, 2, 2, -1, -1], 'schur_index': 1}
  • id: 13974788
    {'cdim': 1, 'counter': 5, 'faithful': False, 'group': '972.525', 'group_order': 972, 'image': None, 'label': '972.525.1e', 'multiplicity': 2, 'nt': [3, 1], 'qdim': 2, 'qvalues': [2, 2, 2, 2, -1, 2, -1, -1, -1, -1, -1, 2, -1, -1, -1, -1, -1, -1, -1, -1, 2, -1, -1, -1, 2, -1, 2, 2, -1, -1, 2, -1, -1, -1, 2, -1, 2, 2, -1, -1, 2, 2, 2, -1, -1, 2, -1, -1, -1, -1, -1, -1, 2, -1, -1, 2, -1, -1, -1, 2, -1, 2, -1, -1, -1, -1, 2, 2], 'schur_index': 1}
  • id: 13974789
    {'cdim': 1, 'counter': 6, 'faithful': False, 'group': '972.525', 'group_order': 972, 'image': None, 'label': '972.525.1f', 'multiplicity': 2, 'nt': [3, 1], 'qdim': 2, 'qvalues': [2, 2, 2, 2, -1, 2, -1, -1, -1, -1, -1, 2, -1, -1, -1, -1, -1, -1, 2, 2, -1, -1, -1, -1, -1, 2, -1, -1, 2, 2, -1, -1, 2, 2, -1, 2, -1, -1, -1, -1, 2, 2, 2, -1, -1, 2, -1, -1, -1, -1, 2, 2, -1, -1, -1, -1, -1, -1, 2, 2, -1, 2, 2, -1, -1, -1, -1, -1], 'schur_index': 1}
  • id: 13974790
    {'cdim': 1, 'counter': 7, 'faithful': False, 'group': '972.525', 'group_order': 972, 'image': None, 'label': '972.525.1g', 'multiplicity': 2, 'nt': [3, 1], 'qdim': 2, 'qvalues': [2, 2, 2, 2, -1, 2, -1, -1, -1, -1, -1, 2, -1, -1, -1, -1, -1, -1, 2, 2, 2, -1, -1, -1, 2, -1, 2, 2, -1, -1, 2, -1, -1, -1, 2, -1, -1, -1, -1, -1, 2, 2, 2, -1, -1, 2, -1, -1, -1, -1, 2, 2, -1, -1, -1, -1, 2, 2, -1, -1, 2, -1, -1, 2, -1, -1, -1, -1], 'schur_index': 1}
  • id: 13974791
    {'cdim': 1, 'counter': 8, 'faithful': False, 'group': '972.525', 'group_order': 972, 'image': None, 'label': '972.525.1h', 'multiplicity': 2, 'nt': [3, 1], 'qdim': 2, 'qvalues': [2, 2, 2, 2, -1, 2, -1, -1, -1, -1, -1, 2, 2, 2, 2, 2, 2, 2, -1, -1, -1, 2, 2, 2, -1, -1, -1, -1, -1, -1, -1, 2, -1, -1, -1, -1, -1, -1, -1, -1, 2, 2, 2, -1, -1, 2, -1, -1, -1, -1, -1, -1, -1, 2, 2, -1, 2, -1, -1, 2, -1, 2, -1, 2, 2, 2, -1, -1], 'schur_index': 1}
  • id: 13974792
    {'cdim': 1, 'counter': 9, 'faithful': False, 'group': '972.525', 'group_order': 972, 'image': None, 'label': '972.525.1i', 'multiplicity': 2, 'nt': [3, 1], 'qdim': 2, 'qvalues': [2, 2, 2, 2, -1, 2, -1, -1, -1, -1, -1, 2, 2, 2, 2, 2, 2, 2, -1, -1, -1, 2, 2, 2, -1, -1, -1, -1, -1, -1, -1, 2, -1, -1, -1, -1, -1, -1, -1, -1, 2, 2, 2, -1, -1, 2, -1, -1, -1, -1, -1, -1, 2, -1, -1, 2, -1, 2, 2, -1, 2, -1, 2, -1, -1, -1, 2, 2], 'schur_index': 1}
  • id: 13974759
    {'cdim': 1, 'counter': 10, 'faithful': False, 'group': '972.525', 'group_order': 972, 'image': None, 'label': '972.525.1j', 'multiplicity': 2, 'nt': [3, 1], 'qdim': 2, 'qvalues': [2, 2, 2, 2, -1, 2, -1, -1, -1, -1, -1, 2, 2, 2, 2, 2, 2, 2, 2, 2, -1, 2, 2, 2, -1, -1, -1, -1, -1, -1, -1, 2, -1, -1, -1, -1, 2, 2, 2, 2, 2, 2, 2, -1, -1, 2, -1, -1, -1, -1, 2, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], 'schur_index': 1}
  • id: 13974760
    {'cdim': 1, 'counter': 11, 'faithful': False, 'group': '972.525', 'group_order': 972, 'image': None, 'label': '972.525.1k', 'multiplicity': 2, 'nt': [3, 1], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, -1, 2, -1, 2, 2, 2, -1, -1, -1, -1, -1, -1], 'schur_index': 1}
  • id: 13974761
    {'cdim': 1, 'counter': 12, 'faithful': False, 'group': '972.525', 'group_order': 972, 'image': None, 'label': '972.525.1l', 'multiplicity': 2, 'nt': [3, 1], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 2, 2, -1, -1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, 2, -1, 2, -1, -1, -1, 2, 2, -1, -1, -1, -1], 'schur_index': 1}
  • id: 13974762
    {'cdim': 1, 'counter': 13, 'faithful': False, 'group': '972.525', 'group_order': 972, 'image': None, 'label': '972.525.1m', 'multiplicity': 2, 'nt': [3, 1], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, 2, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, -1, -1, 2, 2, 2, 2], 'schur_index': 1}
  • id: 13974763
    {'cdim': 1, 'counter': 14, 'faithful': False, 'group': '972.525', 'group_order': 972, 'image': None, 'label': '972.525.1n', 'multiplicity': 2, 'nt': [3, 1], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -1, -1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -1, -1, -1, -1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], 'schur_index': 1}
  • id: 13974764
    {'cdim': 3, 'counter': 15, 'faithful': False, 'group': '972.525', 'group_order': 972, 'image': None, 'label': '972.525.3a', 'multiplicity': 1, 'nt': [4, 4], 'qdim': 3, 'qvalues': [3, -1, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 0, 0, 0, 0, 0, 0, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 3, 3, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, -1], 'schur_index': 1}
  • id: 13974765
    {'cdim': 3, 'counter': 16, 'faithful': False, 'group': '972.525', 'group_order': 972, 'image': None, 'label': '972.525.3b', 'multiplicity': 2, 'nt': [9, 7], 'qdim': 6, 'qvalues': [6, 6, 6, 6, 0, -3, 0, 0, 0, 0, 0, -3, -3, -3, -3, -3, -3, -3, 0, 0, 0, -3, -3, 6, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 6, 6, -3, 0, 0, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 13974766
    {'cdim': 3, 'counter': 17, 'faithful': False, 'group': '972.525', 'group_order': 972, 'image': None, 'label': '972.525.3c', 'multiplicity': 2, 'nt': [9, 7], 'qdim': 6, 'qvalues': [6, 6, 6, 6, 0, -3, 0, 0, 0, 0, 0, -3, -3, -3, -3, -3, -3, -3, 0, 0, 0, 6, 6, -3, 0, 0, 0, 0, 0, 0, 0, -3, 0, 0, 0, 0, 0, 0, 0, 0, 6, 6, -3, 0, 0, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 13974767
    {'cdim': 3, 'counter': 18, 'faithful': False, 'group': '972.525', 'group_order': 972, 'image': None, 'label': '972.525.3d', 'multiplicity': 2, 'nt': [9, 7], 'qdim': 6, 'qvalues': [6, 6, 6, 6, 0, -3, 0, 0, 0, 0, 0, -3, 6, 6, 6, 6, 6, 6, 0, 0, 0, -3, -3, -3, 0, 0, 0, 0, 0, 0, 0, -3, 0, 0, 0, 0, 0, 0, 0, 0, 6, 6, -3, 0, 0, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 13974768
    {'cdim': 3, 'counter': 19, 'faithful': False, 'group': '972.525', 'group_order': 972, 'image': None, 'label': '972.525.3e', 'multiplicity': 2, 'nt': [9, 17], 'qdim': 6, 'qvalues': [6, 6, -3, -3, -3, 0, 3, -3, 3, 0, 0, 0, -3, -3, -3, 6, 6, -3, 0, 0, 0, 0, 0, 0, -3, -3, 0, 3, 3, 3, -3, 0, 0, -3, 3, 0, 0, 0, 0, 0, -3, -3, 0, 0, 0, 0, -3, -3, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 13974770
    {'cdim': 3, 'counter': 20, 'faithful': False, 'group': '972.525', 'group_order': 972, 'image': None, 'label': '972.525.3f', 'multiplicity': 2, 'nt': [9, 17], 'qdim': 6, 'qvalues': [6, 6, -3, -3, -3, 0, 3, -3, 3, 0, 0, 0, -3, 6, 6, -3, -3, -3, 0, 0, -3, 0, 0, 0, 3, 0, -3, 0, -3, -3, 3, 0, 3, 0, 0, 3, 0, 0, 0, 0, -3, -3, 0, 0, 0, 0, -3, -3, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 13974771
    {'cdim': 3, 'counter': 21, 'faithful': False, 'group': '972.525', 'group_order': 972, 'image': None, 'label': '972.525.3g', 'multiplicity': 2, 'nt': [9, 17], 'qdim': 6, 'qvalues': [6, 6, -3, -3, -3, 0, 3, -3, 3, 0, 0, 0, 6, -3, -3, -3, -3, 6, 0, 0, 3, 0, 0, 0, 0, 3, 3, -3, 0, 0, 0, 0, -3, 3, -3, -3, 0, 0, 0, 0, -3, -3, 0, 0, 0, 0, -3, -3, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 13974772
    {'cdim': 3, 'counter': 22, 'faithful': False, 'group': '972.525', 'group_order': 972, 'image': None, 'label': '972.525.3h', 'multiplicity': 2, 'nt': [9, 17], 'qdim': 6, 'qvalues': [6, 6, -3, -3, 0, 0, -3, 0, -3, 3, 3, 0, -3, -3, -3, 6, 6, -3, 0, 0, 3, 0, 0, 0, 0, 0, 3, -3, -3, -3, 0, 0, 3, 0, -3, 3, 0, 0, 0, 0, -3, -3, 0, 3, 3, 0, 0, 0, -3, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 13974773
    {'cdim': 3, 'counter': 23, 'faithful': False, 'group': '972.525', 'group_order': 972, 'image': None, 'label': '972.525.3i', 'multiplicity': 2, 'nt': [9, 17], 'qdim': 6, 'qvalues': [6, 6, -3, -3, 0, 0, -3, 0, -3, 3, 3, 0, -3, 6, 6, -3, -3, -3, 0, 0, 0, 0, 0, 0, -3, 3, 0, 3, 0, 0, -3, 0, -3, 3, 3, -3, 0, 0, 0, 0, -3, -3, 0, 3, 3, 0, 0, 0, -3, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 13974774
    {'cdim': 3, 'counter': 24, 'faithful': False, 'group': '972.525', 'group_order': 972, 'image': None, 'label': '972.525.3j', 'multiplicity': 2, 'nt': [9, 17], 'qdim': 6, 'qvalues': [6, 6, -3, -3, 0, 0, -3, 0, -3, 3, 3, 0, 6, -3, -3, -3, -3, 6, 0, 0, -3, 0, 0, 0, 3, -3, -3, 0, 3, 3, 3, 0, 0, -3, 0, 0, 0, 0, 0, 0, -3, -3, 0, 3, 3, 0, 0, 0, -3, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 13974775
    {'cdim': 3, 'counter': 25, 'faithful': False, 'group': '972.525', 'group_order': 972, 'image': None, 'label': '972.525.3k', 'multiplicity': 2, 'nt': [9, 17], 'qdim': 6, 'qvalues': [6, 6, -3, -3, 3, 0, 0, 3, 0, -3, -3, 0, -3, -3, -3, 6, 6, -3, 0, 0, -3, 0, 0, 0, 3, 3, -3, 0, 0, 0, 3, 0, -3, 3, 0, -3, 0, 0, 0, 0, -3, -3, 0, -3, -3, 0, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 13974776
    {'cdim': 3, 'counter': 26, 'faithful': False, 'group': '972.525', 'group_order': 972, 'image': None, 'label': '972.525.3l', 'multiplicity': 2, 'nt': [9, 17], 'qdim': 6, 'qvalues': [6, 6, -3, -3, 3, 0, 0, 3, 0, -3, -3, 0, -3, 6, 6, -3, -3, -3, 0, 0, 3, 0, 0, 0, 0, -3, 3, -3, 3, 3, 0, 0, 0, -3, -3, 0, 0, 0, 0, 0, -3, -3, 0, -3, -3, 0, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 13974777
    {'cdim': 3, 'counter': 27, 'faithful': False, 'group': '972.525', 'group_order': 972, 'image': None, 'label': '972.525.3m', 'multiplicity': 2, 'nt': [9, 17], 'qdim': 6, 'qvalues': [6, 6, -3, -3, 3, 0, 0, 3, 0, -3, -3, 0, 6, -3, -3, -3, -3, 6, 0, 0, 0, 0, 0, 0, -3, 0, 0, 3, -3, -3, -3, 0, 3, 0, 3, 3, 0, 0, 0, 0, -3, -3, 0, -3, -3, 0, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 13974778
    {'cdim': 3, 'counter': 28, 'faithful': False, 'group': '972.525', 'group_order': 972, 'image': None, 'label': '972.525.3n', 'multiplicity': 2, 'nt': [12, 20], 'qdim': 6, 'qvalues': [6, -2, 6, 6, -3, 6, -3, -3, -3, -3, -3, 6, 0, 0, 0, 0, 0, 0, -3, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, 1, 1, -2, 1, 1, 1, 1, 1, 1, -3, 6, 6, -3, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, 1, 1], 'schur_index': 1}
  • id: 13974779
    {'cdim': 3, 'counter': 29, 'faithful': False, 'group': '972.525', 'group_order': 972, 'image': None, 'label': '972.525.3o', 'multiplicity': 2, 'nt': [12, 20], 'qdim': 6, 'qvalues': [6, -2, 6, 6, -3, 6, -3, -3, -3, -3, -3, 6, 0, 0, 0, 0, 0, 0, -3, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, 1, 1, -2, 1, 1, 1, 1, 1, 1, 6, -3, -3, 6, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, -2, -2], 'schur_index': 1}
  • id: 13974781
    {'cdim': 3, 'counter': 30, 'faithful': False, 'group': '972.525', 'group_order': 972, 'image': None, 'label': '972.525.3p', 'multiplicity': 2, 'nt': [12, 20], 'qdim': 6, 'qvalues': [6, -2, 6, 6, -3, 6, -3, -3, -3, -3, -3, 6, 0, 0, 0, 0, 0, 0, 6, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, 1, 1, -2, 1, 1, 1, 1, -2, -2, -3, -3, -3, -3, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1], 'schur_index': 1}
  • id: 13974782
    {'cdim': 3, 'counter': 31, 'faithful': False, 'group': '972.525', 'group_order': 972, 'image': None, 'label': '972.525.3q', 'multiplicity': 2, 'nt': [12, 20], 'qdim': 6, 'qvalues': [6, -2, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 0, 0, 0, 0, 0, 0, -3, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, 1, 1, -3, -3, -3, -3, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1], 'schur_index': 1}
  • id: 13974783
    {'cdim': 9, 'counter': 32, 'faithful': False, 'group': '972.525', 'group_order': 972, 'image': None, 'label': '972.525.9a', 'multiplicity': 2, 'nt': [36, 537], 'qdim': 18, 'qvalues': [18, -6, 18, 18, 0, -9, 0, 0, 0, 0, 0, -9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6, -6, 3, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 13974784
    {'cdim': 9, 'counter': 33, 'faithful': True, 'group': '972.525', 'group_order': 972, 'image': None, 'label': '972.525.9b', 'multiplicity': 2, 'nt': [36, 1584], 'qdim': 18, 'qvalues': [18, -6, -9, -9, -9, 0, 9, -9, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 0, 0, 0, 0, 3, 3, -3, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 13974785
    {'cdim': 9, 'counter': 34, 'faithful': True, 'group': '972.525', 'group_order': 972, 'image': None, 'label': '972.525.9c', 'multiplicity': 2, 'nt': [36, 1584], 'qdim': 18, 'qvalues': [18, -6, -9, -9, 0, 0, -9, 0, -9, 9, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 0, -3, -3, 0, 0, 0, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 13974786
    {'cdim': 9, 'counter': 35, 'faithful': True, 'group': '972.525', 'group_order': 972, 'image': None, 'label': '972.525.9d', 'multiplicity': 2, 'nt': [36, 1584], 'qdim': 18, 'qvalues': [18, -6, -9, -9, 9, 0, 0, 9, 0, -9, -9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 0, 3, 3, 0, -3, -3, 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: 33080206
    {'center': '1.a1', 'center_index': 1, 'center_order': 972, 'counter': 1, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '972.525', 'group_counter': 525, 'group_order': 972, 'image': None, 'image_isoclass': '1.1', 'image_order': 1, 'indicator': 1, 'kernel': '1.a1', 'kernel_order': 972, 'label': '972.525.1a', 'nt': [1, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 33080217
    {'center': '1.a1', 'center_index': 1, 'center_order': 972, 'counter': 2, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '972.525', 'group_counter': 525, 'group_order': 972, 'image': None, 'image_isoclass': '3.1', 'image_order': 3, 'indicator': 0, 'kernel': '3.g1', 'kernel_order': 324, 'label': '972.525.1b1', 'nt': [3, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 0]], [[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, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[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, 0]], [[1, 0]]]}
  • id: 33080228
    {'center': '1.a1', 'center_index': 1, 'center_order': 972, 'counter': 3, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '972.525', 'group_counter': 525, 'group_order': 972, 'image': None, 'image_isoclass': '3.1', 'image_order': 3, 'indicator': 0, 'kernel': '3.g1', 'kernel_order': 324, 'label': '972.525.1b2', 'nt': [3, 2], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, 0]], [[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, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[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, 0]], [[1, 0]]]}
  • id: 33080239
    {'center': '1.a1', 'center_index': 1, 'center_order': 972, 'counter': 4, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '972.525', 'group_counter': 525, 'group_order': 972, 'image': None, 'image_isoclass': '3.1', 'image_order': 3, 'indicator': 0, 'kernel': '3.g1', 'kernel_order': 324, 'label': '972.525.1c1', 'nt': [3, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 0]], [[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, -1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]]]}
  • id: 33080250
    {'center': '1.a1', 'center_index': 1, 'center_order': 972, 'counter': 5, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '972.525', 'group_counter': 525, 'group_order': 972, 'image': None, 'image_isoclass': '3.1', 'image_order': 3, 'indicator': 0, 'kernel': '3.g1', 'kernel_order': 324, 'label': '972.525.1c2', 'nt': [3, 2], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, 0]], [[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, 1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]]]}
  • id: 33080261
    {'center': '1.a1', 'center_index': 1, 'center_order': 972, 'counter': 6, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '972.525', 'group_counter': 525, 'group_order': 972, 'image': None, 'image_isoclass': '3.1', 'image_order': 3, 'indicator': 0, 'kernel': '3.g1', 'kernel_order': 324, 'label': '972.525.1d1', 'nt': [3, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 0]], [[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, -1]], [[1, 0]], [[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, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]]]}
  • id: 33080271
    {'center': '1.a1', 'center_index': 1, 'center_order': 972, 'counter': 7, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '972.525', 'group_counter': 525, 'group_order': 972, 'image': None, 'image_isoclass': '3.1', 'image_order': 3, 'indicator': 0, 'kernel': '3.g1', 'kernel_order': 324, 'label': '972.525.1d2', 'nt': [3, 2], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, 0]], [[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, 1]], [[1, 0]], [[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, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]]]}
  • id: 33080272
    {'center': '1.a1', 'center_index': 1, 'center_order': 972, 'counter': 8, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '972.525', 'group_counter': 525, 'group_order': 972, 'image': None, 'image_isoclass': '3.1', 'image_order': 3, 'indicator': 0, 'kernel': '3.g1', 'kernel_order': 324, 'label': '972.525.1e1', 'nt': [3, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 0]], [[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, 1]], [[1, 0]], [[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, 0]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]]]}
  • id: 33080273
    {'center': '1.a1', 'center_index': 1, 'center_order': 972, 'counter': 9, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '972.525', 'group_counter': 525, 'group_order': 972, 'image': None, 'image_isoclass': '3.1', 'image_order': 3, 'indicator': 0, 'kernel': '3.g1', 'kernel_order': 324, 'label': '972.525.1e2', 'nt': [3, 2], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, 0]], [[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, -1]], [[1, 0]], [[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, 0]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]]]}
  • id: 33080207
    {'center': '1.a1', 'center_index': 1, 'center_order': 972, 'counter': 10, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '972.525', 'group_counter': 525, 'group_order': 972, 'image': None, 'image_isoclass': '3.1', 'image_order': 3, 'indicator': 0, 'kernel': '3.f1', 'kernel_order': 324, 'label': '972.525.1f1', 'nt': [3, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 0]], [[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, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]]]}
  • id: 33080208
    {'center': '1.a1', 'center_index': 1, 'center_order': 972, 'counter': 11, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '972.525', 'group_counter': 525, 'group_order': 972, 'image': None, 'image_isoclass': '3.1', 'image_order': 3, 'indicator': 0, 'kernel': '3.f1', 'kernel_order': 324, 'label': '972.525.1f2', 'nt': [3, 2], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, 0]], [[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, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]]]}
  • id: 33080209
    {'center': '1.a1', 'center_index': 1, 'center_order': 972, 'counter': 12, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '972.525', 'group_counter': 525, 'group_order': 972, 'image': None, 'image_isoclass': '3.1', 'image_order': 3, 'indicator': 0, 'kernel': '3.f1', 'kernel_order': 324, 'label': '972.525.1g1', 'nt': [3, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 0]], [[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, 0]], [[1, 0]], [[1, 0]], [[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, 0]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]]]}
  • id: 33080210
    {'center': '1.a1', 'center_index': 1, 'center_order': 972, 'counter': 13, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '972.525', 'group_counter': 525, 'group_order': 972, 'image': None, 'image_isoclass': '3.1', 'image_order': 3, 'indicator': 0, 'kernel': '3.f1', 'kernel_order': 324, 'label': '972.525.1g2', 'nt': [3, 2], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, 0]], [[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, 0]], [[1, 0]], [[1, 0]], [[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, 0]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]]]}
  • id: 33080211
    {'center': '1.a1', 'center_index': 1, 'center_order': 972, 'counter': 14, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '972.525', 'group_counter': 525, 'group_order': 972, 'image': None, 'image_isoclass': '3.1', 'image_order': 3, 'indicator': 0, 'kernel': '3.e1', 'kernel_order': 324, 'label': '972.525.1h1', 'nt': [3, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[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, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]]]}
  • id: 33080212
    {'center': '1.a1', 'center_index': 1, 'center_order': 972, 'counter': 15, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '972.525', 'group_counter': 525, 'group_order': 972, 'image': None, 'image_isoclass': '3.1', 'image_order': 3, 'indicator': 0, 'kernel': '3.e1', 'kernel_order': 324, 'label': '972.525.1h2', 'nt': [3, 2], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[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, -1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]]]}
  • id: 33080213
    {'center': '1.a1', 'center_index': 1, 'center_order': 972, 'counter': 16, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '972.525', 'group_counter': 525, 'group_order': 972, 'image': None, 'image_isoclass': '3.1', 'image_order': 3, 'indicator': 0, 'kernel': '3.e1', 'kernel_order': 324, 'label': '972.525.1i1', 'nt': [3, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[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, -1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]]]}
  • id: 33080214
    {'center': '1.a1', 'center_index': 1, 'center_order': 972, 'counter': 17, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '972.525', 'group_counter': 525, 'group_order': 972, 'image': None, 'image_isoclass': '3.1', 'image_order': 3, 'indicator': 0, 'kernel': '3.e1', 'kernel_order': 324, 'label': '972.525.1i2', 'nt': [3, 2], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[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, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]]]}
  • id: 33080215
    {'center': '1.a1', 'center_index': 1, 'center_order': 972, 'counter': 18, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '972.525', 'group_counter': 525, 'group_order': 972, 'image': None, 'image_isoclass': '3.1', 'image_order': 3, 'indicator': 0, 'kernel': '3.d1', 'kernel_order': 324, 'label': '972.525.1j1', 'nt': [3, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]]]}
  • id: 33080216
    {'center': '1.a1', 'center_index': 1, 'center_order': 972, 'counter': 19, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '972.525', 'group_counter': 525, 'group_order': 972, 'image': None, 'image_isoclass': '3.1', 'image_order': 3, 'indicator': 0, 'kernel': '3.d1', 'kernel_order': 324, 'label': '972.525.1j2', 'nt': [3, 2], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]]]}
  • id: 33080218
    {'center': '1.a1', 'center_index': 1, 'center_order': 972, 'counter': 20, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '972.525', 'group_counter': 525, 'group_order': 972, 'image': None, 'image_isoclass': '3.1', 'image_order': 3, 'indicator': 0, 'kernel': '3.c1', 'kernel_order': 324, 'label': '972.525.1k1', 'nt': [3, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]]]}
  • id: 33080219
    {'center': '1.a1', 'center_index': 1, 'center_order': 972, 'counter': 21, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '972.525', 'group_counter': 525, 'group_order': 972, 'image': None, 'image_isoclass': '3.1', 'image_order': 3, 'indicator': 0, 'kernel': '3.c1', 'kernel_order': 324, 'label': '972.525.1k2', 'nt': [3, 2], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]]]}
  • id: 33080220
    {'center': '1.a1', 'center_index': 1, 'center_order': 972, 'counter': 22, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '972.525', 'group_counter': 525, 'group_order': 972, 'image': None, 'image_isoclass': '3.1', 'image_order': 3, 'indicator': 0, 'kernel': '3.c1', 'kernel_order': 324, 'label': '972.525.1l1', 'nt': [3, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]]]}
  • id: 33080221
    {'center': '1.a1', 'center_index': 1, 'center_order': 972, 'counter': 23, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '972.525', 'group_counter': 525, 'group_order': 972, 'image': None, 'image_isoclass': '3.1', 'image_order': 3, 'indicator': 0, 'kernel': '3.c1', 'kernel_order': 324, 'label': '972.525.1l2', 'nt': [3, 2], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]]]}
  • id: 33080222
    {'center': '1.a1', 'center_index': 1, 'center_order': 972, 'counter': 24, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '972.525', 'group_counter': 525, 'group_order': 972, 'image': None, 'image_isoclass': '3.1', 'image_order': 3, 'indicator': 0, 'kernel': '3.b1', 'kernel_order': 324, 'label': '972.525.1m1', 'nt': [3, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 33080223
    {'center': '1.a1', 'center_index': 1, 'center_order': 972, 'counter': 25, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '972.525', 'group_counter': 525, 'group_order': 972, 'image': None, 'image_isoclass': '3.1', 'image_order': 3, 'indicator': 0, 'kernel': '3.b1', 'kernel_order': 324, 'label': '972.525.1m2', 'nt': [3, 2], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 33080224
