Abstract group data - 1296.2922

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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': '12.5', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 3, 'aut_exponent': 36, 'aut_gen_orders': [6, 18, 2, 6], 'aut_gens': [[1, 6, 108, 216], [37, 138, 756, 216], [49, 654, 756, 540], [649, 654, 108, 216], [1, 330, 108, 216]], 'aut_group': '1296.2922', 'aut_hash': 2922, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 1296, 'aut_permdeg': 21, 'aut_perms': [20468662326892277522, 9804819861952518880, 48806195934425707067, 50499856749283212477], 'aut_phi_ratio': 3.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 3, 1, 2], [2, 9, 1, 1], [2, 18, 1, 1], [2, 54, 1, 1], [3, 2, 1, 2], [3, 3, 1, 2], [3, 4, 1, 1], [3, 6, 1, 2], [4, 18, 1, 1], [4, 54, 1, 1], [6, 3, 1, 2], [6, 6, 1, 7], [6, 9, 1, 4], [6, 12, 1, 3], [6, 18, 1, 5], [6, 36, 1, 3], [6, 54, 1, 2], [9, 24, 1, 3], [9, 48, 1, 3], [12, 18, 1, 2], [12, 36, 1, 3], [12, 54, 1, 2], [18, 72, 1, 3]], 'aut_supersolvable': False, 'aut_tex': 'C_6^2.S_3^2', 'autcent_abelian': True, 'autcent_cyclic': True, 'autcent_exponent': 1, 'autcent_group': '1.1', 'autcent_hash': 1, 'autcent_nilpotent': True, 'autcent_order': 1, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_1', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 36, 'autcentquo_group': '1296.2922', 'autcentquo_hash': 2922, 'autcentquo_nilpotent': False, 'autcentquo_order': 1296, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'C_6^2.S_3^2', 'cc_stats': [[1, 1, 1], [2, 3, 2], [2, 9, 1], [2, 18, 1], [2, 54, 1], [3, 2, 2], [3, 3, 2], [3, 4, 1], [3, 6, 2], [4, 18, 1], [4, 54, 1], [6, 3, 2], [6, 6, 7], [6, 9, 4], [6, 12, 3], [6, 18, 5], [6, 36, 3], [6, 54, 2], [9, 24, 3], [9, 48, 3], [12, 18, 2], [12, 36, 3], [12, 54, 2], [18, 72, 3]], 'center_label': '1.1', 'center_order': 1, 'central_product': True, 'central_quotient': '1296.2922', 'commutator_count': 1, 'commutator_label': '108.20', 'complements_known': True, 'complete': True, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '3.1', '3.1', '3.1', '3.1'], 'composition_length': 8, 'conjugacy_classes_known': True, 'counter': 2922, 'cyclic': False, 'derived_length': 3, 'dihedral': False, 'direct_factorization': [['216.90', 1], ['6.1', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 3, 1, 2], [2, 9, 1, 1], [2, 18, 1, 1], [2, 54, 1, 1], [3, 2, 1, 2], [3, 3, 2, 1], [3, 4, 1, 1], [3, 6, 2, 1], [4, 18, 1, 1], [4, 54, 1, 1], [6, 3, 2, 1], [6, 6, 1, 3], [6, 6, 2, 2], [6, 9, 2, 2], [6, 12, 1, 1], [6, 12, 2, 1], [6, 18, 1, 1], [6, 18, 2, 2], [6, 36, 1, 1], [6, 36, 2, 1], [6, 54, 2, 1], [9, 24, 1, 1], [9, 24, 2, 1], [9, 48, 1, 1], [9, 48, 2, 1], [12, 18, 2, 1], [12, 36, 1, 1], [12, 36, 2, 1], [12, 54, 2, 1], [18, 72, 1, 1], [18, 72, 2, 1]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 144, 'exponent': 36, 'exponents_of_order': [4, 4], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [[12, 0, 2], [12, 1, 1]], 'familial': False, 'frattini_label': '3.1', 'frattini_quotient': '432.745', 'hash': 2922, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 36, 'inner_gen_orders': [6, 18, 2, 6], 'inner_gens': [[1, 30, 756, 216], [85, 6, 756, 540], [649, 654, 108, 216], [1, 1194, 108, 216]], 'inner_hash': 2922, 'inner_nilpotent': False, 'inner_order': 1296, 'inner_split': True, 'inner_tex': 'C_6^2.S_3^2', 'inner_used': [1, 2, 3, 4], 'irrC_degree': 12, 'irrQ_degree': 12, 'irrQ_dim': 12, 'irrR_degree': 12, 'irrep_stats': [[1, 12], [2, 12], [3, 12], [4, 3], [6, 14], [12, 4]], 'label': '1296.2922', 'linC_count': 36, 'linC_degree': 8, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 8, 'linQ_degree_count': 4, 'linQ_dim': 8, 'linQ_dim_count': 4, 'linR_count': 4, 'linR_degree': 8, 'maximal_subgroups_known': True, 'metabelian': False, 'metacyclic': False, 'monomial': True, 'name': 'C6^2.S3^2', 'ngens': 8, 'nilpotency_class': -1, 'nilpotent': False, 'normal_counts': [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 57, 'number_characteristic_subgroups': 32, 'number_conjugacy_classes': 57, 'number_divisions': 39, 'number_normal_subgroups': 32, 'number_subgroup_autclasses': 286, 'number_subgroup_classes': 286, 'number_subgroups': 2648, 'old_label': None, 'order': 1296, 'order_factorization_type': 33, 'order_stats': [[1, 1], [2, 87], [3, 26], [4, 72], [6, 426], [9, 216], [12, 252], [18, 216]], 'outer_abelian': True, 'outer_cyclic': True, 'outer_equivalence': False, 'outer_exponent': 1, 'outer_gen_orders': [], 'outer_gen_pows': [], 'outer_gens': [], 'outer_group': '1.1', 'outer_hash': 1, 'outer_nilpotent': True, 'outer_order': 1, 'outer_permdeg': 1, 'outer_perms': [], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_1', 'pc_rank': 4, 'perfect': False, 'permutation_degree': 16, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 3], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 4], [2, 8], [3, 4], [4, 5], [6, 10], [8, 1], [12, 6], [24, 1]], 'representations': {'PC': {'code': 1992825520499251363212401964626711023176825985395168595289, 'gens': [1, 3, 6, 7], 'pres': [8, -2, -3, -2, -3, -3, -2, 2, -3, 16, 722, 514, 66, 1923, 1355, 123, 2884, 36293, 6069, 2621, 5062, 1542, 166, 9239]}, 'Perm': {'d': 16, 'gens': [3628800, 180583616250, 16427, 93405374717, 43545600, 99115, 1313901388800, 2789705318400]}}, 'schur_multiplier': [2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 6], 'solvability_type': 11, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': 'C_6^2.S_3^2', 'transitive_degree': 36, 'wreath_data': None, 'wreath_product': False}
• gps_conj_classes •

  Column	Type
  aut_label	text
  centralizer	text
  counter	integer
  group_counter	integer
  group_order	numeric
  label	text
  order	integer
  powers	integer[]
  representative	numeric
  size	numeric

  
  
  • id: 114718499
    {'aut_label': '1A', 'centralizer': '1.a1.a1', 'counter': 1, 'group_counter': 2922, 'group_order': 1296, 'label': '1A', 'order': 1, 'powers': [1, 1], 'representative': 0, 'size': 1}