    {'center': '1.a1', 'center_index': 1, 'center_order': 972, 'counter': 26, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '972.525', 'group_counter': 525, 'group_order': 972, 'image': None, 'image_isoclass': '3.1', 'image_order': 3, 'indicator': 0, 'kernel': '3.a1', 'kernel_order': 324, 'label': '972.525.1n1', 'nt': [3, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]]]}
  • id: 33080225
    {'center': '1.a1', 'center_index': 1, 'center_order': 972, 'counter': 27, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '972.525', 'group_counter': 525, 'group_order': 972, 'image': None, 'image_isoclass': '3.1', 'image_order': 3, 'indicator': 0, 'kernel': '3.a1', 'kernel_order': 324, 'label': '972.525.1n2', 'nt': [3, 2], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]]]}
  • id: 33080226
    {'center': '12.a1', 'center_index': 12, 'center_order': 81, 'counter': 28, 'cyclotomic_n': 1, 'dim': 3, 'faithful': False, 'field': [0, 1], 'group': '972.525', 'group_counter': 525, 'group_order': 972, 'image': None, 'image_isoclass': '12.3', 'image_order': 12, 'indicator': 1, 'kernel': '12.a1', 'kernel_order': 81, 'label': '972.525.3a', 'nt': [4, 4], 'q_character': None, 'values': [[[3, 0]], [[-1, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 33080227
    {'center': '9.b1', 'center_index': 9, 'center_order': 108, 'counter': 29, 'cyclotomic_n': 3, 'dim': 3, 'faithful': False, 'field': [1, -1, 1], 'group': '972.525', 'group_counter': 525, 'group_order': 972, 'image': None, 'image_isoclass': '27.3', 'image_order': 27, 'indicator': 0, 'kernel': '27.c1', 'kernel_order': 36, 'label': '972.525.3b1', 'nt': [9, 7], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[3, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 1]], [[3, -1]], [[3, 1]], [[3, -1]], [[3, 1]], [[3, -1]], [[3, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 1]], [[3, -1]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[3, 0]], [[3, -1]], [[0, 0]], [[0, 0]], [[3, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 33080229
    {'center': '9.b1', 'center_index': 9, 'center_order': 108, 'counter': 30, 'cyclotomic_n': 3, 'dim': 3, 'faithful': False, 'field': [1, -1, 1], 'group': '972.525', 'group_counter': 525, 'group_order': 972, 'image': None, 'image_isoclass': '27.3', 'image_order': 27, 'indicator': 0, 'kernel': '27.c1', 'kernel_order': 36, 'label': '972.525.3b2', 'nt': [9, 2], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[3, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, -1]], [[3, 1]], [[3, -1]], [[3, 1]], [[3, -1]], [[3, 1]], [[3, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, -1]], [[3, 1]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[3, 0]], [[3, 1]], [[0, 0]], [[0, 0]], [[3, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 33080230
    {'center': '9.b1', 'center_index': 9, 'center_order': 108, 'counter': 31, 'cyclotomic_n': 3, 'dim': 3, 'faithful': False, 'field': [1, -1, 1], 'group': '972.525', 'group_counter': 525, 'group_order': 972, 'image': None, 'image_isoclass': '27.3', 'image_order': 27, 'indicator': 0, 'kernel': '27.c1', 'kernel_order': 36, 'label': '972.525.3c1', 'nt': [9, 7], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[3, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 1]], [[3, 1]], [[3, -1]], [[3, 1]], [[3, -1]], [[3, 1]], [[3, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[3, 0]], [[3, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[3, 0]], [[3, -1]], [[0, 0]], [[0, 0]], [[3, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 33080231
    {'center': '9.b1', 'center_index': 9, 'center_order': 108, 'counter': 32, 'cyclotomic_n': 3, 'dim': 3, 'faithful': False, 'field': [1, -1, 1], 'group': '972.525', 'group_counter': 525, 'group_order': 972, 'image': None, 'image_isoclass': '27.3', 'image_order': 27, 'indicator': 0, 'kernel': '27.c1', 'kernel_order': 36, 'label': '972.525.3c2', 'nt': [9, 2], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[3, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, -1]], [[3, -1]], [[3, 1]], [[3, -1]], [[3, 1]], [[3, -1]], [[3, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[3, 0]], [[3, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[3, 0]], [[3, 1]], [[0, 0]], [[0, 0]], [[3, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 33080232
    {'center': '9.b1', 'center_index': 9, 'center_order': 108, 'counter': 33, 'cyclotomic_n': 3, 'dim': 3, 'faithful': False, 'field': [1, -1, 1], 'group': '972.525', 'group_counter': 525, 'group_order': 972, 'image': None, 'image_isoclass': '27.3', 'image_order': 27, 'indicator': 0, 'kernel': '27.b1', 'kernel_order': 36, 'label': '972.525.3d1', 'nt': [9, 7], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[3, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 1]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, -1]], [[3, 1]], [[3, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[3, 0]], [[3, -1]], [[0, 0]], [[0, 0]], [[3, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 33080233
    {'center': '9.b1', 'center_index': 9, 'center_order': 108, 'counter': 34, 'cyclotomic_n': 3, 'dim': 3, 'faithful': False, 'field': [1, -1, 1], 'group': '972.525', 'group_counter': 525, 'group_order': 972, 'image': None, 'image_isoclass': '27.3', 'image_order': 27, 'indicator': 0, 'kernel': '27.b1', 'kernel_order': 36, 'label': '972.525.3d2', 'nt': [9, 2], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[3, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, -1]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 1]], [[3, -1]], [[3, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[3, 0]], [[3, 1]], [[0, 0]], [[0, 0]], [[3, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 33080234
    {'center': '27.b1', 'center_index': 27, 'center_order': 36, 'counter': 35, 'cyclotomic_n': 3, 'dim': 3, 'faithful': False, 'field': [1, -1, 1], 'group': '972.525', 'group_counter': 525, 'group_order': 972, 'image': None, 'image_isoclass': '81.7', 'image_order': 81, 'indicator': 0, 'kernel': '81.b1', 'kernel_order': 12, 'label': '972.525.3e1', 'nt': [9, 17], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[3, -1]], [[3, 1]], [[-1, 0], [1, 1]], [[0, 0]], [[2, 0], [1, 1]], [[-2, 0], [-1, 1]], [[1, 0], [-1, 1]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[0, 0]], [[3, 1]], [[3, 1]], [[3, -1]], [[3, 0]], [[3, 0]], [[3, -1]], [[0, 0]], [[0, 0]], [[1, 0], [2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0], [-1, 1]], [[-1, 0], [1, 1]], [[-1, 0], [-2, 1]], [[1, 0], [-1, 1]], [[1, 0], [-1, 1]], [[2, 0], [1, 1]], [[-1, 0], [1, 1]], [[0, 0]], [[1, 0], [2, 1]], [[-2, 0], [-1, 1]], [[2, 0], [1, 1]], [[-1, 0], [-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 1]], [[3, -1]], [[0, 0]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[0, 0]], [[-1, 0], [1, 1]], [[-2, 0], [-1, 1]], [[1, 0], [-1, 1]], [[2, 0], [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]]]}
  • id: 33080235
    {'center': '27.b1', 'center_index': 27, 'center_order': 36, 'counter': 36, 'cyclotomic_n': 3, 'dim': 3, 'faithful': False, 'field': [1, -1, 1], 'group': '972.525', 'group_counter': 525, 'group_order': 972, 'image': None, 'image_isoclass': '81.7', 'image_order': 81, 'indicator': 0, 'kernel': '81.b1', 'kernel_order': 12, 'label': '972.525.3e2', 'nt': [9, 2], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[3, 1]], [[3, -1]], [[-2, 0], [-1, 1]], [[0, 0]], [[1, 0], [-1, 1]], [[-1, 0], [1, 1]], [[2, 0], [1, 1]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[0, 0]], [[3, -1]], [[3, -1]], [[3, 1]], [[3, 0]], [[3, 0]], [[3, 1]], [[0, 0]], [[0, 0]], [[-1, 0], [-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0], [1, 1]], [[-2, 0], [-1, 1]], [[1, 0], [2, 1]], [[2, 0], [1, 1]], [[2, 0], [1, 1]], [[1, 0], [-1, 1]], [[-2, 0], [-1, 1]], [[0, 0]], [[-1, 0], [-2, 1]], [[-1, 0], [1, 1]], [[1, 0], [-1, 1]], [[1, 0], [2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, -1]], [[3, 1]], [[0, 0]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[0, 0]], [[-2, 0], [-1, 1]], [[-1, 0], [1, 1]], [[2, 0], [1, 1]], [[1, 0], [-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]]]}
  • id: 33080236
    {'center': '27.b1', 'center_index': 27, 'center_order': 36, 'counter': 37, 'cyclotomic_n': 3, 'dim': 3, 'faithful': False, 'field': [1, -1, 1], 'group': '972.525', 'group_counter': 525, 'group_order': 972, 'image': None, 'image_isoclass': '81.7', 'image_order': 81, 'indicator': 0, 'kernel': '81.b1', 'kernel_order': 12, 'label': '972.525.3f1', 'nt': [9, 17], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[3, -1]], [[3, 1]], [[-1, 0], [1, 1]], [[0, 0]], [[2, 0], [1, 1]], [[-2, 0], [-1, 1]], [[1, 0], [-1, 1]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[0, 0]], [[3, -1]], [[3, 0]], [[3, 0]], [[3, -1]], [[3, 1]], [[3, 1]], [[0, 0]], [[0, 0]], [[-2, 0], [-1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0], [-1, 1]], [[-1, 0], [-2, 1]], [[-1, 0], [1, 1]], [[1, 0], [2, 1]], [[-2, 0], [-1, 1]], [[-1, 0], [1, 1]], [[2, 0], [1, 1]], [[0, 0]], [[1, 0], [-1, 1]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[2, 0], [1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 1]], [[3, -1]], [[0, 0]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[0, 0]], [[-1, 0], [1, 1]], [[-2, 0], [-1, 1]], [[1, 0], [-1, 1]], [[2, 0], [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]]]}
  • id: 33080237
    {'center': '27.b1', 'center_index': 27, 'center_order': 36, 'counter': 38, 'cyclotomic_n': 3, 'dim': 3, 'faithful': False, 'field': [1, -1, 1], 'group': '972.525', 'group_counter': 525, 'group_order': 972, 'image': None, 'image_isoclass': '81.7', 'image_order': 81, 'indicator': 0, 'kernel': '81.b1', 'kernel_order': 12, 'label': '972.525.3f2', 'nt': [9, 2], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[3, 1]], [[3, -1]], [[-2, 0], [-1, 1]], [[0, 0]], [[1, 0], [-1, 1]], [[-1, 0], [1, 1]], [[2, 0], [1, 1]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[0, 0]], [[3, 1]], [[3, 0]], [[3, 0]], [[3, 1]], [[3, -1]], [[3, -1]], [[0, 0]], [[0, 0]], [[-1, 0], [1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0], [1, 1]], [[1, 0], [2, 1]], [[-2, 0], [-1, 1]], [[-1, 0], [-2, 1]], [[-1, 0], [1, 1]], [[-2, 0], [-1, 1]], [[1, 0], [-1, 1]], [[0, 0]], [[2, 0], [1, 1]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[1, 0], [-1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, -1]], [[3, 1]], [[0, 0]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[0, 0]], [[-2, 0], [-1, 1]], [[-1, 0], [1, 1]], [[2, 0], [1, 1]], [[1, 0], [-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]]]}
  • id: 33080238
    {'center': '27.b1', 'center_index': 27, 'center_order': 36, 'counter': 39, 'cyclotomic_n': 3, 'dim': 3, 'faithful': False, 'field': [1, -1, 1], 'group': '972.525', 'group_counter': 525, 'group_order': 972, 'image': None, 'image_isoclass': '81.7', 'image_order': 81, 'indicator': 0, 'kernel': '81.b1', 'kernel_order': 12, 'label': '972.525.3g1', 'nt': [9, 17], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[3, -1]], [[3, 1]], [[-1, 0], [1, 1]], [[0, 0]], [[2, 0], [1, 1]], [[-2, 0], [-1, 1]], [[1, 0], [-1, 1]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[0, 0]], [[3, 0]], [[3, -1]], [[3, 1]], [[3, 1]], [[3, -1]], [[3, 0]], [[0, 0]], [[0, 0]], [[1, 0], [-1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0], [2, 1]], [[2, 0], [1, 1]], [[2, 0], [1, 1]], [[-2, 0], [-1, 1]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[-1, 0], [-2, 1]], [[0, 0]], [[-2, 0], [-1, 1]], [[1, 0], [-1, 1]], [[-1, 0], [1, 1]], [[-1, 0], [1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 1]], [[3, -1]], [[0, 0]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[0, 0]], [[-1, 0], [1, 1]], [[-2, 0], [-1, 1]], [[1, 0], [-1, 1]], [[2, 0], [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]]]}
  • id: 33080240
    {'center': '27.b1', 'center_index': 27, 'center_order': 36, 'counter': 40, 'cyclotomic_n': 3, 'dim': 3, 'faithful': False, 'field': [1, -1, 1], 'group': '972.525', 'group_counter': 525, 'group_order': 972, 'image': None, 'image_isoclass': '81.7', 'image_order': 81, 'indicator': 0, 'kernel': '81.b1', 'kernel_order': 12, 'label': '972.525.3g2', 'nt': [9, 2], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[3, 1]], [[3, -1]], [[-2, 0], [-1, 1]], [[0, 0]], [[1, 0], [-1, 1]], [[-1, 0], [1, 1]], [[2, 0], [1, 1]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[0, 0]], [[3, 0]], [[3, 1]], [[3, -1]], [[3, -1]], [[3, 1]], [[3, 0]], [[0, 0]], [[0, 0]], [[2, 0], [1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0], [-2, 1]], [[1, 0], [-1, 1]], [[1, 0], [-1, 1]], [[-1, 0], [1, 1]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[1, 0], [2, 1]], [[0, 0]], [[-1, 0], [1, 1]], [[2, 0], [1, 1]], [[-2, 0], [-1, 1]], [[-2, 0], [-1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, -1]], [[3, 1]], [[0, 0]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[0, 0]], [[-2, 0], [-1, 1]], [[-1, 0], [1, 1]], [[2, 0], [1, 1]], [[1, 0], [-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]]]}
  • id: 33080241
    {'center': '27.b1', 'center_index': 27, 'center_order': 36, 'counter': 41, 'cyclotomic_n': 3, 'dim': 3, 'faithful': False, 'field': [1, -1, 1], 'group': '972.525', 'group_counter': 525, 'group_order': 972, 'image': None, 'image_isoclass': '81.7', 'image_order': 81, 'indicator': 0, 'kernel': '81.b1', 'kernel_order': 12, 'label': '972.525.3h1', 'nt': [9, 17], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[3, -1]], [[3, 1]], [[-1, 0], [-2, 1]], [[0, 0]], [[-1, 0], [1, 1]], [[1, 0], [2, 1]], [[-2, 0], [-1, 1]], [[2, 0], [1, 1]], [[1, 0], [-1, 1]], [[0, 0]], [[3, 1]], [[3, 1]], [[3, -1]], [[3, 0]], [[3, 0]], [[3, -1]], [[0, 0]], [[0, 0]], [[1, 0], [-1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[2, 0], [1, 1]], [[-2, 0], [-1, 1]], [[-2, 0], [-1, 1]], [[-1, 0], [1, 1]], [[-1, 0], [-2, 1]], [[0, 0]], [[1, 0], [-1, 1]], [[1, 0], [2, 1]], [[-1, 0], [1, 1]], [[2, 0], [1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 1]], [[3, -1]], [[0, 0]], [[1, 0], [-1, 1]], [[2, 0], [1, 1]], [[0, 0]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[-2, 0], [-1, 1]], [[-1, 0], [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]]]}
  • id: 33080242
    {'center': '27.b1', 'center_index': 27, 'center_order': 36, 'counter': 42, 'cyclotomic_n': 3, 'dim': 3, 'faithful': False, 'field': [1, -1, 1], 'group': '972.525', 'group_counter': 525, 'group_order': 972, 'image': None, 'image_isoclass': '81.7', 'image_order': 81, 'indicator': 0, 'kernel': '81.b1', 'kernel_order': 12, 'label': '972.525.3h2', 'nt': [9, 2], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[3, 1]], [[3, -1]], [[1, 0], [2, 1]], [[0, 0]], [[-2, 0], [-1, 1]], [[-1, 0], [-2, 1]], [[-1, 0], [1, 1]], [[1, 0], [-1, 1]], [[2, 0], [1, 1]], [[0, 0]], [[3, -1]], [[3, -1]], [[3, 1]], [[3, 0]], [[3, 0]], [[3, 1]], [[0, 0]], [[0, 0]], [[2, 0], [1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[1, 0], [-1, 1]], [[-1, 0], [1, 1]], [[-1, 0], [1, 1]], [[-2, 0], [-1, 1]], [[1, 0], [2, 1]], [[0, 0]], [[2, 0], [1, 1]], [[-1, 0], [-2, 1]], [[-2, 0], [-1, 1]], [[1, 0], [-1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, -1]], [[3, 1]], [[0, 0]], [[2, 0], [1, 1]], [[1, 0], [-1, 1]], [[0, 0]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[-1, 0], [1, 1]], [[-2, 0], [-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]]]}
  • id: 33080243
    {'center': '27.b1', 'center_index': 27, 'center_order': 36, 'counter': 43, 'cyclotomic_n': 3, 'dim': 3, 'faithful': False, 'field': [1, -1, 1], 'group': '972.525', 'group_counter': 525, 'group_order': 972, 'image': None, 'image_isoclass': '81.7', 'image_order': 81, 'indicator': 0, 'kernel': '81.b1', 'kernel_order': 12, 'label': '972.525.3i1', 'nt': [9, 17], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[3, -1]], [[3, 1]], [[-1, 0], [-2, 1]], [[0, 0]], [[-1, 0], [1, 1]], [[1, 0], [2, 1]], [[-2, 0], [-1, 1]], [[2, 0], [1, 1]], [[1, 0], [-1, 1]], [[0, 0]], [[3, -1]], [[3, 0]], [[3, 0]], [[3, -1]], [[3, 1]], [[3, 1]], [[0, 0]], [[0, 0]], [[1, 0], [2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0], [-1, 1]], [[2, 0], [1, 1]], [[-1, 0], [-2, 1]], [[1, 0], [-1, 1]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[-1, 0], [1, 1]], [[0, 0]], [[-2, 0], [-1, 1]], [[1, 0], [-1, 1]], [[2, 0], [1, 1]], [[-1, 0], [1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 1]], [[3, -1]], [[0, 0]], [[1, 0], [-1, 1]], [[2, 0], [1, 1]], [[0, 0]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[-2, 0], [-1, 1]], [[-1, 0], [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]]]}
  • id: 33080244
    {'center': '27.b1', 'center_index': 27, 'center_order': 36, 'counter': 44, 'cyclotomic_n': 3, 'dim': 3, 'faithful': False, 'field': [1, -1, 1], 'group': '972.525', 'group_counter': 525, 'group_order': 972, 'image': None, 'image_isoclass': '81.7', 'image_order': 81, 'indicator': 0, 'kernel': '81.b1', 'kernel_order': 12, 'label': '972.525.3i2', 'nt': [9, 2], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[3, 1]], [[3, -1]], [[1, 0], [2, 1]], [[0, 0]], [[-2, 0], [-1, 1]], [[-1, 0], [-2, 1]], [[-1, 0], [1, 1]], [[1, 0], [-1, 1]], [[2, 0], [1, 1]], [[0, 0]], [[3, 1]], [[3, 0]], [[3, 0]], [[3, 1]], [[3, -1]], [[3, -1]], [[0, 0]], [[0, 0]], [[-1, 0], [-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0], [1, 1]], [[1, 0], [-1, 1]], [[1, 0], [2, 1]], [[2, 0], [1, 1]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[-2, 0], [-1, 1]], [[0, 0]], [[-1, 0], [1, 1]], [[2, 0], [1, 1]], [[1, 0], [-1, 1]], [[-2, 0], [-1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, -1]], [[3, 1]], [[0, 0]], [[2, 0], [1, 1]], [[1, 0], [-1, 1]], [[0, 0]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[-1, 0], [1, 1]], [[-2, 0], [-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]]]}
  • id: 33080245
    {'center': '27.b1', 'center_index': 27, 'center_order': 36, 'counter': 45, 'cyclotomic_n': 3, 'dim': 3, 'faithful': False, 'field': [1, -1, 1], 'group': '972.525', 'group_counter': 525, 'group_order': 972, 'image': None, 'image_isoclass': '81.7', 'image_order': 81, 'indicator': 0, 'kernel': '81.b1', 'kernel_order': 12, 'label': '972.525.3j1', 'nt': [9, 17], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[3, -1]], [[3, 1]], [[-1, 0], [-2, 1]], [[0, 0]], [[-1, 0], [1, 1]], [[1, 0], [2, 1]], [[-2, 0], [-1, 1]], [[2, 0], [1, 1]], [[1, 0], [-1, 1]], [[0, 0]], [[3, 0]], [[3, -1]], [[3, 1]], [[3, 1]], [[3, -1]], [[3, 0]], [[0, 0]], [[0, 0]], [[-2, 0], [-1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0], [-1, 1]], [[-1, 0], [1, 1]], [[-1, 0], [1, 1]], [[1, 0], [2, 1]], [[1, 0], [-1, 1]], [[2, 0], [1, 1]], [[2, 0], [1, 1]], [[0, 0]], [[1, 0], [2, 1]], [[-2, 0], [-1, 1]], [[-1, 0], [-2, 1]], [[-1, 0], [-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 1]], [[3, -1]], [[0, 0]], [[1, 0], [-1, 1]], [[2, 0], [1, 1]], [[0, 0]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[-2, 0], [-1, 1]], [[-1, 0], [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]]]}
  • id: 33080246
    {'center': '27.b1', 'center_index': 27, 'center_order': 36, 'counter': 46, 'cyclotomic_n': 3, 'dim': 3, 'faithful': False, 'field': [1, -1, 1], 'group': '972.525', 'group_counter': 525, 'group_order': 972, 'image': None, 'image_isoclass': '81.7', 'image_order': 81, 'indicator': 0, 'kernel': '81.b1', 'kernel_order': 12, 'label': '972.525.3j2', 'nt': [9, 2], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[3, 1]], [[3, -1]], [[1, 0], [2, 1]], [[0, 0]], [[-2, 0], [-1, 1]], [[-1, 0], [-2, 1]], [[-1, 0], [1, 1]], [[1, 0], [-1, 1]], [[2, 0], [1, 1]], [[0, 0]], [[3, 0]], [[3, 1]], [[3, -1]], [[3, -1]], [[3, 1]], [[3, 0]], [[0, 0]], [[0, 0]], [[-1, 0], [1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0], [1, 1]], [[-2, 0], [-1, 1]], [[-2, 0], [-1, 1]], [[-1, 0], [-2, 1]], [[2, 0], [1, 1]], [[1, 0], [-1, 1]], [[1, 0], [-1, 1]], [[0, 0]], [[-1, 0], [-2, 1]], [[-1, 0], [1, 1]], [[1, 0], [2, 1]], [[1, 0], [2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, -1]], [[3, 1]], [[0, 0]], [[2, 0], [1, 1]], [[1, 0], [-1, 1]], [[0, 0]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[-1, 0], [1, 1]], [[-2, 0], [-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]]]}
  • id: 33080247
    {'center': '27.b1', 'center_index': 27, 'center_order': 36, 'counter': 47, 'cyclotomic_n': 3, 'dim': 3, 'faithful': False, 'field': [1, -1, 1], 'group': '972.525', 'group_counter': 525, 'group_order': 972, 'image': None, 'image_isoclass': '81.7', 'image_order': 81, 'indicator': 0, 'kernel': '81.b1', 'kernel_order': 12, 'label': '972.525.3k1', 'nt': [9, 17], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[3, -1]], [[3, 1]], [[2, 0], [1, 1]], [[0, 0]], [[-1, 0], [-2, 1]], [[1, 0], [-1, 1]], [[1, 0], [2, 1]], [[-1, 0], [1, 1]], [[-2, 0], [-1, 1]], [[0, 0]], [[3, 1]], [[3, 1]], [[3, -1]], [[3, 0]], [[3, 0]], [[3, -1]], [[0, 0]], [[0, 0]], [[-2, 0], [-1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0], [-1, 1]], [[2, 0], [1, 1]], [[-1, 0], [1, 1]], [[1, 0], [2, 1]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[2, 0], [1, 1]], [[0, 0]], [[-2, 0], [-1, 1]], [[1, 0], [-1, 1]], [[-1, 0], [-2, 1]], [[-1, 0], [1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 1]], [[3, -1]], [[0, 0]], [[-2, 0], [-1, 1]], [[-1, 0], [1, 1]], [[0, 0]], [[2, 0], [1, 1]], [[1, 0], [-1, 1]], [[1, 0], [2, 1]], [[-1, 0], [-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]]]}
  • id: 33080248
    {'center': '27.b1', 'center_index': 27, 'center_order': 36, 'counter': 48, 'cyclotomic_n': 3, 'dim': 3, 'faithful': False, 'field': [1, -1, 1], 'group': '972.525', 'group_counter': 525, 'group_order': 972, 'image': None, 'image_isoclass': '81.7', 'image_order': 81, 'indicator': 0, 'kernel': '81.b1', 'kernel_order': 12, 'label': '972.525.3k2', 'nt': [9, 2], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[3, 1]], [[3, -1]], [[1, 0], [-1, 1]], [[0, 0]], [[1, 0], [2, 1]], [[2, 0], [1, 1]], [[-1, 0], [-2, 1]], [[-2, 0], [-1, 1]], [[-1, 0], [1, 1]], [[0, 0]], [[3, -1]], [[3, -1]], [[3, 1]], [[3, 0]], [[3, 0]], [[3, 1]], [[0, 0]], [[0, 0]], [[-1, 0], [1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0], [1, 1]], [[1, 0], [-1, 1]], [[-2, 0], [-1, 1]], [[-1, 0], [-2, 1]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[1, 0], [-1, 1]], [[0, 0]], [[-1, 0], [1, 1]], [[2, 0], [1, 1]], [[1, 0], [2, 1]], [[-2, 0], [-1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, -1]], [[3, 1]], [[0, 0]], [[-1, 0], [1, 1]], [[-2, 0], [-1, 1]], [[0, 0]], [[1, 0], [-1, 1]], [[2, 0], [1, 1]], [[-1, 0], [-2, 1]], [[1, 0], [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]]]}
  • id: 33080249
    {'center': '27.b1', 'center_index': 27, 'center_order': 36, 'counter': 49, 'cyclotomic_n': 3, 'dim': 3, 'faithful': False, 'field': [1, -1, 1], 'group': '972.525', 'group_counter': 525, 'group_order': 972, 'image': None, 'image_isoclass': '81.7', 'image_order': 81, 'indicator': 0, 'kernel': '81.b1', 'kernel_order': 12, 'label': '972.525.3l1', 'nt': [9, 17], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[3, -1]], [[3, 1]], [[2, 0], [1, 1]], [[0, 0]], [[-1, 0], [-2, 1]], [[1, 0], [-1, 1]], [[1, 0], [2, 1]], [[-1, 0], [1, 1]], [[-2, 0], [-1, 1]], [[0, 0]], [[3, -1]], [[3, 0]], [[3, 0]], [[3, -1]], [[3, 1]], [[3, 1]], [[0, 0]], [[0, 0]], [[1, 0], [-1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0], [2, 1]], [[-1, 0], [1, 1]], [[2, 0], [1, 1]], [[-2, 0], [-1, 1]], [[1, 0], [-1, 1]], [[2, 0], [1, 1]], [[-1, 0], [-2, 1]], [[0, 0]], [[1, 0], [2, 1]], [[-2, 0], [-1, 1]], [[-1, 0], [1, 1]], [[-1, 0], [-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 1]], [[3, -1]], [[0, 0]], [[-2, 0], [-1, 1]], [[-1, 0], [1, 1]], [[0, 0]], [[2, 0], [1, 1]], [[1, 0], [-1, 1]], [[1, 0], [2, 1]], [[-1, 0], [-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]]]}
  • id: 33080251
    {'center': '27.b1', 'center_index': 27, 'center_order': 36, 'counter': 50, 'cyclotomic_n': 3, 'dim': 3, 'faithful': False, 'field': [1, -1, 1], 'group': '972.525', 'group_counter': 525, 'group_order': 972, 'image': None, 'image_isoclass': '81.7', 'image_order': 81, 'indicator': 0, 'kernel': '81.b1', 'kernel_order': 12, 'label': '972.525.3l2', 'nt': [9, 2], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[3, 1]], [[3, -1]], [[1, 0], [-1, 1]], [[0, 0]], [[1, 0], [2, 1]], [[2, 0], [1, 1]], [[-1, 0], [-2, 1]], [[-2, 0], [-1, 1]], [[-1, 0], [1, 1]], [[0, 0]], [[3, 1]], [[3, 0]], [[3, 0]], [[3, 1]], [[3, -1]], [[3, -1]], [[0, 0]], [[0, 0]], [[2, 0], [1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0], [-2, 1]], [[-2, 0], [-1, 1]], [[1, 0], [-1, 1]], [[-1, 0], [1, 1]], [[2, 0], [1, 1]], [[1, 0], [-1, 1]], [[1, 0], [2, 1]], [[0, 0]], [[-1, 0], [-2, 1]], [[-1, 0], [1, 1]], [[-2, 0], [-1, 1]], [[1, 0], [2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, -1]], [[3, 1]], [[0, 0]], [[-1, 0], [1, 1]], [[-2, 0], [-1, 1]], [[0, 0]], [[1, 0], [-1, 1]], [[2, 0], [1, 1]], [[-1, 0], [-2, 1]], [[1, 0], [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]]]}
  • id: 33080252
    {'center': '27.b1', 'center_index': 27, 'center_order': 36, 'counter': 51, 'cyclotomic_n': 3, 'dim': 3, 'faithful': False, 'field': [1, -1, 1], 'group': '972.525', 'group_counter': 525, 'group_order': 972, 'image': None, 'image_isoclass': '81.7', 'image_order': 81, 'indicator': 0, 'kernel': '81.b1', 'kernel_order': 12, 'label': '972.525.3m1', 'nt': [9, 17], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[3, -1]], [[3, 1]], [[2, 0], [1, 1]], [[0, 0]], [[-1, 0], [-2, 1]], [[1, 0], [-1, 1]], [[1, 0], [2, 1]], [[-1, 0], [1, 1]], [[-2, 0], [-1, 1]], [[0, 0]], [[3, 0]], [[3, -1]], [[3, 1]], [[3, 1]], [[3, -1]], [[3, 0]], [[0, 0]], [[0, 0]], [[1, 0], [2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0], [-1, 1]], [[-1, 0], [-2, 1]], [[-1, 0], [-2, 1]], [[1, 0], [-1, 1]], [[-2, 0], [-1, 1]], [[-1, 0], [1, 1]], [[-1, 0], [1, 1]], [[0, 0]], [[1, 0], [-1, 1]], [[1, 0], [2, 1]], [[2, 0], [1, 1]], [[2, 0], [1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 1]], [[3, -1]], [[0, 0]], [[-2, 0], [-1, 1]], [[-1, 0], [1, 1]], [[0, 0]], [[2, 0], [1, 1]], [[1, 0], [-1, 1]], [[1, 0], [2, 1]], [[-1, 0], [-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]]]}
  • id: 33080253
    {'center': '27.b1', 'center_index': 27, 'center_order': 36, 'counter': 52, 'cyclotomic_n': 3, 'dim': 3, 'faithful': False, 'field': [1, -1, 1], 'group': '972.525', 'group_counter': 525, 'group_order': 972, 'image': None, 'image_isoclass': '81.7', 'image_order': 81, 'indicator': 0, 'kernel': '81.b1', 'kernel_order': 12, 'label': '972.525.3m2', 'nt': [9, 2], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[3, 1]], [[3, -1]], [[1, 0], [-1, 1]], [[0, 0]], [[1, 0], [2, 1]], [[2, 0], [1, 1]], [[-1, 0], [-2, 1]], [[-2, 0], [-1, 1]], [[-1, 0], [1, 1]], [[0, 0]], [[3, 0]], [[3, 1]], [[3, -1]], [[3, -1]], [[3, 1]], [[3, 0]], [[0, 0]], [[0, 0]], [[-1, 0], [-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0], [1, 1]], [[1, 0], [2, 1]], [[1, 0], [2, 1]], [[2, 0], [1, 1]], [[-1, 0], [1, 1]], [[-2, 0], [-1, 1]], [[-2, 0], [-1, 1]], [[0, 0]], [[2, 0], [1, 1]], [[-1, 0], [-2, 1]], [[1, 0], [-1, 1]], [[1, 0], [-1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, -1]], [[3, 1]], [[0, 0]], [[-1, 0], [1, 1]], [[-2, 0], [-1, 1]], [[0, 0]], [[1, 0], [-1, 1]], [[2, 0], [1, 1]], [[-1, 0], [-2, 1]], [[1, 0], [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]]]}
  • id: 33080254
    {'center': '12.a1', 'center_index': 12, 'center_order': 81, 'counter': 53, 'cyclotomic_n': 3, 'dim': 3, 'faithful': False, 'field': [1, -1, 1], 'group': '972.525', 'group_counter': 525, 'group_order': 972, 'image': None, 'image_isoclass': '36.11', 'image_order': 36, 'indicator': 0, 'kernel': '36.c1', 'kernel_order': 27, 'label': '972.525.3n1', 'nt': [12, 20], 'q_character': None, 'values': [[[3, 0]], [[-1, 0]], [[3, 0]], [[3, 0]], [[3, -1]], [[3, 0]], [[3, -1]], [[3, 1]], [[3, 1]], [[3, -1]], [[3, 1]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 1]], [[3, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[3, 1]], [[3, 0]], [[3, 0]], [[3, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[-1, -1]]]}
  • id: 33080255
    {'center': '12.a1', 'center_index': 12, 'center_order': 81, 'counter': 54, 'cyclotomic_n': 3, 'dim': 3, 'faithful': False, 'field': [1, -1, 1], 'group': '972.525', 'group_counter': 525, 'group_order': 972, 'image': None, 'image_isoclass': '36.11', 'image_order': 36, 'indicator': 0, 'kernel': '36.c1', 'kernel_order': 27, 'label': '972.525.3n2', 'nt': [12, 2], 'q_character': None, 'values': [[[3, 0]], [[-1, 0]], [[3, 0]], [[3, 0]], [[3, 1]], [[3, 0]], [[3, 1]], [[3, -1]], [[3, -1]], [[3, 1]], [[3, -1]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, -1]], [[3, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[3, -1]], [[3, 0]], [[3, 0]], [[3, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, -1]], [[-1, 1]]]}
  • id: 33080256
    {'center': '12.a1', 'center_index': 12, 'center_order': 81, 'counter': 55, 'cyclotomic_n': 3, 'dim': 3, 'faithful': False, 'field': [1, -1, 1], 'group': '972.525', 'group_counter': 525, 'group_order': 972, 'image': None, 'image_isoclass': '36.11', 'image_order': 36, 'indicator': 0, 'kernel': '36.c1', 'kernel_order': 27, 'label': '972.525.3o1', 'nt': [12, 20], 'q_character': None, 'values': [[[3, 0]], [[-1, 0]], [[3, 0]], [[3, 0]], [[3, -1]], [[3, 0]], [[3, -1]], [[3, 1]], [[3, 1]], [[3, -1]], [[3, 1]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, -1]], [[3, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[3, 0]], [[3, 1]], [[3, -1]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1]], [[-1, -1]], [[-1, 0]], [[-1, 0]]]}
  • id: 33080257
    {'center': '12.a1', 'center_index': 12, 'center_order': 81, 'counter': 56, 'cyclotomic_n': 3, 'dim': 3, 'faithful': False, 'field': [1, -1, 1], 'group': '972.525', 'group_counter': 525, 'group_order': 972, 'image': None, 'image_isoclass': '36.11', 'image_order': 36, 'indicator': 0, 'kernel': '36.c1', 'kernel_order': 27, 'label': '972.525.3o2', 'nt': [12, 2], 'q_character': None, 'values': [[[3, 0]], [[-1, 0]], [[3, 0]], [[3, 0]], [[3, 1]], [[3, 0]], [[3, 1]], [[3, -1]], [[3, -1]], [[3, 1]], [[3, -1]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 1]], [[3, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[3, 0]], [[3, -1]], [[3, 1]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, -1]], [[-1, 1]], [[-1, 0]], [[-1, 0]]]}
  • id: 33080258
    {'center': '12.a1', 'center_index': 12, 'center_order': 81, 'counter': 57, 'cyclotomic_n': 3, 'dim': 3, 'faithful': False, 'field': [1, -1, 1], 'group': '972.525', 'group_counter': 525, 'group_order': 972, 'image': None, 'image_isoclass': '36.11', 'image_order': 36, 'indicator': 0, 'kernel': '36.b1', 'kernel_order': 27, 'label': '972.525.3p1', 'nt': [12, 20], 'q_character': None, 'values': [[[3, 0]], [[-1, 0]], [[3, 0]], [[3, 0]], [[3, -1]], [[3, 0]], [[3, -1]], [[3, 1]], [[3, 1]], [[3, -1]], [[3, 1]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, 0]], [[-1, 0]], [[3, -1]], [[3, -1]], [[3, 1]], [[3, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]]]}
  • id: 33080259
    {'center': '12.a1', 'center_index': 12, 'center_order': 81, 'counter': 58, 'cyclotomic_n': 3, 'dim': 3, 'faithful': False, 'field': [1, -1, 1], 'group': '972.525', 'group_counter': 525, 'group_order': 972, 'image': None, 'image_isoclass': '36.11', 'image_order': 36, 'indicator': 0, 'kernel': '36.b1', 'kernel_order': 27, 'label': '972.525.3p2', 'nt': [12, 2], 'q_character': None, 'values': [[[3, 0]], [[-1, 0]], [[3, 0]], [[3, 0]], [[3, 1]], [[3, 0]], [[3, 1]], [[3, -1]], [[3, -1]], [[3, 1]], [[3, -1]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, 0]], [[-1, 0]], [[3, 1]], [[3, 1]], [[3, -1]], [[3, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]]]}
  • id: 33080260
    {'center': '12.a1', 'center_index': 12, 'center_order': 81, 'counter': 59, 'cyclotomic_n': 3, 'dim': 3, 'faithful': False, 'field': [1, -1, 1], 'group': '972.525', 'group_counter': 525, 'group_order': 972, 'image': None, 'image_isoclass': '36.11', 'image_order': 36, 'indicator': 0, 'kernel': '36.a1', 'kernel_order': 27, 'label': '972.525.3q1', 'nt': [12, 20], 'q_character': None, 'values': [[[3, 0]], [[-1, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, -1]], [[3, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[3, 1]], [[3, -1]], [[3, 1]], [[3, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, -1]]]}
  • id: 33080262
    {'center': '12.a1', 'center_index': 12, 'center_order': 81, 'counter': 60, 'cyclotomic_n': 3, 'dim': 3, 'faithful': False, 'field': [1, -1, 1], 'group': '972.525', 'group_counter': 525, 'group_order': 972, 'image': None, 'image_isoclass': '36.11', 'image_order': 36, 'indicator': 0, 'kernel': '36.a1', 'kernel_order': 27, 'label': '972.525.3q2', 'nt': [12, 2], 'q_character': None, 'values': [[[3, 0]], [[-1, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 1]], [[3, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[3, -1]], [[3, 1]], [[3, -1]], [[3, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 1]]]}
  • id: 33080263
    {'center': '108.a1', 'center_index': 108, 'center_order': 9, 'counter': 61, 'cyclotomic_n': 3, 'dim': 9, 'faithful': False, 'field': [1, -1, 1], 'group': '972.525', 'group_counter': 525, 'group_order': 972, 'image': None, 'image_isoclass': '324.130', 'image_order': 324, 'indicator': 0, 'kernel': '324.a1', 'kernel_order': 3, 'label': '972.525.9a1', 'nt': [36, 537], 'q_character': None, 'values': [[[9, 0]], [[-3, 0]], [[9, 0]], [[9, 0]], [[0, 0]], [[9, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[9, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[-3, -1]], [[0, 0]], [[0, 0]], [[-3, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 33080264
    {'center': '108.a1', 'center_index': 108, 'center_order': 9, 'counter': 62, 'cyclotomic_n': 3, 'dim': 9, 'faithful': False, 'field': [1, -1, 1], 'group': '972.525', 'group_counter': 525, 'group_order': 972, 'image': None, 'image_isoclass': '324.130', 'image_order': 324, 'indicator': 0, 'kernel': '324.a1', 'kernel_order': 3, 'label': '972.525.9a2', 'nt': [36, 2], 'q_character': None, 'values': [[[9, 0]], [[-3, 0]], [[9, 0]], [[9, 0]], [[0, 0]], [[9, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[9, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[-3, 1]], [[0, 0]], [[0, 0]], [[-3, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 33080265
    {'center': '324.a1', 'center_index': 324, 'center_order': 3, 'counter': 63, 'cyclotomic_n': 3, 'dim': 9, 'faithful': True, 'field': [1, -1, 1], 'group': '972.525', 'group_counter': 525, 'group_order': 972, 'image': None, 'image_isoclass': '972.525', 'image_order': 972, 'indicator': 0, 'kernel': '972.a1', 'kernel_order': 1, 'label': '972.525.9b1', 'nt': [36, 1584], 'q_character': None, 'values': [[[9, 0]], [[-3, 0]], [[9, -1]], [[9, 1]], [[-3, 0], [3, 1]], [[0, 0]], [[6, 0], [3, 1]], [[-6, 0], [-3, 1]], [[3, 0], [-3, 1]], [[-3, 0], [-6, 1]], [[3, 0], [6, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 1]], [[-3, -1]], [[0, 0]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[0, 0]], [[1, 0], [-1, 1]], [[2, 0], [1, 1]], [[-1, 0], [1, 1]], [[-2, 0], [-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]]]}
  • id: 33080266
    {'center': '324.a1', 'center_index': 324, 'center_order': 3, 'counter': 64, 'cyclotomic_n': 3, 'dim': 9, 'faithful': True, 'field': [1, -1, 1], 'group': '972.525', 'group_counter': 525, 'group_order': 972, 'image': None, 'image_isoclass': '972.525', 'image_order': 972, 'indicator': 0, 'kernel': '972.a1', 'kernel_order': 1, 'label': '972.525.9b2', 'nt': [36, 2], 'q_character': None, 'values': [[[9, 0]], [[-3, 0]], [[9, 1]], [[9, -1]], [[-6, 0], [-3, 1]], [[0, 0]], [[3, 0], [-3, 1]], [[-3, 0], [3, 1]], [[6, 0], [3, 1]], [[3, 0], [6, 1]], [[-3, 0], [-6, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, -1]], [[-3, 1]], [[0, 0]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[0, 0]], [[2, 0], [1, 1]], [[1, 0], [-1, 1]], [[-2, 0], [-1, 1]], [[-1, 0], [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]]]}
  • id: 33080267
    {'center': '324.a1', 'center_index': 324, 'center_order': 3, 'counter': 65, 'cyclotomic_n': 3, 'dim': 9, 'faithful': True, 'field': [1, -1, 1], 'group': '972.525', 'group_counter': 525, 'group_order': 972, 'image': None, 'image_isoclass': '972.525', 'image_order': 972, 'indicator': 0, 'kernel': '972.a1', 'kernel_order': 1, 'label': '972.525.9c1', 'nt': [36, 1584], 'q_character': None, 'values': [[[9, 0]], [[-3, 0]], [[9, -1]], [[9, 1]], [[-3, 0], [-6, 1]], [[0, 0]], [[-3, 0], [3, 1]], [[3, 0], [6, 1]], [[-6, 0], [-3, 1]], [[6, 0], [3, 1]], [[3, 0], [-3, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 1]], [[-3, -1]], [[0, 0]], [[-1, 0], [1, 1]], [[-2, 0], [-1, 1]], [[0, 0]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[2, 0], [1, 1]], [[1, 0], [-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]]]}
  • id: 33080268
    {'center': '324.a1', 'center_index': 324, 'center_order': 3, 'counter': 66, 'cyclotomic_n': 3, 'dim': 9, 'faithful': True, 'field': [1, -1, 1], 'group': '972.525', 'group_counter': 525, 'group_order': 972, 'image': None, 'image_isoclass': '972.525', 'image_order': 972, 'indicator': 0, 'kernel': '972.a1', 'kernel_order': 1, 'label': '972.525.9c2', 'nt': [36, 2], 'q_character': None, 'values': [[[9, 0]], [[-3, 0]], [[9, 1]], [[9, -1]], [[3, 0], [6, 1]], [[0, 0]], [[-6, 0], [-3, 1]], [[-3, 0], [-6, 1]], [[-3, 0], [3, 1]], [[3, 0], [-3, 1]], [[6, 0], [3, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, -1]], [[-3, 1]], [[0, 0]], [[-2, 0], [-1, 1]], [[-1, 0], [1, 1]], [[0, 0]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[1, 0], [-1, 1]], [[2, 0], [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]]]}
  • id: 33080269
    {'center': '324.a1', 'center_index': 324, 'center_order': 3, 'counter': 67, 'cyclotomic_n': 3, 'dim': 9, 'faithful': True, 'field': [1, -1, 1], 'group': '972.525', 'group_counter': 525, 'group_order': 972, 'image': None, 'image_isoclass': '972.525', 'image_order': 972, 'indicator': 0, 'kernel': '972.a1', 'kernel_order': 1, 'label': '972.525.9d1', 'nt': [36, 1584], 'q_character': None, 'values': [[[9, 0]], [[-3, 0]], [[9, -1]], [[9, 1]], [[6, 0], [3, 1]], [[0, 0]], [[-3, 0], [-6, 1]], [[3, 0], [-3, 1]], [[3, 0], [6, 1]], [[-3, 0], [3, 1]], [[-6, 0], [-3, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 1]], [[-3, -1]], [[0, 0]], [[2, 0], [1, 1]], [[1, 0], [-1, 1]], [[0, 0]], [[-2, 0], [-1, 1]], [[-1, 0], [1, 1]], [[-1, 0], [-2, 1]], [[1, 0], [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]]]}
  • id: 33080270
    {'center': '324.a1', 'center_index': 324, 'center_order': 3, 'counter': 68, 'cyclotomic_n': 3, 'dim': 9, 'faithful': True, 'field': [1, -1, 1], 'group': '972.525', 'group_counter': 525, 'group_order': 972, 'image': None, 'image_isoclass': '972.525', 'image_order': 972, 'indicator': 0, 'kernel': '972.a1', 'kernel_order': 1, 'label': '972.525.9d2', 'nt': [36, 2], 'q_character': None, 'values': [[[9, 0]], [[-3, 0]], [[9, 1]], [[9, -1]], [[3, 0], [-3, 1]], [[0, 0]], [[3, 0], [6, 1]], [[6, 0], [3, 1]], [[-3, 0], [-6, 1]], [[-6, 0], [-3, 1]], [[-3, 0], [3, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, -1]], [[-3, 1]], [[0, 0]], [[1, 0], [-1, 1]], [[2, 0], [1, 1]], [[0, 0]], [[-1, 0], [1, 1]], [[-2, 0], [-1, 1]], [[1, 0], [2, 1]], [[-1, 0], [-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]]]}
• 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: 115709535
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '972.525', 'ambient_counter': 525, 'ambient_order': 972, 'ambient_tex': 'C_6^2.C_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': True, 'core_order': 972, 'counter': 1, 'cyclic': False, 'direct': True, 'hall': 6, 'label': '972.525.1.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': '972.525', 'subgroup_hash': 525, 'subgroup_order': 972, 'subgroup_tex': 'C_6^2.C_3^3', 'supersolvable': False, 'sylow': 0}
  • id: 115709553
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '972.525', 'ambient_counter': 525, 'ambient_order': 972, 'ambient_tex': 'C_6^2.C_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': True, 'core_order': 324, 'counter': 2, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '972.525.3.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': '324.171', 'subgroup_hash': 171, 'subgroup_order': 324, 'subgroup_tex': 'A_4\\times C_3^3', 'supersolvable': False, 'sylow': 0}
  • id: 115709564
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '972.525', 'ambient_counter': 525, 'ambient_order': 972, 'ambient_tex': 'C_6^2.C_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': True, 'core_order': 324, 'counter': 3, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '972.525.3.b1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '3.b1', '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': ['F'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '324.86', 'subgroup_hash': 86, 'subgroup_order': 324, 'subgroup_tex': 'C_3^2.C_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 115709575
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '972.525', 'ambient_counter': 525, 'ambient_order': 972, 'ambient_tex': 'C_6^2.C_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 324, 'counter': 4, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '972.525.3.c1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '3.c1', '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': '324.60', 'subgroup_hash': 60, 'subgroup_order': 324, 'subgroup_tex': 'C_3^3:A_4', 'supersolvable': False, 'sylow': 0}
  • id: 115709586
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '972.525', 'ambient_counter': 525, 'ambient_order': 972, 'ambient_tex': 'C_6^2.C_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': True, 'core_order': 324, 'counter': 5, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '972.525.3.d1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '3.d1', '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': ['C1'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '324.130', 'subgroup_hash': 130, 'subgroup_order': 324, 'subgroup_tex': 'A_4\\times \\He_3', 'supersolvable': False, 'sylow': 0}
  • id: 115709597
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '972.525', 'ambient_counter': 525, 'ambient_order': 972, 'ambient_tex': 'C_6^2.C_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 324, 'counter': 6, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '972.525.3.e1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '3.e1', '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': '324.131', 'subgroup_hash': 131, 'subgroup_order': 324, 'subgroup_tex': 'C_6^2.C_3^2', 'supersolvable': False, 'sylow': 0}
  • id: 115709608
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '972.525', 'ambient_counter': 525, 'ambient_order': 972, 'ambient_tex': 'C_6^2.C_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 324, 'counter': 7, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '972.525.3.f1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '3.f1', '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': '324.55', 'subgroup_hash': 55, 'subgroup_order': 324, 'subgroup_tex': '\\He_3:A_4', 'supersolvable': False, 'sylow': 0}
  • id: 115709619
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '972.525', 'ambient_counter': 525, 'ambient_order': 972, 'ambient_tex': 'C_6^2.C_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 324, 'counter': 8, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '972.525.3.g1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '3.g1', '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': '324.58', 'subgroup_hash': 58, 'subgroup_order': 324, 'subgroup_tex': 'C_6^2.C_3^2', 'supersolvable': False, 'sylow': 0}
  • id: 115709630
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '972.525', 'ambient_counter': 525, 'ambient_order': 972, 'ambient_tex': 'C_6^2.C_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 81, 'counter': 9, 'cyclic': False, 'direct': None, 'hall': 3, 'label': '972.525.4.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4.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': 4, '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': '243.51', 'subgroup_hash': 51, 'subgroup_order': 243, 'subgroup_tex': 'C_3^4:C_3', 'supersolvable': True, 'sylow': 3}
  • id: 115709536
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '972.525', 'ambient_counter': 525, 'ambient_order': 972, 'ambient_tex': 'C_6^2.C_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 81, 'counter': 10, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '972.525.6.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '6.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': 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': '162.28', 'subgroup_hash': 28, 'subgroup_order': 162, 'subgroup_tex': 'C_3^3:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 115709544
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '972.525', 'ambient_counter': 525, 'ambient_order': 972, 'ambient_tex': 'C_6^2.C_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': True, 'core_order': 108, 'counter': 11, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '972.525.9.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '9.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '9.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 9, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '108.45', 'subgroup_hash': 45, 'subgroup_order': 108, 'subgroup_tex': 'C_3\\times C_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 115709545
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '972.525', 'ambient_counter': 525, 'ambient_order': 972, 'ambient_tex': 'C_6^2.C_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': True, 'core_order': 108, 'counter': 12, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '972.525.9.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '9.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '9.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 9, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '108.41', 'subgroup_hash': 41, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 115709546
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '972.525', 'ambient_counter': 525, 'ambient_order': 972, 'ambient_tex': 'C_6^2.C_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': True, 'core_order': 108, 'counter': 13, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '972.525.9.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '9.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '9.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 9, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3^2', 'simple': False, 'solvable': True, 'special_labels': ['C2'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '108.30', 'subgroup_hash': 30, 'subgroup_order': 108, 'subgroup_tex': 'C_2^2\\times \\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 115709547
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '972.525', 'ambient_counter': 525, 'ambient_order': 972, 'ambient_tex': 'C_6^2.C_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 108, 'counter': 14, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '972.525.9.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '9.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '9.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 9, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '108.41', 'subgroup_hash': 41, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 115709548
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '972.525', 'ambient_counter': 525, 'ambient_order': 972, 'ambient_tex': 'C_6^2.C_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 108, 'counter': 15, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '972.525.9.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '9.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '9.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 9, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '108.22', 'subgroup_hash': 22, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:A_4', 'supersolvable': False, 'sylow': 0}
  • id: 115709549
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '972.525', 'ambient_counter': 525, 'ambient_order': 972, 'ambient_tex': 'C_6^2.C_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 108, 'counter': 16, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '972.525.9.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '9.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '9.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 9, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '108.31', 'subgroup_hash': 31, 'subgroup_order': 108, 'subgroup_tex': 'C_{18}:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 115709550
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '972.525', 'ambient_counter': 525, 'ambient_order': 972, 'ambient_tex': 'C_6^2.C_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 108, 'counter': 17, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '972.525.9.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '9.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '9.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 9, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '108.21', 'subgroup_hash': 21, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2.A_4', 'supersolvable': False, 'sylow': 0}
  • id: 115709551
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '972.525', 'ambient_counter': 525, 'ambient_order': 972, 'ambient_tex': 'C_6^2.C_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 36, 'counter': 18, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '972.525.9.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '9.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': 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': '108.41', 'subgroup_hash': 41, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 115709552