  • id: 114718510
    {'aut_label': '2A', 'centralizer': '3.c1.a1', 'counter': 2, 'group_counter': 2922, 'group_order': 1296, 'label': '2A', 'order': 2, 'powers': [1, 2], 'representative': 108, 'size': 3}
  • id: 114718521
    {'aut_label': '2B', 'centralizer': '3.b1.a1', 'counter': 3, 'group_counter': 2922, 'group_order': 1296, 'label': '2B', 'order': 2, 'powers': [1, 3], 'representative': 54, 'size': 3}
  • id: 114718532
    {'aut_label': '2C', 'centralizer': '9.a1.a1', 'counter': 4, 'group_counter': 2922, 'group_order': 1296, 'label': '2C', 'order': 2, 'powers': [1, 4], 'representative': 162, 'size': 9}
  • id: 114718543
    {'aut_label': '2D', 'centralizer': '18.e1.a1', 'counter': 5, 'group_counter': 2922, 'group_order': 1296, 'label': '2D', 'order': 2, 'powers': [1, 5], 'representative': 3, 'size': 18}
  • id: 114718552
    {'aut_label': '2E', 'centralizer': '54.b1.a1', 'counter': 6, 'group_counter': 2922, 'group_order': 1296, 'label': '2E', 'order': 2, 'powers': [1, 6], 'representative': 945, 'size': 54}
  • id: 114718553
    {'aut_label': '3A', 'centralizer': '2.a1.a1', 'counter': 7, 'group_counter': 2922, 'group_order': 1296, 'label': '3A', 'order': 3, 'powers': [7, 1], 'representative': 72, 'size': 2}
  • id: 114718554
    {'aut_label': '3B', 'centralizer': '2.b1.a1', 'counter': 8, 'group_counter': 2922, 'group_order': 1296, 'label': '3B', 'order': 3, 'powers': [8, 1], 'representative': 864, 'size': 2}
  • id: 114718555
    {'aut_label': '3C1', 'centralizer': '3.c1.a1', 'counter': 9, 'group_counter': 2922, 'group_order': 1296, 'label': '3C1', 'order': 3, 'powers': [10, 1], 'representative': 4, 'size': 3}
  • id: 114718500
    {'aut_label': '3C-1', 'centralizer': '3.c1.a1', 'counter': 10, 'group_counter': 2922, 'group_order': 1296, 'label': '3C-1', 'order': 3, 'powers': [9, 1], 'representative': 2, 'size': 3}
  • id: 114718501
    {'aut_label': '3D', 'centralizer': '4.a1.a1', 'counter': 11, 'group_counter': 2922, 'group_order': 1296, 'label': '3D', 'order': 3, 'powers': [11, 1], 'representative': 504, 'size': 4}
  • id: 114718502
    {'aut_label': '3E1', 'centralizer': '6.l1.a1', 'counter': 12, 'group_counter': 2922, 'group_order': 1296, 'label': '3E1', 'order': 3, 'powers': [13, 1], 'representative': 868, 'size': 6}
  • id: 114718503
    {'aut_label': '3E-1', 'centralizer': '6.l1.a1', 'counter': 13, 'group_counter': 2922, 'group_order': 1296, 'label': '3E-1', 'order': 3, 'powers': [12, 1], 'representative': 434, 'size': 6}
  • id: 114718504
    {'aut_label': '4A', 'centralizer': '18.h1.a1', 'counter': 14, 'group_counter': 2922, 'group_order': 1296, 'label': '4A', 'order': 4, 'powers': [2, 14], 'representative': 759, 'size': 18}
  • id: 114718505
    {'aut_label': '4B', 'centralizer': '54.e1.a1', 'counter': 15, 'group_counter': 2922, 'group_order': 1296, 'label': '4B', 'order': 4, 'powers': [2, 15], 'representative': 633, 'size': 54}
  • id: 114718506