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '972.525', 'ambient_counter': 525, 'ambient_order': 972, 'ambient_tex': 'C_6^2.C_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 36, 'counter': 19, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '972.525.9.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '9.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': 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': '108.41', 'subgroup_hash': 41, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 115709554
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '972.525', 'ambient_counter': 525, 'ambient_order': 972, 'ambient_tex': 'C_6^2.C_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 36, 'counter': 20, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '972.525.9.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '9.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': 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': '108.41', 'subgroup_hash': 41, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 115709555
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '972.525', 'ambient_counter': 525, 'ambient_order': 972, 'ambient_tex': 'C_6^2.C_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 36, 'counter': 21, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '972.525.9.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '9.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': 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': '108.18', 'subgroup_hash': 18, 'subgroup_order': 108, 'subgroup_tex': 'C_9\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 115709556
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '972.525', 'ambient_counter': 525, 'ambient_order': 972, 'ambient_tex': 'C_6^2.C_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 36, 'counter': 22, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '972.525.9.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '9.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': 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': '108.22', 'subgroup_hash': 22, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:A_4', 'supersolvable': False, 'sylow': 0}
  • id: 115709557
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '972.525', 'ambient_counter': 525, 'ambient_order': 972, 'ambient_tex': 'C_6^2.C_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 36, 'counter': 23, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '972.525.9.m1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '9.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': 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': '108.19', 'subgroup_hash': 19, 'subgroup_order': 108, 'subgroup_tex': 'C_9:A_4', 'supersolvable': False, 'sylow': 0}
  • id: 115709558
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '972.525', 'ambient_counter': 525, 'ambient_order': 972, 'ambient_tex': 'C_6^2.C_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 12, 'counter': 24, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '972.525.9.n1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '9.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': 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': '108.41', 'subgroup_hash': 41, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 115709559
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '972.525', 'ambient_counter': 525, 'ambient_order': 972, 'ambient_tex': 'C_6^2.C_3^3', 'central': False, 'central_factor': True, 'centralizer_order': 36, 'characteristic': True, 'core_order': 81, 'counter': 25, 'cyclic': False, 'direct': True, 'hall': 0, 'label': '972.525.12.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': '12.3', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'A_4', 'simple': False, 'solvable': True, 'special_labels': ['U0'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '81.7', 'subgroup_hash': 7, 'subgroup_order': 81, 'subgroup_tex': 'C_3\\wr C_3', 'supersolvable': True, 'sylow': 0}
  • id: 115709560
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '972.525', 'ambient_counter': 525, 'ambient_order': 972, 'ambient_tex': 'C_6^2.C_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 27, 'counter': 26, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '972.525.12.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.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': 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': '81.15', 'subgroup_hash': 15, 'subgroup_order': 81, 'subgroup_tex': 'C_3^4', 'supersolvable': True, 'sylow': 0}
  • id: 115709561
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '972.525', 'ambient_counter': 525, 'ambient_order': 972, 'ambient_tex': 'C_6^2.C_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 27, 'counter': 27, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '972.525.12.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.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': 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': '81.7', 'subgroup_hash': 7, 'subgroup_order': 81, 'subgroup_tex': 'C_3\\wr C_3', 'supersolvable': True, 'sylow': 0}
  • id: 115709562
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '972.525', 'ambient_counter': 525, 'ambient_order': 972, 'ambient_tex': 'C_6^2.C_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 27, 'counter': 28, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '972.525.12.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': '81.12', 'subgroup_hash': 12, 'subgroup_order': 81, 'subgroup_tex': 'C_3\\times \\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 115709563
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '972.525', 'ambient_counter': 525, 'ambient_order': 972, 'ambient_tex': 'C_6^2.C_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 27, 'counter': 29, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '972.525.12.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': '81.13', 'subgroup_hash': 13, 'subgroup_order': 81, 'subgroup_tex': 'C_9:C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 115709565
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '972.525', 'ambient_counter': 525, 'ambient_order': 972, 'ambient_tex': 'C_6^2.C_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 27, 'counter': 30, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '972.525.12.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': '81.7', 'subgroup_hash': 7, 'subgroup_order': 81, 'subgroup_tex': 'C_3\\wr C_3', 'supersolvable': True, 'sylow': 0}
  • id: 115709566
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '972.525', 'ambient_counter': 525, 'ambient_order': 972, 'ambient_tex': 'C_6^2.C_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 27, 'counter': 31, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '972.525.12.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': '81.7', 'subgroup_hash': 7, 'subgroup_order': 81, 'subgroup_tex': 'C_3\\wr C_3', 'supersolvable': True, 'sylow': 0}
  • id: 115709567
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '972.525', 'ambient_counter': 525, 'ambient_order': 972, 'ambient_tex': 'C_6^2.C_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 27, 'counter': 32, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '972.525.18.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '18.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': 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': '54.15', 'subgroup_hash': 15, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 115709568
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '972.525', 'ambient_counter': 525, 'ambient_order': 972, 'ambient_tex': 'C_6^2.C_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 27, 'counter': 33, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '972.525.18.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '18.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': 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': '54.10', 'subgroup_hash': 10, 'subgroup_order': 54, 'subgroup_tex': 'C_2\\times \\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 115709569
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '972.525', 'ambient_counter': 525, 'ambient_order': 972, 'ambient_tex': 'C_6^2.C_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 27, 'counter': 34, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '972.525.18.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '18.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': 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': '54.11', 'subgroup_hash': 11, 'subgroup_order': 54, 'subgroup_tex': 'C_9:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 115709570
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '972.525', 'ambient_counter': 525, 'ambient_order': 972, 'ambient_tex': 'C_6^2.C_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': True, 'core_order': 36, 'counter': 35, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '972.525.27.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '27.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '27.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 27, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3^3', 'simple': False, 'solvable': True, 'special_labels': ['D', 'L1', 'D1', 'C3'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '36.14', 'subgroup_hash': 14, 'subgroup_order': 36, 'subgroup_tex': 'C_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 115709571
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '972.525', 'ambient_counter': 525, 'ambient_order': 972, 'ambient_tex': 'C_6^2.C_3^3', 'central': False, 'central_factor': True, 'centralizer_order': 81, 'characteristic': True, 'core_order': 36, 'counter': 36, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '972.525.27.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '27.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '27.3', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 27, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': '\\He_3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '36.11', 'subgroup_hash': 11, 'subgroup_order': 36, 'subgroup_tex': 'C_3\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 115709572
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '972.525', 'ambient_counter': 525, 'ambient_order': 972, 'ambient_tex': 'C_6^2.C_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 36, 'counter': 37, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '972.525.27.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '27.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '27.3', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 27, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': '\\He_3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '36.11', 'subgroup_hash': 11, 'subgroup_order': 36, 'subgroup_tex': 'C_3\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 115709573
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '972.525', 'ambient_counter': 525, 'ambient_order': 972, 'ambient_tex': 'C_6^2.C_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 12, 'counter': 38, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '972.525.27.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '27.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': 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': '36.14', 'subgroup_hash': 14, 'subgroup_order': 36, 'subgroup_tex': 'C_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 115709574
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '972.525', 'ambient_counter': 525, 'ambient_order': 972, 'ambient_tex': 'C_6^2.C_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 12, 'counter': 39, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '972.525.27.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '27.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': 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': '36.14', 'subgroup_hash': 14, 'subgroup_order': 36, 'subgroup_tex': 'C_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 115709576
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '972.525', 'ambient_counter': 525, 'ambient_order': 972, 'ambient_tex': 'C_6^2.C_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 12, 'counter': 40, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '972.525.27.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '27.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': 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': '36.11', 'subgroup_hash': 11, 'subgroup_order': 36, 'subgroup_tex': 'C_3\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 115709577
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '972.525', 'ambient_counter': 525, 'ambient_order': 972, 'ambient_tex': 'C_6^2.C_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 12, 'counter': 41, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '972.525.27.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '27.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': 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': '36.11', 'subgroup_hash': 11, 'subgroup_order': 36, 'subgroup_tex': 'C_3\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 115709578
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '972.525', 'ambient_counter': 525, 'ambient_order': 972, 'ambient_tex': 'C_6^2.C_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 12, 'counter': 42, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '972.525.27.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '27.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': 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': '36.5', 'subgroup_hash': 5, 'subgroup_order': 36, 'subgroup_tex': 'C_2\\times C_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 115709579
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '972.525', 'ambient_counter': 525, 'ambient_order': 972, 'ambient_tex': 'C_6^2.C_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 12, 'counter': 43, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '972.525.27.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '27.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': 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': '36.3', 'subgroup_hash': 3, 'subgroup_order': 36, 'subgroup_tex': 'C_2^2:C_9', 'supersolvable': False, 'sylow': 0}
  • id: 115709580
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '972.525', 'ambient_counter': 525, 'ambient_order': 972, 'ambient_tex': 'C_6^2.C_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 4, 'counter': 44, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '972.525.27.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '27.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': 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': '36.14', 'subgroup_hash': 14, 'subgroup_order': 36, 'subgroup_tex': 'C_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 115709581
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '972.525', 'ambient_counter': 525, 'ambient_order': 972, 'ambient_tex': 'C_6^2.C_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 12, 'counter': 45, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '972.525.27.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '27.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': 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': '36.11', 'subgroup_hash': 11, 'subgroup_order': 36, 'subgroup_tex': 'C_3\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 115709582
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '972.525', 'ambient_counter': 525, 'ambient_order': 972, 'ambient_tex': 'C_6^2.C_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 4, 'counter': 46, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '972.525.27.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '27.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': 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': '36.11', 'subgroup_hash': 11, 'subgroup_order': 36, 'subgroup_tex': 'C_3\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 115709583
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '972.525', 'ambient_counter': 525, 'ambient_order': 972, 'ambient_tex': 'C_6^2.C_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 12, 'counter': 47, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '972.525.27.m1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '27.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': 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': '36.11', 'subgroup_hash': 11, 'subgroup_order': 36, 'subgroup_tex': 'C_3\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 115709584
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '972.525', 'ambient_counter': 525, 'ambient_order': 972, 'ambient_tex': 'C_6^2.C_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 4, 'counter': 48, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '972.525.27.n1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '27.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': 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': '36.11', 'subgroup_hash': 11, 'subgroup_order': 36, 'subgroup_tex': 'C_3\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 115709585
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '972.525', 'ambient_counter': 525, 'ambient_order': 972, 'ambient_tex': 'C_6^2.C_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 12, 'counter': 49, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '972.525.27.o1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '27.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': 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': '36.11', 'subgroup_hash': 11, 'subgroup_order': 36, 'subgroup_tex': 'C_3\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 115709587
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '972.525', 'ambient_counter': 525, 'ambient_order': 972, 'ambient_tex': 'C_6^2.C_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 324, 'characteristic': True, 'core_order': 27, 'counter': 50, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '972.525.36.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '36.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '36.11', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 11, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 36, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_3\\times A_4', '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: 115709588
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '972.525', 'ambient_counter': 525, 'ambient_order': 972, 'ambient_tex': 'C_6^2.C_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': True, 'core_order': 27, 'counter': 51, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '972.525.36.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '36.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '36.11', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 11, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 36, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_3\\times A_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '27.3', 'subgroup_hash': 3, 'subgroup_order': 27, 'subgroup_tex': '\\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 115709589
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '972.525', 'ambient_counter': 525, 'ambient_order': 972, 'ambient_tex': 'C_6^2.C_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 27, 'counter': 52, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '972.525.36.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': '36.11', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 11, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 36, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_3\\times A_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '27.4', 'subgroup_hash': 4, 'subgroup_order': 27, 'subgroup_tex': 'C_9:C_3', 'supersolvable': True, 'sylow': 0}
  • id: 115709590
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '972.525', 'ambient_counter': 525, 'ambient_order': 972, 'ambient_tex': 'C_6^2.C_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 9, 'counter': 53, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '972.525.36.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.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': 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': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 115709591
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '972.525', 'ambient_counter': 525, 'ambient_order': 972, 'ambient_tex': 'C_6^2.C_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 9, 'counter': 54, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '972.525.36.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 115709592
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '972.525', 'ambient_counter': 525, 'ambient_order': 972, 'ambient_tex': 'C_6^2.C_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 9, 'counter': 55, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '972.525.36.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '27.3', 'subgroup_hash': 3, 'subgroup_order': 27, 'subgroup_tex': '\\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 115709593
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '972.525', 'ambient_counter': 525, 'ambient_order': 972, 'ambient_tex': 'C_6^2.C_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 9, 'counter': 56, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '972.525.36.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': '27.4', 'subgroup_hash': 4, 'subgroup_order': 27, 'subgroup_tex': 'C_9:C_3', 'supersolvable': True, 'sylow': 0}
  • id: 115709594
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '972.525', 'ambient_counter': 525, 'ambient_order': 972, 'ambient_tex': 'C_6^2.C_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 3, 'counter': 57, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '972.525.36.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 115709595
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '972.525', 'ambient_counter': 525, 'ambient_order': 972, 'ambient_tex': 'C_6^2.C_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 3, 'counter': 58, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '972.525.36.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 115709596
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '972.525', 'ambient_counter': 525, 'ambient_order': 972, 'ambient_tex': 'C_6^2.C_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 3, 'counter': 59, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '972.525.36.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 115709598
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '972.525', 'ambient_counter': 525, 'ambient_order': 972, 'ambient_tex': 'C_6^2.C_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 3, 'counter': 60, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '972.525.36.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': '27.2', 'subgroup_hash': 2, 'subgroup_order': 27, 'subgroup_tex': 'C_3\\times C_9', 'supersolvable': True, 'sylow': 0}
  • id: 115709599
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '972.525', 'ambient_counter': 525, 'ambient_order': 972, 'ambient_tex': 'C_6^2.C_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 3, 'counter': 61, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '972.525.36.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '27.3', 'subgroup_hash': 3, 'subgroup_order': 27, 'subgroup_tex': '\\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 115709600
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '972.525', 'ambient_counter': 525, 'ambient_order': 972, 'ambient_tex': 'C_6^2.C_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 3, 'counter': 62, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '972.525.36.m1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.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': 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': '27.4', 'subgroup_hash': 4, 'subgroup_order': 27, 'subgroup_tex': 'C_9:C_3', 'supersolvable': True, 'sylow': 0}
  • id: 115709601
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '972.525', 'ambient_counter': 525, 'ambient_order': 972, 'ambient_tex': 'C_6^2.C_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 1, 'counter': 63, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '972.525.36.n1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.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': 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': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 115709602
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '972.525', 'ambient_counter': 525, 'ambient_order': 972, 'ambient_tex': 'C_6^2.C_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 9, 'counter': 64, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '972.525.54.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '54.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': 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': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 115709603
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '972.525', 'ambient_counter': 525, 'ambient_order': 972, 'ambient_tex': 'C_6^2.C_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 3, 'counter': 65, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '972.525.54.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': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 115709604
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '972.525', 'ambient_counter': 525, 'ambient_order': 972, 'ambient_tex': 'C_6^2.C_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 3, 'counter': 66, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '972.525.54.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': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 115709605
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '972.525', 'ambient_counter': 525, 'ambient_order': 972, 'ambient_tex': 'C_6^2.C_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 3, 'counter': 67, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '972.525.54.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': '18.2', 'subgroup_hash': 2, 'subgroup_order': 18, 'subgroup_tex': 'C_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 115709606
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '972.525', 'ambient_counter': 525, 'ambient_order': 972, 'ambient_tex': 'C_6^2.C_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 1, 'counter': 68, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '972.525.54.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': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 115709607
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '972.525', 'ambient_counter': 525, 'ambient_order': 972, 'ambient_tex': 'C_6^2.C_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 324, 'characteristic': True, 'core_order': 12, 'counter': 69, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '972.525.81.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '81.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '81.12', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 12, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 81, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3\\times \\He_3', 'simple': False, 'solvable': True, 'special_labels': ['S', 'L2', 'C4'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 115709609
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '972.525', 'ambient_counter': 525, 'ambient_order': 972, 'ambient_tex': 'C_6^2.C_3^3', 'central': False, 'central_factor': True, 'centralizer_order': 81, 'characteristic': False, 'core_order': 12, 'counter': 70, 'cyclic': False, 'direct': True, 'hall': 0, 'label': '972.525.81.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '81.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '81.7', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 7, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 81, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3\\wr C_3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '12.3', 'subgroup_hash': 3, 'subgroup_order': 12, 'subgroup_tex': 'A_4', 'supersolvable': False, 'sylow': 0}
  • id: 115709610
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '972.525', 'ambient_counter': 525, 'ambient_order': 972, 'ambient_tex': 'C_6^2.C_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 4, 'counter': 71, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '972.525.81.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '81.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': 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': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 115709611
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '972.525', 'ambient_counter': 525, 'ambient_order': 972, 'ambient_tex': 'C_6^2.C_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 4, 'counter': 72, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '972.525.81.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '81.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': 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': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 115709612
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '972.525', 'ambient_counter': 525, 'ambient_order': 972, 'ambient_tex': 'C_6^2.C_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 4, 'counter': 73, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '972.525.81.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '81.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': 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': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 115709613
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '972.525', 'ambient_counter': 525, 'ambient_order': 972, 'ambient_tex': 'C_6^2.C_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 4, 'counter': 74, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '972.525.81.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '81.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': 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': '12.3', 'subgroup_hash': 3, 'subgroup_order': 12, 'subgroup_tex': 'A_4', 'supersolvable': False, 'sylow': 0}
  • id: 115709614
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '972.525', 'ambient_counter': 525, 'ambient_order': 972, 'ambient_tex': 'C_6^2.C_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 4, 'counter': 75, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '972.525.81.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '81.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': 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': '12.3', 'subgroup_hash': 3, 'subgroup_order': 12, 'subgroup_tex': 'A_4', 'supersolvable': False, 'sylow': 0}
  • id: 115709615
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '972.525', 'ambient_counter': 525, 'ambient_order': 972, 'ambient_tex': 'C_6^2.C_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 4, 'counter': 76, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '972.525.81.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '81.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': 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': '12.3', 'subgroup_hash': 3, 'subgroup_order': 12, 'subgroup_tex': 'A_4', 'supersolvable': False, 'sylow': 0}
  • id: 115709616
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '972.525', 'ambient_counter': 525, 'ambient_order': 972, 'ambient_tex': 'C_6^2.C_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 324, 'characteristic': True, 'core_order': 9, 'counter': 77, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '972.525.108.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '108.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '108.41', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 41, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 108, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_3^2\\times A_4', 'simple': False, 'solvable': True, 'special_labels': ['Phi', 'U1'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 115709617
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '972.525', 'ambient_counter': 525, 'ambient_order': 972, 'ambient_tex': 'C_6^2.C_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 324, 'characteristic': False, 'core_order': 3, 'counter': 78, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '972.525.108.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.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': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 115709618
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '972.525', 'ambient_counter': 525, 'ambient_order': 972, 'ambient_tex': 'C_6^2.C_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 3, 'counter': 79, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '972.525.108.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.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': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 115709620
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '972.525', 'ambient_counter': 525, 'ambient_order': 972, 'ambient_tex': 'C_6^2.C_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 3, 'counter': 80, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '972.525.108.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, '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': 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: 115709621
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '972.525', 'ambient_counter': 525, 'ambient_order': 972, 'ambient_tex': 'C_6^2.C_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 3, 'counter': 81, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '972.525.108.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, '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': 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: 115709622
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '972.525', 'ambient_counter': 525, 'ambient_order': 972, 'ambient_tex': 'C_6^2.C_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 3, 'counter': 82, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '972.525.108.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, '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': 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: 115709623
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '972.525', 'ambient_counter': 525, 'ambient_order': 972, 'ambient_tex': 'C_6^2.C_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 3, 'counter': 83, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '972.525.108.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, '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': 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: 115709624
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '972.525', 'ambient_counter': 525, 'ambient_order': 972, 'ambient_tex': 'C_6^2.C_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 3, 'counter': 84, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '972.525.108.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.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': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '9.1', 'subgroup_hash': 1, 'subgroup_order': 9, 'subgroup_tex': 'C_9', 'supersolvable': True, 'sylow': 0}
  • id: 115709625
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '972.525', 'ambient_counter': 525, 'ambient_order': 972, 'ambient_tex': 'C_6^2.C_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 3, 'counter': 85, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '972.525.108.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.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': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '9.1', 'subgroup_hash': 1, 'subgroup_order': 9, 'subgroup_tex': 'C_9', 'supersolvable': True, 'sylow': 0}
  • id: 115709626
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '972.525', 'ambient_counter': 525, 'ambient_order': 972, 'ambient_tex': 'C_6^2.C_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 324, 'characteristic': False, 'core_order': 1, 'counter': 86, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '972.525.108.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.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': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 115709627
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '972.525', 'ambient_counter': 525, 'ambient_order': 972, 'ambient_tex': 'C_6^2.C_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 1, 'counter': 87, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '972.525.108.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.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': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 115709628
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '972.525', 'ambient_counter': 525, 'ambient_order': 972, 'ambient_tex': 'C_6^2.C_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 1, 'counter': 88, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '972.525.108.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.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': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 115709629
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '972.525', 'ambient_counter': 525, 'ambient_order': 972, 'ambient_tex': 'C_6^2.C_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 1, 'counter': 89, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '972.525.108.m1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.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': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 115709631
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '972.525', 'ambient_counter': 525, 'ambient_order': 972, 'ambient_tex': 'C_6^2.C_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 1, 'counter': 90, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '972.525.108.n1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.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': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 115709632
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '972.525', 'ambient_counter': 525, 'ambient_order': 972, 'ambient_tex': 'C_6^2.C_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 91, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '972.525.108.o1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.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': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 115709633
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '972.525', 'ambient_counter': 525, 'ambient_order': 972, 'ambient_tex': 'C_6^2.C_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 324, 'characteristic': False, 'core_order': 3, 'counter': 92, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '972.525.162.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, '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': 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: 115709634
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '972.525', 'ambient_counter': 525, 'ambient_order': 972, 'ambient_tex': 'C_6^2.C_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 1, 'counter': 93, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '972.525.162.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, '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': 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: 115709635
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '972.525', 'ambient_counter': 525, 'ambient_order': 972, 'ambient_tex': 'C_6^2.C_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 1, 'counter': 94, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '972.525.162.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, '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': 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: 115709636
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '972.525', 'ambient_counter': 525, 'ambient_order': 972, 'ambient_tex': 'C_6^2.C_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1, 'counter': 95, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '972.525.162.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '162.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': 162, '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: 115709637
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '972.525', 'ambient_counter': 525, 'ambient_order': 972, 'ambient_tex': 'C_6^2.C_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 324, 'characteristic': True, 'core_order': 4, 'counter': 96, 'cyclic': False, 'direct': False, 'hall': 2, 'label': '972.525.243.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '243.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '243.51', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 51, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 243, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3^4:C_3', 'simple': False, 'solvable': True, 'special_labels': ['L3', 'C5'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 2}
  • id: 115709638
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '972.525', 'ambient_counter': 525, 'ambient_order': 972, 'ambient_tex': 'C_6^2.C_3^3', 'central': True, 'central_factor': False, 'centralizer_order': 972, 'characteristic': True, 'core_order': 3, 'counter': 97, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '972.525.324.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '324.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '324.130', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 130, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 324, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'A_4\\times \\He_3', 'simple': True, 'solvable': True, 'special_labels': ['Z', 'U2'], 'split': False, 'standard_generators': False, 'stem': True, 'subgroup': '3.1', 'subgroup_hash': 1, 'subgroup_order': 3, 'subgroup_tex': 'C_3', 'supersolvable': True, 'sylow': 0}
  • id: 115709639
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '972.525', 'ambient_counter': 525, 'ambient_order': 972, 'ambient_tex': 'C_6^2.C_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 324, 'characteristic': False, 'core_order': 1, 'counter': 98, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '972.525.324.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '324.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': 324, '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: 115709640
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '972.525', 'ambient_counter': 525, 'ambient_order': 972, 'ambient_tex': 'C_6^2.C_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 324, 'characteristic': False, 'core_order': 1, 'counter': 99, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '972.525.324.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '324.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': 324, '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: 115709537
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '972.525', 'ambient_counter': 525, 'ambient_order': 972, 'ambient_tex': 'C_6^2.C_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 243, 'characteristic': False, 'core_order': 1, 'counter': 100, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '972.525.324.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '324.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': 324, '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: 115709538
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '972.525', 'ambient_counter': 525, 'ambient_order': 972, 'ambient_tex': 'C_6^2.C_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 1, 'counter': 101, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '972.525.324.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '324.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': 324, '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: 115709539
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '972.525', 'ambient_counter': 525, 'ambient_order': 972, 'ambient_tex': 'C_6^2.C_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 1, 'counter': 102, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '972.525.324.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '324.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': 324, '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: 115709540
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '972.525', 'ambient_counter': 525, 'ambient_order': 972, 'ambient_tex': 'C_6^2.C_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 1, 'counter': 103, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '972.525.324.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '324.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': 324, '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: 115709541
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '972.525', 'ambient_counter': 525, 'ambient_order': 972, 'ambient_tex': 'C_6^2.C_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 104, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '972.525.324.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '324.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': 324, '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: 115709542
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '972.525', 'ambient_counter': 525, 'ambient_order': 972, 'ambient_tex': 'C_6^2.C_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 324, 'characteristic': False, 'core_order': 1, 'counter': 105, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '972.525.486.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '486.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': 486, '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: 115709543
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '972.525', 'ambient_counter': 525, 'ambient_order': 972, 'ambient_tex': 'C_6^2.C_3^3', 'central': True, 'central_factor': False, 'centralizer_order': 972, 'characteristic': True, 'core_order': 1, 'counter': 106, 'cyclic': True, 'direct': True, 'hall': 1, 'label': '972.525.972.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '972.a1', 'outer_equivalence': True, 'perfect': True, 'proper': False, 'quotient': '972.525', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 525, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 972, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_6^2.C_3^3', 'simple': False, 'solvable': True, 'special_labels': ['PC', 'U3', '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: 115709636
    {'ambient': '972.525', 'aut_centralizer_order': 432, 'aut_label': '162.d1', 'aut_quo_index': None, 'aut_stab_index': 27, 'aut_weyl_group': '2.1', 'aut_weyl_index': 11664, 'centralizer': '27.e1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['54.c1', '81.e1'], 'contains': ['324.e1', '486.a1'], 'core': '972.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [8400, -1, 6820, -1], 'generators': [27, 1], 'label': '972.525.162.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '9.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.e1', 'old_label': '162.d1', 'projective_image': '972.525', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '162.d1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 115709630
    {'ambient': '972.525', 'aut_centralizer_order': 3, 'aut_label': '4.a1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '1944.3565', 'aut_weyl_index': 12, 'centralizer': '108.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1'], 'contains': ['12.a1', '12.b1', '12.c1', '12.d1', '12.e1', '12.f1', '12.g1'], 'core': '12.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [6169, -1, 6551, -1], 'generators': [1, 3, 108], 'label': '972.525.4.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1', 'old_label': '4.a1', 'projective_image': '324.130', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.a1', 'subgroup_fusion': None, 'weyl_group': '27.3'}
  • id: 115709631
    {'ambient': '972.525', 'aut_centralizer_order': 27, 'aut_label': '108.n1', 'aut_quo_index': None, 'aut_stab_index': 216, 'aut_weyl_group': '4.2', 'aut_weyl_index': 5832, 'centralizer': '12.b1', 'complements': None, 'conjugacy_class_count': 18, 'contained_in': ['27.n1', '36.i1', '36.n1'], 'contains': ['324.c1', '324.f1', '324.g1'], 'core': '972.a1', 'coset_action_label': None, 'count': 216, 'diagramx': [1159, -1, 1898, -1], 'generators': [109, 345], 'label': '972.525.108.n1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.b1', 'old_label': '108.n1', 'projective_image': '972.525', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.n1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 115709632
    {'ambient': '972.525', 'aut_centralizer_order': 54, 'aut_label': '108.o1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '4.2', 'aut_weyl_index': 5832, 'centralizer': '36.j1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['27.o1', '36.j1'], 'contains': ['324.d1', '324.e1', '324.h1'], 'core': '972.a1', 'coset_action_label': None, 'count': 108, 'diagramx': [9726, -1, 8480, -1], 'generators': [1, 3], 'label': '972.525.108.o1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.j1', 'old_label': '108.o1', 'projective_image': '972.525', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.o1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 115709633
    {'ambient': '972.525', 'aut_centralizer_order': 3888, 'aut_label': '162.a1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '2.1', 'aut_weyl_index': 11664, 'centralizer': '3.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['54.a1', '54.b1', '54.c1', '54.d1', '81.a1'], 'contains': ['324.a1', '486.a1'], 'core': '324.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5845, -1, 4713, -1], 'generators': [27, 324], 'label': '972.525.162.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '81.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '162.a1', 'projective_image': '324.130', '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: 115709634