    {'aut_label': '6A1', 'centralizer': '3.c1.a1', 'counter': 16, 'group_counter': 2922, 'group_order': 1296, 'label': '6A1', 'order': 6, 'powers': [9, 2], 'representative': 650, 'size': 3}
  • id: 114718507
    {'aut_label': '6A-1', 'centralizer': '3.c1.a1', 'counter': 17, 'group_counter': 2922, 'group_order': 1296, 'label': '6A-1', 'order': 6, 'powers': [10, 2], 'representative': 652, 'size': 3}
  • id: 114718508
    {'aut_label': '6B', 'centralizer': '6.a1.a1', 'counter': 18, 'group_counter': 2922, 'group_order': 1296, 'label': '6B', 'order': 6, 'powers': [7, 2], 'representative': 144, 'size': 6}
  • id: 114718509
    {'aut_label': '6C', 'centralizer': '6.l1.a1', 'counter': 19, 'group_counter': 2922, 'group_order': 1296, 'label': '6C', 'order': 6, 'powers': [8, 2], 'representative': 216, 'size': 6}
  • id: 114718511
    {'aut_label': '6D', 'centralizer': '6.j1.a1', 'counter': 20, 'group_counter': 2922, 'group_order': 1296, 'label': '6D', 'order': 6, 'powers': [7, 3], 'representative': 18, 'size': 6}
  • id: 114718512
    {'aut_label': '6E1', 'centralizer': '6.a1.a1', 'counter': 21, 'group_counter': 2922, 'group_order': 1296, 'label': '6E1', 'order': 6, 'powers': [9, 2], 'representative': 110, 'size': 6}
  • id: 114718513
    {'aut_label': '6E-1', 'centralizer': '6.a1.a1', 'counter': 22, 'group_counter': 2922, 'group_order': 1296, 'label': '6E-1', 'order': 6, 'powers': [10, 2], 'representative': 112, 'size': 6}
  • id: 114718514
    {'aut_label': '6F1', 'centralizer': '6.l1.a1', 'counter': 23, 'group_counter': 2922, 'group_order': 1296, 'label': '6F1', 'order': 6, 'powers': [12, 2], 'representative': 218, 'size': 6}
  • id: 114718515
    {'aut_label': '6F-1', 'centralizer': '6.l1.a1', 'counter': 24, 'group_counter': 2922, 'group_order': 1296, 'label': '6F-1', 'order': 6, 'powers': [13, 2], 'representative': 1084, 'size': 6}
  • id: 114718516
    {'aut_label': '6G1', 'centralizer': '9.a1.a1', 'counter': 25, 'group_counter': 2922, 'group_order': 1296, 'label': '6G1', 'order': 6, 'powers': [9, 3], 'representative': 20, 'size': 9}
  • id: 114718517
    {'aut_label': '6G-1', 'centralizer': '9.a1.a1', 'counter': 26, 'group_counter': 2922, 'group_order': 1296, 'label': '6G-1', 'order': 6, 'powers': [10, 3], 'representative': 22, 'size': 9}
  • id: 114718518
    {'aut_label': '6H1', 'centralizer': '9.a1.a1', 'counter': 27, 'group_counter': 2922, 'group_order': 1296, 'label': '6H1', 'order': 6, 'powers': [9, 4], 'representative': 128, 'size': 9}
  • id: 114718519
    {'aut_label': '6H-1', 'centralizer': '9.a1.a1', 'counter': 28, 'group_counter': 2922, 'group_order': 1296, 'label': '6H-1', 'order': 6, 'powers': [10, 4], 'representative': 346, 'size': 9}
  • id: 114718520
    {'aut_label': '6I', 'centralizer': '12.a1.a1', 'counter': 29, 'group_counter': 2922, 'group_order': 1296, 'label': '6I', 'order': 6, 'powers': [11, 2], 'representative': 252, 'size': 12}
  • id: 114718522
    {'aut_label': '6J1', 'centralizer': '12.a1.a1', 'counter': 30, 'group_counter': 2922, 'group_order': 1296, 'label': '6J1', 'order': 6, 'powers': [12, 2], 'representative': 542, 'size': 12}