    {'ambient': '972.525', 'aut_centralizer_order': 1296, 'aut_label': '162.b1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '2.1', 'aut_weyl_index': 11664, 'centralizer': '9.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['54.a1', '54.e1', '81.c1'], 'contains': ['324.b1', '486.a1'], 'core': '972.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [2457, -1, 3377, -1], 'generators': [27, 666], 'label': '972.525.162.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '27.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '162.b1', 'projective_image': '972.525', '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: 115709635
    {'ambient': '972.525', 'aut_centralizer_order': 432, 'aut_label': '162.c1', 'aut_quo_index': None, 'aut_stab_index': 27, 'aut_weyl_group': '2.1', 'aut_weyl_index': 11664, 'centralizer': '9.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['54.b1', '54.e1', '81.d1'], 'contains': ['324.c1', '486.a1'], 'core': '972.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [1933, -1, 2866, -1], 'generators': [27, 109], 'label': '972.525.162.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '9.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '162.c1', 'projective_image': '972.525', '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: 115709537
    {'ambient': '972.525', 'aut_centralizer_order': 972, 'aut_label': '324.d1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '2.1', 'aut_weyl_index': 11664, 'centralizer': '4.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['81.b1', '108.c1', '108.k1', '108.m1', '108.o1'], 'contains': ['972.a1'], 'core': '972.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [5781, -1, 4130, -1], 'generators': [3], 'label': '972.525.324.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '81.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1', 'old_label': '324.d1', 'projective_image': '972.525', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.d1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 115709538
    {'ambient': '972.525', 'aut_centralizer_order': 1296, 'aut_label': '324.e1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '2.1', 'aut_weyl_index': 11664, 'centralizer': '9.j1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.d1', '108.o1', '162.d1'], 'contains': ['972.a1'], 'core': '972.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [8784, -1, 6921, -1], 'generators': [1], 'label': '972.525.324.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.j1', 'old_label': '324.e1', 'projective_image': '972.525', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.e1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 115709539
    {'ambient': '972.525', 'aut_centralizer_order': 486, 'aut_label': '324.f1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '2.1', 'aut_weyl_index': 11664, 'centralizer': '12.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['81.f1', '108.e1', '108.k1', '108.n1'], 'contains': ['972.a1'], 'core': '972.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [2337, -1, 3742, -1], 'generators': [345], 'label': '972.525.324.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '27.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.b1', 'old_label': '324.f1', 'projective_image': '972.525', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.f1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 115709540
    {'ambient': '972.525', 'aut_centralizer_order': 162, 'aut_label': '324.g1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '2.1', 'aut_weyl_index': 11664, 'centralizer': '12.b1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['81.g1', '108.f1', '108.l1', '108.m1', '108.n1'], 'contains': ['972.a1'], 'core': '972.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [997, -1, 1789, -1], 'generators': [112], 'label': '972.525.324.g1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '9.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.b1', 'old_label': '324.g1', 'projective_image': '972.525', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.g1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 115709541
    {'ambient': '972.525', 'aut_centralizer_order': 162, 'aut_label': '324.h1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '2.1', 'aut_weyl_index': 11664, 'centralizer': '36.j1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['81.h1', '108.g1', '108.o1'], 'contains': ['972.a1'], 'core': '972.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [9151, -1, 8371, -1], 'generators': [4], 'label': '972.525.324.h1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '9.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.j1', 'old_label': '324.h1', 'projective_image': '972.525', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.h1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 115709542
    {'ambient': '972.525', 'aut_centralizer_order': 7776, 'aut_label': '486.a1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '1.1', 'aut_weyl_index': 23328, 'centralizer': '3.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['162.a1', '162.b1', '162.c1', '162.d1', '243.a1'], 'contains': ['972.a1'], 'core': '972.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4170, -1, 3933, -1], 'generators': [27], 'label': '972.525.486.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '243.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '486.a1', 'projective_image': '972.525', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '486.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 115709543
    {'ambient': '972.525', 'aut_centralizer_order': None, 'aut_label': '972.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': ['324.a1', '324.b1', '324.c1', '324.d1', '324.e1', '324.f1', '324.g1', '324.h1', '486.a1'], 'contains': [], 'core': '972.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4170, 8705, 3933, 9205], 'generators': [], 'label': '972.525.972.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '972.a1', 'normal_contained_in': ['243.a1', '324.a1'], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '972.a1', 'projective_image': '972.525', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 115709563
    {'ambient': '972.525', 'aut_centralizer_order': 9, 'aut_label': '12.e1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '324.122', 'aut_weyl_index': 72, 'centralizer': '108.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['3.e1', '4.a1'], 'contains': ['36.c1', '36.d1', '36.g1', '36.k1', '36.m1'], 'core': '36.c1', 'coset_action_label': None, 'count': 8, 'diagramx': [7295, -1, 7841, -1], 'generators': [217, 3, 342], 'label': '972.525.12.e1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '3.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1', 'old_label': '12.e1', 'projective_image': '324.130', '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': '27.3'}
  • id: 115709585
    {'ambient': '972.525', 'aut_centralizer_order': 18, 'aut_label': '27.o1', 'aut_quo_index': None, 'aut_stab_index': 27, 'aut_weyl_group': '48.48', 'aut_weyl_index': 486, 'centralizer': '108.d1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['9.j1'], 'contains': ['81.b1', '81.e1', '81.h1', '108.o1'], 'core': '81.b1', 'coset_action_label': None, 'count': 27, 'diagramx': [9005, -1, 9844, -1], 'generators': [1, 3, 513, 486], 'label': '972.525.27.o1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.j1', 'old_label': '27.o1', 'projective_image': '972.525', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '27.o1', 'subgroup_fusion': None, 'weyl_group': '12.3'}
  • id: 115709628
    {'ambient': '972.525', 'aut_centralizer_order': 81, 'aut_label': '108.l1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '4.2', 'aut_weyl_index': 5832, 'centralizer': '12.b1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['27.l1', '36.e1', '36.n1'], 'contains': ['324.b1', '324.g1'], 'core': '972.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [532, -1, 1462, -1], 'generators': [112, 666], 'label': '972.525.108.l1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '9.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.b1', 'old_label': '108.l1', 'projective_image': '972.525', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.l1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 115709629
    {'ambient': '972.525', 'aut_centralizer_order': 54, 'aut_label': '108.m1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '4.2', 'aut_weyl_index': 5832, 'centralizer': '12.b1', 'complements': None, 'conjugacy_class_count': 9, 'contained_in': ['27.m1', '36.h1', '36.n1'], 'contains': ['324.c1', '324.d1', '324.g1'], 'core': '972.a1', 'coset_action_label': None, 'count': 108, 'diagramx': [905, -1, 1680, -1], 'generators': [109, 3], 'label': '972.525.108.m1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.b1', 'old_label': '108.m1', 'projective_image': '972.525', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.m1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 115709535
    {'ambient': '972.525', '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': '324.a1', 'complements': ['972.a1'], 'conjugacy_class_count': 1, 'contained_in': [], 'contains': ['3.a1', '3.b1', '3.c1', '3.d1', '3.e1', '3.f1', '3.g1', '4.a1'], 'core': '1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5533, 5188, 6059, 4402], 'generators': [1, 513, 324, 3, 486, 108, 342], 'label': '972.525.1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '1.a1', 'normal_contained_in': [], 'normal_contains': ['3.a1', '3.b1', '3.c1', '3.d1', '3.e1', '3.f1', '3.g1'], 'normalizer': '1.a1', 'old_label': '1.a1', 'projective_image': '324.130', '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': '324.130'}
  • id: 115709536
    {'ambient': '972.525', 'aut_centralizer_order': 24, 'aut_label': '6.a1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '324.117', 'aut_weyl_index': 72, 'centralizer': '81.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.b1'], 'contains': ['12.a1', '18.a1', '18.b1', '18.c1'], 'core': '12.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4608, -1, 4375, -1], 'generators': [27, 324, 1, 108, 342], 'label': '972.525.6.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '6.a1', 'projective_image': '324.130', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.a1', 'subgroup_fusion': None, 'weyl_group': '27.3'}
  • id: 115709544
    {'ambient': '972.525', 'aut_centralizer_order': 108, 'aut_label': '9.a1', 'aut_quo_index': 12, 'aut_stab_index': 1, 'aut_weyl_group': '216.170', 'aut_weyl_index': 108, 'centralizer': '9.a1', 'complements': ['108.o1'], 'conjugacy_class_count': 1, 'contained_in': ['3.a1', '3.b1', '3.c1'], 'contains': ['18.a1', '27.a1', '27.d1', '27.j1'], 'core': '9.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3494, 5349, 2944, 2011], 'generators': [27, 324, 486, 109, 342], 'label': '972.525.9.a1', 'mobius_quo': 0, 'mobius_sub': 3, 'normal_closure': '9.a1', 'normal_contained_in': ['3.a1', '3.b1', '3.c1'], 'normal_contains': ['27.a1', '36.a1'], 'normalizer': '1.a1', 'old_label': '9.a1', 'projective_image': '324.130', 'quotient_action_image': '9.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '9.a1', 'subgroup_fusion': None, 'weyl_group': '9.2'}
  • id: 115709545
    {'ambient': '972.525', 'aut_centralizer_order': 27, 'aut_label': '9.b1', 'aut_quo_index': 12, 'aut_stab_index': 1, 'aut_weyl_group': '864.4673', 'aut_weyl_index': 27, 'centralizer': '36.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['3.a1', '3.d1', '3.e1'], 'contains': ['27.a1', '27.b1', '27.c1', '27.k1', '36.d1'], 'core': '9.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [4092, 1065, 3667, 962], 'generators': [3, 486, 342, 324, 513], 'label': '972.525.9.b1', 'mobius_quo': 0, 'mobius_sub': 3, 'normal_closure': '9.b1', 'normal_contained_in': ['3.a1', '3.d1', '3.e1'], 'normal_contains': ['27.a1', '27.b1', '27.c1'], 'normalizer': '1.a1', 'old_label': '9.b1', 'projective_image': '324.130', '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': '36.11'}
  • id: 115709546
    {'ambient': '972.525', 'aut_centralizer_order': 36, 'aut_label': '9.c1', 'aut_quo_index': 12, 'aut_stab_index': 1, 'aut_weyl_group': '648.555', 'aut_weyl_index': 36, 'centralizer': '81.a1', 'complements': ['108.m1', '108.n1'], 'conjugacy_class_count': 1, 'contained_in': ['3.b1', '3.d1', '3.f1'], 'contains': ['18.b1', '27.a1', '27.e1'], 'core': '9.c1', 'coset_action_label': None, 'count': 1, 'diagramx': [6828, 2482, 5463, 4509], 'generators': [27, 324, 486, 1, 342], 'label': '972.525.9.c1', 'mobius_quo': 0, 'mobius_sub': 3, 'normal_closure': '9.c1', 'normal_contained_in': ['3.b1', '3.d1', '3.f1'], 'normal_contains': ['27.a1', '36.b1'], 'normalizer': '1.a1', 'old_label': '9.c1', 'projective_image': '324.130', 'quotient_action_image': '9.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '9.c1', 'subgroup_fusion': None, 'weyl_group': '81.12'}
  • id: 115709547
    {'ambient': '972.525', 'aut_centralizer_order': 27, 'aut_label': '9.d1', 'aut_quo_index': 12, 'aut_stab_index': 2, 'aut_weyl_group': '432.745', 'aut_weyl_index': 54, 'centralizer': '36.a1', 'complements': ['108.o1'], 'conjugacy_class_count': 2, 'contained_in': ['3.a1', '3.f1', '3.g1'], 'contains': ['27.a1', '27.f1', '27.l1', '36.e1'], 'core': '9.d1', 'coset_action_label': None, 'count': 2, 'diagramx': [1703, 8276, 1334, 6506], 'generators': [112, 486, 342, 324, 513], 'label': '972.525.9.d1', 'mobius_quo': 0, 'mobius_sub': 3, 'normal_closure': '9.d1', 'normal_contained_in': ['3.a1', '3.f1', '3.g1'], 'normal_contains': ['27.a1'], 'normalizer': '1.a1', 'old_label': '9.d1', 'projective_image': '324.130', 'quotient_action_image': '9.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '9.d1', 'subgroup_fusion': None, 'weyl_group': '36.11'}
  • id: 115709548
    {'ambient': '972.525', 'aut_centralizer_order': 9, 'aut_label': '9.e1', 'aut_quo_index': 12, 'aut_stab_index': 2, 'aut_weyl_group': '1296.2931', 'aut_weyl_index': 18, 'centralizer': '324.a1', 'complements': ['108.m1', '108.n1'], 'conjugacy_class_count': 2, 'contained_in': ['3.c1', '3.d1', '3.g1'], 'contains': ['27.a1', '27.g1', '36.f1'], 'core': '9.e1', 'coset_action_label': None, 'count': 2, 'diagramx': [7254, 6383, 7708, 5605], 'generators': [4, 486, 342, 324, 513], 'label': '972.525.9.e1', 'mobius_quo': 0, 'mobius_sub': 3, 'normal_closure': '9.e1', 'normal_contained_in': ['3.c1', '3.d1', '3.g1'], 'normal_contains': ['27.a1'], 'normalizer': '1.a1', 'old_label': '9.e1', 'projective_image': '324.130', 'quotient_action_image': '9.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '9.e1', 'subgroup_fusion': None, 'weyl_group': '324.130'}
  • id: 115709549
    {'ambient': '972.525', 'aut_centralizer_order': 36, 'aut_label': '9.f1', 'aut_quo_index': 12, 'aut_stab_index': 2, 'aut_weyl_group': '324.122', 'aut_weyl_index': 72, 'centralizer': '81.a1', 'complements': ['108.o1', '108.m1', '108.n1'], 'conjugacy_class_count': 2, 'contained_in': ['3.b1', '3.e1', '3.g1'], 'contains': ['18.c1', '27.a1', '27.h1'], 'core': '9.f1', 'coset_action_label': None, 'count': 2, 'diagramx': [4996, 4023, 4928, 3166], 'generators': [27, 324, 486, 217, 342], 'label': '972.525.9.f1', 'mobius_quo': 0, 'mobius_sub': 3, 'normal_closure': '9.f1', 'normal_contained_in': ['3.b1', '3.e1', '3.g1'], 'normal_contains': ['27.a1', '36.c1'], 'normalizer': '1.a1', 'old_label': '9.f1', 'projective_image': '324.130', 'quotient_action_image': '9.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '9.f1', 'subgroup_fusion': None, 'weyl_group': '81.12'}
  • id: 115709550
    {'ambient': '972.525', 'aut_centralizer_order': 9, 'aut_label': '9.g1', 'aut_quo_index': 24, 'aut_stab_index': 4, 'aut_weyl_group': '648.575', 'aut_weyl_index': 36, 'centralizer': '324.a1', 'complements': ['108.o1', '108.m1', '108.n1'], 'conjugacy_class_count': 4, 'contained_in': ['3.c1', '3.e1', '3.f1', '3.g1'], 'contains': ['27.a1', '27.i1', '36.g1'], 'core': '9.g1', 'coset_action_label': None, 'count': 4, 'diagramx': [5479, 7250, 6099, 7401], 'generators': [111, 486, 342, 324, 513], 'label': '972.525.9.g1', 'mobius_quo': 0, 'mobius_sub': 3, 'normal_closure': '9.g1', 'normal_contained_in': ['3.c1', '3.e1', '3.f1', '3.g1'], 'normal_contains': ['27.a1'], 'normalizer': '1.a1', 'old_label': '9.g1', 'projective_image': '324.130', 'quotient_action_image': '9.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '9.g1', 'subgroup_fusion': None, 'weyl_group': '324.130'}
  • id: 115709551
    {'ambient': '972.525', 'aut_centralizer_order': 18, 'aut_label': '9.h1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '432.745', 'aut_weyl_index': 54, 'centralizer': '36.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1'], 'contains': ['27.b1', '27.d1', '27.f1', '27.m1', '36.h1'], 'core': '27.b1', 'coset_action_label': None, 'count': 3, 'diagramx': [2104, -1, 1749, -1], 'generators': [109, 486, 3, 324, 513], 'label': '972.525.9.h1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '9.h1', 'projective_image': '324.130', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '9.h1', 'subgroup_fusion': None, 'weyl_group': '12.3'}
  • id: 115709552
    {'ambient': '972.525', 'aut_centralizer_order': 9, 'aut_label': '9.i1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '432.745', 'aut_weyl_index': 54, 'centralizer': '36.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['3.a1'], 'contains': ['27.c1', '27.d1', '27.f1', '27.n1', '36.i1'], 'core': '27.c1', 'coset_action_label': None, 'count': 6, 'diagramx': [2503, -1, 2265, -1], 'generators': [109, 486, 345, 324, 513], 'label': '972.525.9.i1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '9.i1', 'projective_image': '324.130', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '9.i1', 'subgroup_fusion': None, 'weyl_group': '12.3'}
  • id: 115709553
    {'ambient': '972.525', 'aut_centralizer_order': 9, 'aut_label': '3.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '2592.na', 'aut_weyl_index': 9, 'centralizer': '36.a1', 'complements': ['324.e1', '324.h1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1'], 'contains': ['9.a1', '9.b1', '9.d1', '9.h1', '9.i1', '9.n1', '12.b1'], 'core': '3.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2748, 5188, 2138, 461], 'generators': [109, 486, 513, 3, 342, 324], 'label': '972.525.3.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '3.a1', 'normal_contained_in': ['1.a1'], 'normal_contains': ['9.a1', '9.b1', '9.d1'], 'normalizer': '1.a1', 'old_label': '3.a1', 'projective_image': '324.130', 'quotient_action_image': '3.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '3.a1', 'subgroup_fusion': None, 'weyl_group': '36.11'}
  • id: 115709554
    {'ambient': '972.525', 'aut_centralizer_order': 9, 'aut_label': '9.j1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '864.4673', 'aut_weyl_index': 27, 'centralizer': '108.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.d1'], 'contains': ['27.b1', '27.e1', '27.g1', '27.o1', '36.j1'], 'core': '27.b1', 'coset_action_label': None, 'count': 3, 'diagramx': [9744, -1, 8998, -1], 'generators': [1, 486, 3, 324, 513], 'label': '972.525.9.j1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.d1', 'old_label': '9.j1', 'projective_image': '324.130', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '9.j1', 'subgroup_fusion': None, 'weyl_group': '36.11'}
  • id: 115709555
    {'ambient': '972.525', 'aut_centralizer_order': 9, 'aut_label': '9.k1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '432.745', 'aut_weyl_index': 54, 'centralizer': '108.h1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['3.e1'], 'contains': ['27.b1', '27.h1', '27.i1', '36.k1'], 'core': '27.b1', 'coset_action_label': None, 'count': 6, 'diagramx': [8045, -1, 7378, -1], 'generators': [217, 486, 3, 324, 513], 'label': '972.525.9.k1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.e1', 'old_label': '9.k1', 'projective_image': '324.130', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '9.k1', 'subgroup_fusion': None, 'weyl_group': '36.11'}
  • id: 115709556
    {'ambient': '972.525', 'aut_centralizer_order': 9, 'aut_label': '9.l1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '432.747', 'aut_weyl_index': 54, 'centralizer': '324.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['3.d1'], 'contains': ['27.c1', '27.e1', '27.g1', '36.l1'], 'core': '27.c1', 'coset_action_label': None, 'count': 6, 'diagramx': [9326, -1, 8214, -1], 'generators': [1, 486, 345, 324, 513], 'label': '972.525.9.l1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.d1', 'old_label': '9.l1', 'projective_image': '324.130', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '9.l1', 'subgroup_fusion': None, 'weyl_group': '108.41'}
  • id: 115709557
    {'ambient': '972.525', 'aut_centralizer_order': 9, 'aut_label': '9.m1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '216.166', 'aut_weyl_index': 108, 'centralizer': '324.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['3.e1'], 'contains': ['27.c1', '27.h1', '27.i1', '36.m1'], 'core': '27.c1', 'coset_action_label': None, 'count': 12, 'diagramx': [7655, -1, 7078, -1], 'generators': [217, 486, 345, 324, 513], 'label': '972.525.9.m1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.e1', 'old_label': '9.m1', 'projective_image': '324.130', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '9.m1', 'subgroup_fusion': None, 'weyl_group': '108.41'}
  • id: 115709558
    {'ambient': '972.525', 'aut_centralizer_order': 9, 'aut_label': '9.n1', 'aut_quo_index': None, 'aut_stab_index': 27, 'aut_weyl_group': '96.226', 'aut_weyl_index': 243, 'centralizer': '36.a1', 'complements': None, 'conjugacy_class_count': 9, 'contained_in': ['3.a1'], 'contains': ['27.j1', '27.k1', '27.l1', '27.m1', '27.n1', '36.n1'], 'core': '81.b1', 'coset_action_label': None, 'count': 27, 'diagramx': [538, -1, 874, -1], 'generators': [109, 486, 3, 666, 513], 'label': '972.525.9.n1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '9.n1', 'projective_image': '972.525', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '9.n1', 'subgroup_fusion': None, 'weyl_group': '12.3'}
  • id: 115709559
    {'ambient': '972.525', 'aut_centralizer_order': 72, 'aut_label': '12.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '324.117', 'aut_weyl_index': 72, 'centralizer': '27.b1', 'complements': ['81.b1', '81.f1', '81.h1', '81.g1'], 'conjugacy_class_count': 1, 'contained_in': ['4.a1', '6.a1'], 'contains': ['36.a1', '36.b1', '36.c1'], 'core': '12.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5120, 8705, 4843, 9205], 'generators': [1, 108], 'label': '972.525.12.a1', 'mobius_quo': 0, 'mobius_sub': 4, 'normal_closure': '12.a1', 'normal_contained_in': ['3.b1'], 'normal_contains': ['36.a1', '36.b1', '36.c1'], 'normalizer': '1.a1', 'old_label': '12.a1', 'projective_image': '324.130', 'quotient_action_image': '1.1', 'quotient_action_kernel': '12.3', 'quotient_action_kernel_order': 12, 'quotient_fusion': None, 'short_label': '12.a1', 'subgroup_fusion': None, 'weyl_group': '27.3'}
  • id: 115709560
    {'ambient': '972.525', 'aut_centralizer_order': 27, 'aut_label': '12.b1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '216.170', 'aut_weyl_index': 108, 'centralizer': '12.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1', '4.a1'], 'contains': ['36.a1', '36.d1', '36.e1', '36.h1', '36.i1', '36.n1'], 'core': '36.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [2843, -1, 1728, -1], 'generators': [109, 3, 342, 324], 'label': '972.525.12.b1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '3.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1', 'old_label': '12.b1', 'projective_image': '324.130', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.b1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 115709561
    {'ambient': '972.525', 'aut_centralizer_order': 9, 'aut_label': '12.c1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '324.117', 'aut_weyl_index': 72, 'centralizer': '108.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['3.c1', '4.a1'], 'contains': ['36.a1', '36.f1', '36.g1'], 'core': '36.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [6005, -1, 7115, -1], 'generators': [109, 111], 'label': '972.525.12.c1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '3.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1', 'old_label': '12.c1', 'projective_image': '324.130', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.c1', 'subgroup_fusion': None, 'weyl_group': '27.3'}
  • id: 115709562