  • id: 114718523
    {'aut_label': '6J-1', 'centralizer': '12.a1.a1', 'counter': 31, 'group_counter': 2922, 'group_order': 1296, 'label': '6J-1', 'order': 6, 'powers': [13, 2], 'representative': 544, 'size': 12}
  • id: 114718524
    {'aut_label': '6K', 'centralizer': '18.o1.a1', 'counter': 32, 'group_counter': 2922, 'group_order': 1296, 'label': '6K', 'order': 6, 'powers': [7, 4], 'representative': 234, 'size': 18}
  • id: 114718525
    {'aut_label': '6L1', 'centralizer': '18.e1.a1', 'counter': 33, 'group_counter': 2922, 'group_order': 1296, 'label': '6L1', 'order': 6, 'powers': [10, 5], 'representative': 1, 'size': 18}
  • id: 114718526
    {'aut_label': '6L-1', 'centralizer': '18.e1.a1', 'counter': 34, 'group_counter': 2922, 'group_order': 1296, 'label': '6L-1', 'order': 6, 'powers': [9, 5], 'representative': 5, 'size': 18}
  • id: 114718527
    {'aut_label': '6M1', 'centralizer': '18.o1.a1', 'counter': 35, 'group_counter': 2922, 'group_order': 1296, 'label': '6M1', 'order': 6, 'powers': [9, 4], 'representative': 236, 'size': 18}
  • id: 114718528
    {'aut_label': '6M-1', 'centralizer': '18.o1.a1', 'counter': 36, 'group_counter': 2922, 'group_order': 1296, 'label': '6M-1', 'order': 6, 'powers': [10, 4], 'representative': 238, 'size': 18}
  • id: 114718529
    {'aut_label': '6N', 'centralizer': '36.l1.a1', 'counter': 37, 'group_counter': 2922, 'group_order': 1296, 'label': '6N', 'order': 6, 'powers': [8, 5], 'representative': 435, 'size': 36}
  • id: 114718530
    {'aut_label': '6O1', 'centralizer': '36.l1.a1', 'counter': 38, 'group_counter': 2922, 'group_order': 1296, 'label': '6O1', 'order': 6, 'powers': [13, 5], 'representative': 433, 'size': 36}
  • id: 114718531
    {'aut_label': '6O-1', 'centralizer': '36.l1.a1', 'counter': 39, 'group_counter': 2922, 'group_order': 1296, 'label': '6O-1', 'order': 6, 'powers': [12, 5], 'representative': 437, 'size': 36}
  • id: 114718533
    {'aut_label': '6P1', 'centralizer': '54.b1.a1', 'counter': 40, 'group_counter': 2922, 'group_order': 1296, 'label': '6P1', 'order': 6, 'powers': [10, 6], 'representative': 871, 'size': 54}
  • id: 114718534
    {'aut_label': '6P-1', 'centralizer': '54.b1.a1', 'counter': 41, 'group_counter': 2922, 'group_order': 1296, 'label': '6P-1', 'order': 6, 'powers': [9, 6], 'representative': 911, 'size': 54}
  • id: 114718535
    {'aut_label': '9A', 'centralizer': '24.d1.a1', 'counter': 42, 'group_counter': 2922, 'group_order': 1296, 'label': '9A', 'order': 9, 'powers': [42, 7], 'representative': 84, 'size': 24}
  • id: 114718536
    {'aut_label': '9B1', 'centralizer': '24.e1.a1', 'counter': 43, 'group_counter': 2922, 'group_order': 1296, 'label': '9B1', 'order': 9, 'powers': [44, 7], 'representative': 808, 'size': 24}
  • id: 114718537
    {'aut_label': '9B-1', 'centralizer': '24.e1.a1', 'counter': 44, 'group_counter': 2922, 'group_order': 1296, 'label': '9B-1', 'order': 9, 'powers': [43, 7], 'representative': 746, 'size': 24}