    {'ambient': '972.525', 'aut_centralizer_order': 9, 'aut_label': '12.d1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '648.555', 'aut_weyl_index': 36, 'centralizer': '108.c1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.d1', '4.a1'], 'contains': ['36.b1', '36.d1', '36.f1', '36.j1', '36.l1'], 'core': '36.b1', 'coset_action_label': None, 'count': 4, 'diagramx': [9028, -1, 8538, -1], 'generators': [1, 3, 342], 'label': '972.525.12.d1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '3.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1', 'old_label': '12.d1', 'projective_image': '324.130', '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': '27.3'}
  • id: 115709564
    {'ambient': '972.525', 'aut_centralizer_order': 12, 'aut_label': '3.b1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '1944.3565', 'aut_weyl_index': 12, 'centralizer': '81.a1', 'complements': ['324.d1', '324.f1', '324.h1', '324.g1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1'], 'contains': ['6.a1', '9.a1', '9.c1', '9.f1'], 'core': '3.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [4267, 3632, 4928, 2926], 'generators': [27, 324, 342, 486, 1, 108], 'label': '972.525.3.b1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '3.b1', 'normal_contained_in': ['1.a1'], 'normal_contains': ['9.a1', '9.c1', '9.f1', '12.a1'], 'normalizer': '1.a1', 'old_label': '3.b1', 'projective_image': '324.130', 'quotient_action_image': '3.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '3.b1', 'subgroup_fusion': None, 'weyl_group': '81.12'}
  • id: 115709565
    {'ambient': '972.525', 'aut_centralizer_order': 9, 'aut_label': '12.f1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '324.117', 'aut_weyl_index': 72, 'centralizer': '108.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['3.f1', '4.a1'], 'contains': ['36.b1', '36.e1', '36.g1'], 'core': '36.b1', 'coset_action_label': None, 'count': 8, 'diagramx': [6397, -1, 6197, -1], 'generators': [1, 111], 'label': '972.525.12.f1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '3.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1', 'old_label': '12.f1', 'projective_image': '324.130', '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': '27.3'}
  • id: 115709566
    {'ambient': '972.525', 'aut_centralizer_order': 9, 'aut_label': '12.g1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '162.41', 'aut_weyl_index': 144, 'centralizer': '108.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['3.g1', '4.a1'], 'contains': ['36.c1', '36.e1', '36.f1', '36.g1'], 'core': '36.c1', 'coset_action_label': None, 'count': 16, 'diagramx': [5612, -1, 6604, -1], 'generators': [217, 111], 'label': '972.525.12.g1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '3.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1', 'old_label': '12.g1', 'projective_image': '324.130', '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': '27.3'}
  • id: 115709567
    {'ambient': '972.525', 'aut_centralizer_order': 216, 'aut_label': '18.a1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '36.12', 'aut_weyl_index': 648, 'centralizer': '9.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.a1', '9.a1'], 'contains': ['36.a1', '54.a1', '54.b1', '54.e1'], 'core': '36.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3261, -1, 2944, -1], 'generators': [27, 109, 342, 324], 'label': '972.525.18.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '9.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '18.a1', 'projective_image': '324.130', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.a1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 115709568
    {'ambient': '972.525', 'aut_centralizer_order': 72, 'aut_label': '18.b1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '108.17', 'aut_weyl_index': 216, 'centralizer': '81.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.a1', '9.c1'], 'contains': ['36.b1', '54.a1', '54.c1'], 'core': '36.b1', 'coset_action_label': None, 'count': 3, 'diagramx': [7163, -1, 5303, -1], 'generators': [27, 1, 342, 324], 'label': '972.525.18.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '9.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '18.b1', 'projective_image': '324.130', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.b1', 'subgroup_fusion': None, 'weyl_group': '27.3'}
  • id: 115709569
    {'ambient': '972.525', 'aut_centralizer_order': 72, 'aut_label': '18.c1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '54.8', 'aut_weyl_index': 432, 'centralizer': '81.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['6.a1', '9.f1'], 'contains': ['36.c1', '54.a1', '54.d1'], 'core': '36.c1', 'coset_action_label': None, 'count': 6, 'diagramx': [5237, -1, 4417, -1], 'generators': [27, 217, 342, 324], 'label': '972.525.18.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '9.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '18.c1', 'projective_image': '324.130', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.c1', 'subgroup_fusion': None, 'weyl_group': '27.3'}
  • id: 115709570
    {'ambient': '972.525', 'aut_centralizer_order': 324, 'aut_label': '27.a1', 'aut_quo_index': 1404, 'aut_stab_index': 1, 'aut_weyl_group': '72.46', 'aut_weyl_index': 324, 'centralizer': '9.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['9.a1', '9.b1', '9.c1', '9.d1', '9.e1', '9.f1', '9.g1'], 'contains': ['54.a1', '81.a1', '81.c1'], 'core': '27.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4098, 4430, 3263, 3834], 'generators': [27, 486, 342, 324], 'label': '972.525.27.a1', 'mobius_quo': 0, 'mobius_sub': -27, 'normal_closure': '27.a1', 'normal_contained_in': ['9.a1', '9.b1', '9.c1', '9.d1', '9.e1', '9.f1', '9.g1'], 'normal_contains': ['81.a1', '108.a1'], 'normalizer': '1.a1', 'old_label': '27.a1', 'projective_image': '324.130', 'quotient_action_image': '9.2', 'quotient_action_kernel': '3.1', 'quotient_action_kernel_order': 3, 'quotient_fusion': None, 'short_label': '27.a1', 'subgroup_fusion': None, 'weyl_group': '9.2'}
  • id: 115709571
    {'ambient': '972.525', 'aut_centralizer_order': 162, 'aut_label': '27.b1', 'aut_quo_index': 12, 'aut_stab_index': 1, 'aut_weyl_group': '144.183', 'aut_weyl_index': 162, 'centralizer': '12.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['9.b1', '9.h1', '9.j1', '9.k1'], 'contains': ['81.a1', '81.b1', '108.c1'], 'core': '27.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [6410, 2100, 4016, 962], 'generators': [3, 324, 513, 486], 'label': '972.525.27.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '27.b1', 'normal_contained_in': ['9.b1'], 'normal_contains': ['81.a1', '81.b1'], 'normalizer': '1.a1', 'old_label': '27.b1', 'projective_image': '324.130', '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': '12.3'}
  • id: 115709572
    {'ambient': '972.525', 'aut_centralizer_order': 81, 'aut_label': '27.c1', 'aut_quo_index': 12, 'aut_stab_index': 2, 'aut_weyl_group': '144.183', 'aut_weyl_index': 162, 'centralizer': '36.a1', 'complements': [], 'conjugacy_class_count': 2, 'contained_in': ['9.b1', '9.i1', '9.l1', '9.m1'], 'contains': ['81.a1', '81.f1', '108.e1'], 'core': '27.c1', 'coset_action_label': None, 'count': 2, 'diagramx': [4988, 1065, 3553, 1864], 'generators': [345, 324, 513, 486], 'label': '972.525.27.c1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '27.c1', 'normal_contained_in': ['9.b1'], 'normal_contains': ['81.a1'], 'normalizer': '1.a1', 'old_label': '27.c1', 'projective_image': '324.130', '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': '36.11'}
  • id: 115709573
    {'ambient': '972.525', 'aut_centralizer_order': 216, 'aut_label': '27.d1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '36.12', 'aut_weyl_index': 648, 'centralizer': '9.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['9.a1', '9.h1', '9.i1'], 'contains': ['54.b1', '81.a1', '81.d1'], 'core': '81.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [2522, -1, 2265, -1], 'generators': [27, 486, 109, 324], 'label': '972.525.27.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '9.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '27.d1', 'projective_image': '324.130', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '27.d1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 115709574
    {'ambient': '972.525', 'aut_centralizer_order': 108, 'aut_label': '27.e1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '72.46', 'aut_weyl_index': 324, 'centralizer': '27.e1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['9.c1', '9.j1', '9.l1'], 'contains': ['54.c1', '81.a1', '81.e1'], 'core': '81.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8379, -1, 8171, -1], 'generators': [27, 486, 1, 324], 'label': '972.525.27.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '9.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.d1', 'old_label': '27.e1', 'projective_image': '324.130', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '27.e1', 'subgroup_fusion': None, 'weyl_group': '9.2'}
  • id: 115709575
    {'ambient': '972.525', 'aut_centralizer_order': 3, 'aut_label': '3.c1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '3888.km', 'aut_weyl_index': 6, 'centralizer': '324.a1', 'complements': ['324.e1', '324.h1', '324.d1', '324.f1', '324.g1'], 'conjugacy_class_count': 2, 'contained_in': ['1.a1'], 'contains': ['9.a1', '9.e1', '9.g1', '12.c1'], 'core': '3.c1', 'coset_action_label': None, 'count': 2, 'diagramx': [5725, 6545, 6535, 5705], 'generators': [109, 486, 513, 111, 666, 324], 'label': '972.525.3.c1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '3.c1', 'normal_contained_in': ['1.a1'], 'normal_contains': ['9.a1', '9.e1', '9.g1'], 'normalizer': '1.a1', 'old_label': '3.c1', 'projective_image': '324.130', 'quotient_action_image': '3.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '3.c1', 'subgroup_fusion': None, 'weyl_group': '324.130'}
  • id: 115709576
    {'ambient': '972.525', 'aut_centralizer_order': 54, 'aut_label': '27.f1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '72.42', 'aut_weyl_index': 324, 'centralizer': '36.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['9.d1', '9.h1', '9.i1'], 'contains': ['81.a1', '81.g1', '108.f1'], 'core': '81.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [1502, -1, 1337, -1], 'generators': [112, 324, 513, 486], 'label': '972.525.27.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '9.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '27.f1', 'projective_image': '324.130', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '27.f1', 'subgroup_fusion': None, 'weyl_group': '12.3'}
  • id: 115709577
    {'ambient': '972.525', 'aut_centralizer_order': 27, 'aut_label': '27.g1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '144.183', 'aut_weyl_index': 162, 'centralizer': '108.d1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['9.e1', '9.j1', '9.l1'], 'contains': ['81.a1', '81.h1', '108.g1'], 'core': '81.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [8659, -1, 9382, -1], 'generators': [4, 324, 513, 486], 'label': '972.525.27.g1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '9.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.d1', 'old_label': '27.g1', 'projective_image': '324.130', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '27.g1', 'subgroup_fusion': None, 'weyl_group': '36.11'}
  • id: 115709578
    {'ambient': '972.525', 'aut_centralizer_order': 108, 'aut_label': '27.h1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '36.12', 'aut_weyl_index': 648, 'centralizer': '27.h1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['9.f1', '9.k1', '9.m1'], 'contains': ['54.d1', '81.a1'], 'core': '81.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [7381, -1, 5777, -1], 'generators': [27, 486, 217, 324], 'label': '972.525.27.h1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '9.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.e1', 'old_label': '27.h1', 'projective_image': '324.130', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '27.h1', 'subgroup_fusion': None, 'weyl_group': '9.2'}
  • id: 115709579
    {'ambient': '972.525', 'aut_centralizer_order': 27, 'aut_label': '27.i1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '72.42', 'aut_weyl_index': 324, 'centralizer': '108.h1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['9.g1', '9.k1', '9.m1'], 'contains': ['81.a1', '108.i1'], 'core': '81.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [7835, -1, 7469, -1], 'generators': [111, 324, 513, 486], 'label': '972.525.27.i1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '9.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.e1', 'old_label': '27.i1', 'projective_image': '324.130', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '27.i1', 'subgroup_fusion': None, 'weyl_group': '36.11'}
  • id: 115709580
    {'ambient': '972.525', 'aut_centralizer_order': 108, 'aut_label': '27.j1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '24.14', 'aut_weyl_index': 972, 'centralizer': '9.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['9.a1', '9.n1'], 'contains': ['54.e1', '81.c1', '81.d1'], 'core': '243.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [1224, -1, 2047, -1], 'generators': [27, 486, 109, 666], 'label': '972.525.27.j1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '9.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '27.j1', 'projective_image': '972.525', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '27.j1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 115709581
    {'ambient': '972.525', 'aut_centralizer_order': 54, 'aut_label': '27.k1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '48.48', 'aut_weyl_index': 486, 'centralizer': '36.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['9.b1', '9.n1'], 'contains': ['81.b1', '81.c1', '81.f1', '108.k1'], 'core': '81.b1', 'coset_action_label': None, 'count': 9, 'diagramx': [1949, -1, 2555, -1], 'generators': [3, 666, 513, 486], 'label': '972.525.27.k1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '9.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '27.k1', 'projective_image': '972.525', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '27.k1', 'subgroup_fusion': None, 'weyl_group': '12.3'}
  • id: 115709582
    {'ambient': '972.525', 'aut_centralizer_order': 27, 'aut_label': '27.l1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '48.48', 'aut_weyl_index': 486, 'centralizer': '36.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['9.d1', '9.n1'], 'contains': ['81.c1', '81.g1', '108.l1'], 'core': '243.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [150, -1, 156, -1], 'generators': [112, 666, 513, 486], 'label': '972.525.27.l1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '9.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '27.l1', 'projective_image': '972.525', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '27.l1', 'subgroup_fusion': None, 'weyl_group': '12.3'}
  • id: 115709583
    {'ambient': '972.525', 'aut_centralizer_order': 18, 'aut_label': '27.m1', 'aut_quo_index': None, 'aut_stab_index': 27, 'aut_weyl_group': '48.48', 'aut_weyl_index': 486, 'centralizer': '36.a1', 'complements': None, 'conjugacy_class_count': 9, 'contained_in': ['9.h1', '9.n1'], 'contains': ['81.b1', '81.d1', '81.g1', '108.m1'], 'core': '81.b1', 'coset_action_label': None, 'count': 27, 'diagramx': [597, -1, 515, -1], 'generators': [109, 3, 513, 486], 'label': '972.525.27.m1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '27.m1', 'projective_image': '972.525', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '27.m1', 'subgroup_fusion': None, 'weyl_group': '12.3'}
  • id: 115709584
    {'ambient': '972.525', 'aut_centralizer_order': 9, 'aut_label': '27.n1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '48.48', 'aut_weyl_index': 486, 'centralizer': '36.a1', 'complements': None, 'conjugacy_class_count': 18, 'contained_in': ['9.i1', '9.n1'], 'contains': ['81.d1', '81.f1', '81.g1', '108.n1'], 'core': '243.a1', 'coset_action_label': None, 'count': 54, 'diagramx': [944, -1, 874, -1], 'generators': [109, 21, 513, 486], 'label': '972.525.27.n1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '27.n1', 'projective_image': '972.525', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '27.n1', 'subgroup_fusion': None, 'weyl_group': '12.3'}
  • id: 115709586
    {'ambient': '972.525', 'aut_centralizer_order': 3, 'aut_label': '3.d1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': None, 'aut_weyl_index': 3, 'centralizer': '324.a1', 'complements': ['324.c1', '324.g1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1'], 'contains': ['9.b1', '9.c1', '9.e1', '9.j1', '9.l1', '12.d1'], 'core': '3.d1', 'coset_action_label': None, 'count': 1, 'diagramx': [7768, 666, 7708, 4402], 'generators': [1, 486, 513, 3, 342, 324], 'label': '972.525.3.d1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '3.d1', 'normal_contained_in': ['1.a1'], 'normal_contains': ['9.b1', '9.c1', '9.e1'], 'normalizer': '1.a1', 'old_label': '3.d1', 'projective_image': '324.130', 'quotient_action_image': '3.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '3.d1', 'subgroup_fusion': None, 'weyl_group': '324.130'}
  • id: 115709587
    {'ambient': '972.525', 'aut_centralizer_order': 648, 'aut_label': '36.a1', 'aut_quo_index': 3, 'aut_stab_index': 1, 'aut_weyl_group': '36.12', 'aut_weyl_index': 648, 'centralizer': '3.a1', 'complements': ['27.o1'], 'conjugacy_class_count': 1, 'contained_in': ['12.a1', '12.b1', '12.c1', '18.a1'], 'contains': ['108.a1', '108.b1', '108.j1'], 'core': '36.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3974, 8116, 3931, 8690], 'generators': [109, 342, 324], 'label': '972.525.36.a1', 'mobius_quo': 0, 'mobius_sub': -12, 'normal_closure': '36.a1', 'normal_contained_in': ['9.a1', '12.a1'], 'normal_contains': ['108.a1'], 'normalizer': '1.a1', 'old_label': '36.a1', 'projective_image': '324.130', 'quotient_action_image': '3.1', 'quotient_action_kernel': '12.3', 'quotient_action_kernel_order': 12, 'quotient_fusion': None, 'short_label': '36.a1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 115709588
    {'ambient': '972.525', 'aut_centralizer_order': 216, 'aut_label': '36.b1', 'aut_quo_index': 3, 'aut_stab_index': 1, 'aut_weyl_group': '108.17', 'aut_weyl_index': 216, 'centralizer': '27.b1', 'complements': ['27.m1', '27.n1'], 'conjugacy_class_count': 1, 'contained_in': ['12.a1', '12.d1', '12.f1', '18.b1'], 'contains': ['108.a1', '108.d1'], 'core': '36.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [6739, 8705, 6075, 9205], 'generators': [1, 342], 'label': '972.525.36.b1', 'mobius_quo': 0, 'mobius_sub': -12, 'normal_closure': '36.b1', 'normal_contained_in': ['9.c1', '12.a1'], 'normal_contains': ['108.a1'], 'normalizer': '1.a1', 'old_label': '36.b1', 'projective_image': '324.130', 'quotient_action_image': '3.1', 'quotient_action_kernel': '12.3', 'quotient_action_kernel_order': 12, 'quotient_fusion': None, 'short_label': '36.b1', 'subgroup_fusion': None, 'weyl_group': '27.3'}
  • id: 115709589
    {'ambient': '972.525', 'aut_centralizer_order': 216, 'aut_label': '36.c1', 'aut_quo_index': 3, 'aut_stab_index': 2, 'aut_weyl_group': '54.8', 'aut_weyl_index': 432, 'centralizer': '27.b1', 'complements': ['27.o1', '27.m1', '27.n1'], 'conjugacy_class_count': 2, 'contained_in': ['12.a1', '12.e1', '12.g1', '18.c1'], 'contains': ['108.a1', '108.h1'], 'core': '36.c1', 'coset_action_label': None, 'count': 2, 'diagramx': [5666, 9334, 5732, 9753], 'generators': [217, 342], 'label': '972.525.36.c1', 'mobius_quo': 0, 'mobius_sub': -12, 'normal_closure': '36.c1', 'normal_contained_in': ['9.f1', '12.a1'], 'normal_contains': ['108.a1'], 'normalizer': '1.a1', 'old_label': '36.c1', 'projective_image': '324.130', 'quotient_action_image': '3.1', 'quotient_action_kernel': '12.3', 'quotient_action_kernel_order': 12, 'quotient_fusion': None, 'short_label': '36.c1', 'subgroup_fusion': None, 'weyl_group': '27.3'}
  • id: 115709590
    {'ambient': '972.525', 'aut_centralizer_order': 81, 'aut_label': '36.d1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '72.46', 'aut_weyl_index': 324, 'centralizer': '12.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['9.b1', '12.b1', '12.d1', '12.e1'], 'contains': ['108.a1', '108.c1', '108.e1', '108.k1'], 'core': '108.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [5142, -1, 5165, -1], 'generators': [3, 342, 324], 'label': '972.525.36.d1', 'mobius_quo': None, 'mobius_sub': -3, 'normal_closure': '9.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1', 'old_label': '36.d1', 'projective_image': '324.130', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.d1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 115709591
    {'ambient': '972.525', 'aut_centralizer_order': 81, 'aut_label': '36.e1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '36.12', 'aut_weyl_index': 648, 'centralizer': '12.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['9.d1', '12.b1', '12.f1', '12.g1'], 'contains': ['108.a1', '108.f1', '108.l1'], 'core': '108.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [3066, -1, 2116, -1], 'generators': [112, 342, 324], 'label': '972.525.36.e1', 'mobius_quo': None, 'mobius_sub': -3, 'normal_closure': '9.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1', 'old_label': '36.e1', 'projective_image': '324.130', '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': '3.1'}
  • id: 115709592
    {'ambient': '972.525', 'aut_centralizer_order': 27, 'aut_label': '36.f1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '108.17', 'aut_weyl_index': 216, 'centralizer': '108.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['9.e1', '12.c1', '12.d1', '12.g1'], 'contains': ['108.a1', '108.g1'], 'core': '108.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [7021, -1, 7115, -1], 'generators': [4, 342], 'label': '972.525.36.f1', 'mobius_quo': None, 'mobius_sub': -3, 'normal_closure': '9.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1', 'old_label': '36.f1', 'projective_image': '324.130', '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': '27.3'}
  • id: 115709593
    {'ambient': '972.525', 'aut_centralizer_order': 27, 'aut_label': '36.g1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '54.8', 'aut_weyl_index': 432, 'centralizer': '108.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['9.g1', '12.c1', '12.e1', '12.f1', '12.g1'], 'contains': ['108.a1', '108.i1'], 'core': '108.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [5902, -1, 6434, -1], 'generators': [111, 342], 'label': '972.525.36.g1', 'mobius_quo': None, 'mobius_sub': -3, 'normal_closure': '9.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1', 'old_label': '36.g1', 'projective_image': '324.130', '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': '27.3'}
  • id: 115709594
    {'ambient': '972.525', 'aut_centralizer_order': 54, 'aut_label': '36.h1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '36.12', 'aut_weyl_index': 648, 'centralizer': '12.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['9.h1', '12.b1'], 'contains': ['108.b1', '108.c1', '108.f1', '108.m1'], 'core': '324.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [2855, -1, 1536, -1], 'generators': [109, 3, 324], 'label': '972.525.36.h1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.b1', 'old_label': '36.h1', 'projective_image': '324.130', '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': '1.1'}
  • id: 115709595
    {'ambient': '972.525', 'aut_centralizer_order': 27, 'aut_label': '36.i1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '36.12', 'aut_weyl_index': 648, 'centralizer': '12.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['9.i1', '12.b1'], 'contains': ['108.b1', '108.e1', '108.f1', '108.n1'], 'core': '324.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [3276, -1, 2335, -1], 'generators': [109, 345, 324], 'label': '972.525.36.i1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.b1', 'old_label': '36.i1', 'projective_image': '324.130', '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: 115709596
    {'ambient': '972.525', 'aut_centralizer_order': 27, 'aut_label': '36.j1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '72.46', 'aut_weyl_index': 324, 'centralizer': '36.j1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['9.j1', '12.d1'], 'contains': ['108.c1', '108.d1', '108.g1', '108.o1'], 'core': '324.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [9850, -1, 8480, -1], 'generators': [1, 3, 324], 'label': '972.525.36.j1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.d1', 'old_label': '36.j1', 'projective_image': '324.130', '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': '3.1'}
  • id: 115709597
    {'ambient': '972.525', 'aut_centralizer_order': 3, 'aut_label': '3.e1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': None, 'aut_weyl_index': 6, 'centralizer': '324.a1', 'complements': ['324.e1', '324.c1', '324.h1', '324.g1'], 'conjugacy_class_count': 2, 'contained_in': ['1.a1'], 'contains': ['9.b1', '9.f1', '9.g1', '9.k1', '9.m1', '12.e1'], 'core': '3.e1', 'coset_action_label': None, 'count': 2, 'diagramx': [6192, 2038, 7019, 1536], 'generators': [217, 486, 513, 3, 342, 324], 'label': '972.525.3.e1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '3.e1', 'normal_contained_in': ['1.a1'], 'normal_contains': ['9.b1', '9.f1', '9.g1'], 'normalizer': '1.a1', 'old_label': '3.e1', 'projective_image': '324.130', 'quotient_action_image': '3.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '3.e1', 'subgroup_fusion': None, 'weyl_group': '324.130'}
  • id: 115709598
    {'ambient': '972.525', 'aut_centralizer_order': 27, 'aut_label': '36.k1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '36.12', 'aut_weyl_index': 648, 'centralizer': '36.k1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['9.k1', '12.e1'], 'contains': ['108.c1', '108.h1', '108.i1'], 'core': '324.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [9241, -1, 7636, -1], 'generators': [217, 3], 'label': '972.525.36.k1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.e1', 'old_label': '36.k1', 'projective_image': '324.130', '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': '3.1'}
  • id: 115709599
    {'ambient': '972.525', 'aut_centralizer_order': 27, 'aut_label': '36.l1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '36.10', 'aut_weyl_index': 648, 'centralizer': '108.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['9.l1', '12.d1'], 'contains': ['108.d1', '108.e1', '108.g1'], 'core': '324.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [9651, -1, 8275, -1], 'generators': [1, 345], 'label': '972.525.36.l1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.d1', 'old_label': '36.l1', 'projective_image': '324.130', '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': '9.2'}
  • id: 115709600
    {'ambient': '972.525', 'aut_centralizer_order': 27, 'aut_label': '36.m1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '18.3', 'aut_weyl_index': 1296, 'centralizer': '108.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['9.m1', '12.e1'], 'contains': ['108.e1', '108.h1', '108.i1'], 'core': '324.a1', 'coset_action_label': None, 'count': 48, 'diagramx': [8949, -1, 7333, -1], 'generators': [217, 345], 'label': '972.525.36.m1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.e1', 'old_label': '36.m1', 'projective_image': '324.130', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.m1', 'subgroup_fusion': None, 'weyl_group': '9.2'}
  • id: 115709601
    {'ambient': '972.525', 'aut_centralizer_order': 27, 'aut_label': '36.n1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '8.5', 'aut_weyl_index': 2916, 'centralizer': '12.b1', 'complements': None, 'conjugacy_class_count': 9, 'contained_in': ['9.n1', '12.b1'], 'contains': ['108.j1', '108.k1', '108.l1', '108.m1', '108.n1'], 'core': '972.a1', 'coset_action_label': '36T1584', 'count': 108, 'diagramx': [207, -1, 1217, -1], 'generators': [109, 3, 666], 'label': '972.525.36.n1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.b1', 'old_label': '36.n1', 'projective_image': '972.525', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.n1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 115709602
    {'ambient': '972.525', 'aut_centralizer_order': 648, 'aut_label': '54.a1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '12.4', 'aut_weyl_index': 1944, 'centralizer': '9.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.a1', '18.b1', '18.c1', '27.a1'], 'contains': ['108.a1', '162.a1', '162.b1'], 'core': '108.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4736, -1, 4412, -1], 'generators': [27, 342, 324], 'label': '972.525.54.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '27.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1', 'old_label': '54.a1', 'projective_image': '324.130', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.a1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 115709603
    {'ambient': '972.525', 'aut_centralizer_order': 432, 'aut_label': '54.b1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '6.2', 'aut_weyl_index': 3888, 'centralizer': '9.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.a1', '27.d1'], 'contains': ['108.b1', '162.a1', '162.c1'], 'core': '324.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [3510, -1, 3348, -1], 'generators': [27, 109, 324], 'label': '972.525.54.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '9.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '54.b1', 'projective_image': '324.130', '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: 115709604
    {'ambient': '972.525', 'aut_centralizer_order': 216, 'aut_label': '54.c1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '12.4', 'aut_weyl_index': 1944, 'centralizer': '27.e1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.b1', '27.e1'], 'contains': ['108.d1', '162.a1', '162.d1'], 'core': '324.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [8512, -1, 6838, -1], 'generators': [27, 1, 324], 'label': '972.525.54.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '9.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1', 'old_label': '54.c1', 'projective_image': '324.130', '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': '3.1'}
  • id: 115709605
    {'ambient': '972.525', 'aut_centralizer_order': 216, 'aut_label': '54.d1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '6.2', 'aut_weyl_index': 3888, 'centralizer': '27.h1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['18.c1', '27.h1'], 'contains': ['108.h1', '162.a1'], 'core': '324.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [7347, -1, 5492, -1], 'generators': [27, 217, 324], 'label': '972.525.54.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '9.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.f1', 'old_label': '54.d1', 'projective_image': '324.130', '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': '3.1'}
  • id: 115709606
    {'ambient': '972.525', 'aut_centralizer_order': 216, 'aut_label': '54.e1', 'aut_quo_index': None, 'aut_stab_index': 27, 'aut_weyl_group': '4.2', 'aut_weyl_index': 5832, 'centralizer': '9.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['18.a1', '27.j1'], 'contains': ['108.j1', '162.b1', '162.c1'], 'core': '972.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [1308, -1, 2624, -1], 'generators': [27, 109, 666], 'label': '972.525.54.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '9.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '54.e1', 'projective_image': '972.525', '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: 115709607
    {'ambient': '972.525', 'aut_centralizer_order': 1944, 'aut_label': '81.a1', 'aut_quo_index': 324, 'aut_stab_index': 1, 'aut_weyl_group': '12.4', 'aut_weyl_index': 1944, 'centralizer': '3.b1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['27.a1', '27.b1', '27.c1', '27.d1', '27.e1', '27.f1', '27.g1', '27.h1', '27.i1'], 'contains': ['162.a1', '243.a1'], 'core': '81.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6091, 2659, 4875, 1764], 'generators': [27, 486, 324], 'label': '972.525.81.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '81.a1', 'normal_contained_in': ['27.a1', '27.b1', '27.c1'], 'normal_contains': ['243.a1', '324.a1'], 'normalizer': '1.a1', 'old_label': '81.a1', 'projective_image': '324.130', 'quotient_action_image': '3.1', 'quotient_action_kernel': '27.3', 'quotient_action_kernel_order': 27, 'quotient_fusion': None, 'short_label': '81.a1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 115709608
    {'ambient': '972.525', 'aut_centralizer_order': 3, 'aut_label': '3.f1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '3888.km', 'aut_weyl_index': 6, 'centralizer': '324.a1', 'complements': ['324.c1', '324.g1', '324.d1', '324.f1', '324.h1'], 'conjugacy_class_count': 2, 'contained_in': ['1.a1'], 'contains': ['9.c1', '9.d1', '9.g1', '12.f1'], 'core': '3.f1', 'coset_action_label': None, 'count': 2, 'diagramx': [5340, 9265, 5492, 8076], 'generators': [1, 486, 513, 111, 342, 324], 'label': '972.525.3.f1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '3.f1', 'normal_contained_in': ['1.a1'], 'normal_contains': ['9.c1', '9.d1', '9.g1'], 'normalizer': '1.a1', 'old_label': '3.f1', 'projective_image': '324.130', 'quotient_action_image': '3.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '3.f1', 'subgroup_fusion': None, 'weyl_group': '324.130'}
  • id: 115709609
    {'ambient': '972.525', 'aut_centralizer_order': 324, 'aut_label': '81.b1', 'aut_quo_index': 1, 'aut_stab_index': 3, 'aut_weyl_group': '24.12', 'aut_weyl_index': 972, 'centralizer': '12.a1', 'complements': ['12.a1', '12.g1', '12.f1', '12.c1'], 'conjugacy_class_count': 3, 'contained_in': ['27.b1', '27.k1', '27.m1', '27.o1'], 'contains': ['243.a1', '324.d1'], 'core': '81.b1', 'coset_action_label': None, 'count': 3, 'diagramx': [5142, 1863, 4135, 1015], 'generators': [3, 513, 486], 'label': '972.525.81.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '81.b1', 'normal_contained_in': ['27.b1'], 'normal_contains': ['243.a1'], 'normalizer': '1.a1', 'old_label': '81.b1', 'projective_image': '972.525', 'quotient_action_image': '1.1', 'quotient_action_kernel': '81.7', 'quotient_action_kernel_order': 81, 'quotient_fusion': None, 'short_label': '81.b1', 'subgroup_fusion': None, 'weyl_group': '12.3'}
  • id: 115709610
    {'ambient': '972.525', 'aut_centralizer_order': 648, 'aut_label': '81.c1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '12.4', 'aut_weyl_index': 1944, 'centralizer': '9.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['27.a1', '27.j1', '27.k1', '27.l1'], 'contains': ['162.b1', '243.a1'], 'core': '243.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [2380, -1, 2986, -1], 'generators': [27, 486, 666], 'label': '972.525.81.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '27.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '81.c1', 'projective_image': '972.525', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '81.c1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 115709611
    {'ambient': '972.525', 'aut_centralizer_order': 216, 'aut_label': '81.d1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '12.4', 'aut_weyl_index': 1944, 'centralizer': '9.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['27.d1', '27.j1', '27.m1', '27.n1'], 'contains': ['162.c1', '243.a1'], 'core': '243.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [1933, -1, 1826, -1], 'generators': [27, 486, 109], 'label': '972.525.81.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '9.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '81.d1', 'projective_image': '972.525', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '81.d1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 115709612
    {'ambient': '972.525', 'aut_centralizer_order': 216, 'aut_label': '81.e1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '12.4', 'aut_weyl_index': 1944, 'centralizer': '27.e1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['27.e1', '27.o1'], 'contains': ['162.d1', '243.a1'], 'core': '243.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [7547, -1, 7998, -1], 'generators': [27, 486, 1], 'label': '972.525.81.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '9.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.j1', 'old_label': '81.e1', 'projective_image': '972.525', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '81.e1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 115709613
    {'ambient': '972.525', 'aut_centralizer_order': 162, 'aut_label': '81.f1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '24.12', 'aut_weyl_index': 972, 'centralizer': '36.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['27.c1', '27.k1', '27.n1'], 'contains': ['243.a1', '324.f1'], 'core': '243.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [3330, -1, 3726, -1], 'generators': [21, 513, 486], 'label': '972.525.81.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '27.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '81.f1', 'projective_image': '972.525', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '81.f1', 'subgroup_fusion': None, 'weyl_group': '12.3'}
  • id: 115709614
    {'ambient': '972.525', 'aut_centralizer_order': 54, 'aut_label': '81.g1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '24.12', 'aut_weyl_index': 972, 'centralizer': '36.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['27.f1', '27.l1', '27.m1', '27.n1'], 'contains': ['243.a1', '324.g1'], 'core': '243.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [645, -1, 885, -1], 'generators': [112, 513, 486], 'label': '972.525.81.g1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '9.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '81.g1', 'projective_image': '972.525', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '81.g1', 'subgroup_fusion': None, 'weyl_group': '12.3'}
  • id: 115709615
    {'ambient': '972.525', 'aut_centralizer_order': 54, 'aut_label': '81.h1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '24.12', 'aut_weyl_index': 972, 'centralizer': '108.d1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['27.g1', '27.o1'], 'contains': ['243.a1', '324.h1'], 'core': '243.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [8106, -1, 9232, -1], 'generators': [4, 513, 486], 'label': '972.525.81.h1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '9.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.j1', 'old_label': '81.h1', 'projective_image': '972.525', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '81.h1', 'subgroup_fusion': None, 'weyl_group': '12.3'}
  • id: 115709616
    {'ambient': '972.525', 'aut_centralizer_order': 1944, 'aut_label': '108.a1', 'aut_quo_index': 108, 'aut_stab_index': 1, 'aut_weyl_group': '12.4', 'aut_weyl_index': 1944, 'centralizer': '3.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['36.a1', '36.b1', '36.c1', '36.d1', '36.e1', '36.f1', '36.g1', '54.a1'], 'contains': ['324.a1', '324.b1'], 'core': '108.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4854, 8705, 4918, 9205], 'generators': [342, 324], 'label': '972.525.108.a1', 'mobius_quo': 0, 'mobius_sub': 108, 'normal_closure': '108.a1', 'normal_contained_in': ['27.a1', '36.a1', '36.b1', '36.c1'], 'normal_contains': ['324.a1'], 'normalizer': '1.a1', 'old_label': '108.a1', 'projective_image': '324.130', 'quotient_action_image': '3.1', 'quotient_action_kernel': '36.11', 'quotient_action_kernel_order': 36, 'quotient_fusion': None, 'short_label': '108.a1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 115709617
    {'ambient': '972.525', 'aut_centralizer_order': 1296, 'aut_label': '108.b1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '6.2', 'aut_weyl_index': 3888, 'centralizer': '3.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.a1', '36.h1', '36.i1', '54.b1'], 'contains': ['324.a1', '324.c1'], 'core': '324.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3651, -1, 3106, -1], 'generators': [109, 324], 'label': '972.525.108.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '108.b1', 'projective_image': '324.130', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 115709618
    {'ambient': '972.525', 'aut_centralizer_order': 486, 'aut_label': '108.c1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '12.4', 'aut_weyl_index': 1944, 'centralizer': '4.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['27.b1', '36.d1', '36.h1', '36.j1', '36.k1'], 'contains': ['324.a1', '324.d1'], 'core': '324.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [7144, -1, 5354, -1], 'generators': [3, 324], 'label': '972.525.108.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '27.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1', 'old_label': '108.c1', 'projective_image': '324.130', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.c1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 115709619
    {'ambient': '972.525', 'aut_centralizer_order': 3, 'aut_label': '3.g1', 'aut_quo_index': 1, 'aut_stab_index': 4, 'aut_weyl_group': '1944.3611', 'aut_weyl_index': 12, 'centralizer': '324.a1', 'complements': ['324.e1', '324.c1', '324.g1', '324.h1', '324.d1', '324.f1'], 'conjugacy_class_count': 4, 'contained_in': ['1.a1'], 'contains': ['9.d1', '9.e1', '9.f1', '9.g1', '12.g1'], 'core': '3.g1', 'coset_action_label': None, 'count': 4, 'diagramx': [4947, 8093, 5899, 7054], 'generators': [217, 486, 513, 111, 18, 324], 'label': '972.525.3.g1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '3.g1', 'normal_contained_in': ['1.a1'], 'normal_contains': ['9.d1', '9.e1', '9.f1', '9.g1'], 'normalizer': '1.a1', 'old_label': '3.g1', 'projective_image': '324.130', 'quotient_action_image': '3.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '3.g1', 'subgroup_fusion': None, 'weyl_group': '324.130'}
  • id: 115709620
    {'ambient': '972.525', 'aut_centralizer_order': 648, 'aut_label': '108.d1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '12.4', 'aut_weyl_index': 1944, 'centralizer': '9.j1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.b1', '36.j1', '36.l1', '54.c1'], 'contains': ['324.a1', '324.e1'], 'core': '324.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [9100, -1, 7025, -1], 'generators': [1, 324], 'label': '972.525.108.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.d1', 'old_label': '108.d1', 'projective_image': '324.130', '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': '3.1'}
  • id: 115709621
    {'ambient': '972.525', 'aut_centralizer_order': 243, 'aut_label': '108.e1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '12.4', 'aut_weyl_index': 1944, 'centralizer': '12.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['27.c1', '36.d1', '36.i1', '36.l1', '36.m1'], 'contains': ['324.a1', '324.f1'], 'core': '324.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [5632, -1, 5136, -1], 'generators': [345, 324], 'label': '972.525.108.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '27.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1', 'old_label': '108.e1', 'projective_image': '324.130', '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': '3.1'}
  • id: 115709622
    {'ambient': '972.525', 'aut_centralizer_order': 162, 'aut_label': '108.f1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '6.2', 'aut_weyl_index': 3888, 'centralizer': '12.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['27.f1', '36.e1', '36.h1', '36.i1'], 'contains': ['324.a1', '324.g1'], 'core': '324.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [3022, -1, 2116, -1], 'generators': [112, 324], 'label': '972.525.108.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '9.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.b1', 'old_label': '108.f1', 'projective_image': '324.130', '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': '1.1'}
  • id: 115709623
    {'ambient': '972.525', 'aut_centralizer_order': 81, 'aut_label': '108.g1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '12.4', 'aut_weyl_index': 1944, 'centralizer': '36.j1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['27.g1', '36.f1', '36.j1', '36.l1'], 'contains': ['324.a1', '324.h1'], 'core': '324.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [9516, -1, 8262, -1], 'generators': [4, 324], 'label': '972.525.108.g1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '9.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.d1', 'old_label': '108.g1', 'projective_image': '324.130', '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': '3.1'}
  • id: 115709624
    {'ambient': '972.525', 'aut_centralizer_order': 648, 'aut_label': '108.h1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '6.2', 'aut_weyl_index': 3888, 'centralizer': '9.k1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.c1', '36.k1', '36.m1', '54.d1'], 'contains': ['324.a1'], 'core': '324.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [8301, -1, 5732, -1], 'generators': [217], 'label': '972.525.108.h1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.e1', 'old_label': '108.h1', 'projective_image': '324.130', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.h1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 115709625
    {'ambient': '972.525', 'aut_centralizer_order': 81, 'aut_label': '108.i1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '6.2', 'aut_weyl_index': 3888, 'centralizer': '36.k1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['27.i1', '36.g1', '36.k1', '36.m1'], 'contains': ['324.a1'], 'core': '324.a1', 'coset_action_label': None, 'count': 48, 'diagramx': [8780, -1, 6607, -1], 'generators': [111], 'label': '972.525.108.i1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '9.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.e1', 'old_label': '108.i1', 'projective_image': '324.130', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.i1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 115709626
    {'ambient': '972.525', 'aut_centralizer_order': 648, 'aut_label': '108.j1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '4.2', 'aut_weyl_index': 5832, 'centralizer': '3.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['36.a1', '36.n1', '54.e1'], 'contains': ['324.b1', '324.c1'], 'core': '972.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [1370, -1, 2662, -1], 'generators': [109, 666], 'label': '972.525.108.j1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '108.j1', 'projective_image': '972.525', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.j1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 115709627
    {'ambient': '972.525', 'aut_centralizer_order': 162, 'aut_label': '108.k1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '4.2', 'aut_weyl_index': 5832, 'centralizer': '12.b1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['27.k1', '36.d1', '36.n1'], 'contains': ['324.b1', '324.d1', '324.f1'], 'core': '972.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [2304, -1, 3582, -1], 'generators': [3, 666], 'label': '972.525.108.k1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '9.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.b1', 'old_label': '108.k1', 'projective_image': '972.525', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.k1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 115709637
    {'ambient': '972.525', 'aut_centralizer_order': 3888, 'aut_label': '243.a1', 'aut_quo_index': 9, 'aut_stab_index': 1, 'aut_weyl_group': '6.1', 'aut_weyl_index': 3888, 'centralizer': '3.b1', 'complements': ['4.a1'], 'conjugacy_class_count': 1, 'contained_in': ['81.a1', '81.b1', '81.c1', '81.d1', '81.e1', '81.f1', '81.g1', '81.h1'], 'contains': ['486.a1'], 'core': '243.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4170, 2200, 3933, 1363], 'generators': [27, 486], 'label': '972.525.243.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '243.a1', 'normal_contained_in': ['81.a1', '81.b1'], 'normal_contains': ['972.a1'], 'normalizer': '1.a1', 'old_label': '243.a1', 'projective_image': '972.525', 'quotient_action_image': '3.1', 'quotient_action_kernel': '81.7', 'quotient_action_kernel_order': 81, 'quotient_fusion': None, 'short_label': '243.a1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 115709638
    {'ambient': '972.525', 'aut_centralizer_order': 11664, 'aut_label': '324.a1', 'aut_quo_index': 36, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 11664, 'centralizer': '1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['108.a1', '108.b1', '108.c1', '108.d1', '108.e1', '108.f1', '108.g1', '108.h1', '108.i1', '162.a1'], 'contains': ['972.a1'], 'core': '324.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6084, 8705, 5136, 9205], 'generators': [324], 'label': '972.525.324.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '324.a1', 'normal_contained_in': ['81.a1', '108.a1'], 'normal_contains': ['972.a1'], 'normalizer': '1.a1', 'old_label': '324.a1', 'projective_image': '324.130', 'quotient_action_image': '1.1', 'quotient_action_kernel': '324.130', 'quotient_action_kernel_order': 324, 'quotient_fusion': None, 'short_label': '324.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 115709639
    {'ambient': '972.525', 'aut_centralizer_order': 3888, 'aut_label': '324.b1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '2.1', 'aut_weyl_index': 11664, 'centralizer': '3.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.a1', '108.j1', '108.k1', '108.l1', '162.b1'], 'contains': ['972.a1'], 'core': '972.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [1849, -1, 3465, -1], 'generators': [666], 'label': '972.525.324.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '108.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '324.b1', 'projective_image': '972.525', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 115709640
    {'ambient': '972.525', 'aut_centralizer_order': 1296, 'aut_label': '324.c1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '2.1', 'aut_weyl_index': 11664, 'centralizer': '3.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['108.b1', '108.j1', '108.m1', '108.n1', '162.c1'], 'contains': ['972.a1'], 'core': '972.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [1551, -1, 2765, -1], 'generators': [109], 'label': '972.525.324.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '324.c1', 'projective_image': '972.525', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.c1', 'subgroup_fusion': None, 'weyl_group': '1.1'}