  • id: 114718538
    {'aut_label': '9C', 'centralizer': '48.b1.a1', 'counter': 45, 'group_counter': 2922, 'group_order': 1296, 'label': '9C', 'order': 9, 'powers': [45, 7], 'representative': 1212, 'size': 48}
  • id: 114718539
    {'aut_label': '9D1', 'centralizer': '48.c1.a1', 'counter': 46, 'group_counter': 2922, 'group_order': 1296, 'label': '9D1', 'order': 9, 'powers': [47, 7], 'representative': 530, 'size': 48}
  • id: 114718540
    {'aut_label': '9D-1', 'centralizer': '48.c1.a1', 'counter': 47, 'group_counter': 2922, 'group_order': 1296, 'label': '9D-1', 'order': 9, 'powers': [46, 7], 'representative': 916, 'size': 48}
  • id: 114718541
    {'aut_label': '12A1', 'centralizer': '18.h1.a1', 'counter': 48, 'group_counter': 2922, 'group_order': 1296, 'label': '12A1', 'order': 12, 'powers': [16, 14], 'representative': 109, 'size': 18}
  • id: 114718542
    {'aut_label': '12A-1', 'centralizer': '18.h1.a1', 'counter': 49, 'group_counter': 2922, 'group_order': 1296, 'label': '12A-1', 'order': 12, 'powers': [17, 14], 'representative': 113, 'size': 18}
  • id: 114718544
    {'aut_label': '12B', 'centralizer': '36.y1.a1', 'counter': 50, 'group_counter': 2922, 'group_order': 1296, 'label': '12B', 'order': 12, 'powers': [19, 14], 'representative': 543, 'size': 36}
  • id: 114718545
    {'aut_label': '12C1', 'centralizer': '36.y1.a1', 'counter': 51, 'group_counter': 2922, 'group_order': 1296, 'label': '12C1', 'order': 12, 'powers': [23, 14], 'representative': 541, 'size': 36}
  • id: 114718546
    {'aut_label': '12C-1', 'centralizer': '36.y1.a1', 'counter': 52, 'group_counter': 2922, 'group_order': 1296, 'label': '12C-1', 'order': 12, 'powers': [24, 14], 'representative': 545, 'size': 36}
  • id: 114718547
    {'aut_label': '12D1', 'centralizer': '54.e1.a1', 'counter': 53, 'group_counter': 2922, 'group_order': 1296, 'label': '12D1', 'order': 12, 'powers': [17, 15], 'representative': 1283, 'size': 54}
  • id: 114718548
    {'aut_label': '12D-1', 'centralizer': '54.e1.a1', 'counter': 54, 'group_counter': 2922, 'group_order': 1296, 'label': '12D-1', 'order': 12, 'powers': [16, 15], 'representative': 631, 'size': 54}
  • id: 114718549
    {'aut_label': '18A', 'centralizer': '72.j1.a1', 'counter': 55, 'group_counter': 2922, 'group_order': 1296, 'label': '18A', 'order': 18, 'powers': [42, 20], 'representative': 474, 'size': 72}
  • id: 114718550
    {'aut_label': '18B1', 'centralizer': '72.k1.a1', 'counter': 56, 'group_counter': 2922, 'group_order': 1296, 'label': '18B1', 'order': 18, 'powers': [43, 20], 'representative': 656, 'size': 72}
  • id: 114718551
    {'aut_label': '18B-1', 'centralizer': '72.k1.a1', 'counter': 57, 'group_counter': 2922, 'group_order': 1296, 'label': '18B-1', 'order': 18, 'powers': [44, 20], 'representative': 790, 'size': 72}
• 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: 5445477
    {'cdim': 1, 'counter': 1, 'faithful': False, 'group': '1296.2922', 'group_order': 1296, 'image': None, 'label': '1296.2922.1a', '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], 'schur_index': 1}
  • id: 5445488
    {'cdim': 1, 'counter': 2, 'faithful': False, 'group': '1296.2922', 'group_order': 1296, 'image': None, 'label': '1296.2922.1b', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 1, 1, 1, 1, -1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, 1, 1, -1, -1, -1], 'schur_index': 1}
  • id: 5445499
    {'cdim': 1, 'counter': 3, 'faithful': False, 'group': '1296.2922', 'group_order': 1296, 'image': None, 'label': '1296.2922.1c', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, -1, -1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 1, 1, 1, -1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, -1, 1, 1, -1, -1, 1, 1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1], 'schur_index': 1}
  • id: 5445510
    {'cdim': 1, 'counter': 4, 'faithful': False, 'group': '1296.2922', 'group_order': 1296, 'image': None, 'label': '1296.2922.1d', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, 1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1], 'schur_index': 1}
  • id: 5445511
    {'cdim': 1, 'counter': 5, 'faithful': False, 'group': '1296.2922', 'group_order': 1296, 'image': None, 'label': '1296.2922.1e', 'multiplicity': 2, 'nt': [3, 1], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 2, 2, 2, 2, -1, -1, 2, -1, -1, 2, 2, -1, -1, -1, 2, 2, -1, -1, -1, 2, -1, -1, -1, -1, 2, -1, -1, 2, -1, -1, -1, -1, -1, -1, 2, -1, -1, 2, -1, -1, -1, -1, 2, -1, -1, -1, 2, -1, -1, -1, 2, -1, -1], 'schur_index': 1}
  • id: 5445512
    {'cdim': 1, 'counter': 6, 'faithful': False, 'group': '1296.2922', 'group_order': 1296, 'image': None, 'label': '1296.2922.1f', 'multiplicity': 2, 'nt': [6, 1], 'qdim': 2, 'qvalues': [2, 2, -2, -2, -2, 2, 2, 2, -1, -1, 2, -1, -1, -2, 2, -1, -1, -1, -2, 2, -1, -1, -1, 2, 1, 1, 1, 1, 2, -1, -1, -2, 1, 1, 1, 1, 1, 1, -2, -1, -1, 2, -1, -1, -1, -1, 2, 1, 1, 1, -2, 1, -1, -1, -2, 1, 1], 'schur_index': 1}
  • id: 5445513
    {'cdim': 1, 'counter': 7, 'faithful': False, 'group': '1296.2922', 'group_order': 1296, 'image': None, 'label': '1296.2922.1g', 'multiplicity': 2, 'nt': [6, 1], 'qdim': 2, 'qvalues': [2, 2, -2, -2, 2, -2, 2, 2, -1, -1, 2, -1, -1, 2, -2, -1, -1, -1, -2, 2, -1, -1, -1, 2, 1, 1, 1, 1, 2, -1, -1, -2, -1, -1, 1, 1, -1, -1, 2, 1, 1, 2, -1, -1, -1, -1, 2, -1, -1, -1, 2, -1, 1, 1, -2, 1, 1], 'schur_index': 1}
  • id: 5445514
    {'cdim': 1, 'counter': 8, 'faithful': False, 'group': '1296.2922', 'group_order': 1296, 'image': None, 'label': '1296.2922.1h', 'multiplicity': 2, 'nt': [6, 1], 'qdim': 2, 'qvalues': [2, 2, 2, 2, -2, -2, 2, 2, -1, -1, 2, -1, -1, -2, -2, -1, -1, -1, 2, 2, -1, -1, -1, 2, -1, -1, -1, -1, 2, -1, -1, 2, 1, 1, -1, -1, 1, 1, -2, 1, 1, 2, -1, -1, -1, -1, 2, 1, 1, 1, -2, 1, 1, 1, 2, -1, -1], 'schur_index': 1}
  • id: 5445515
    {'cdim': 2, 'counter': 9, 'faithful': False, 'group': '1296.2922', 'group_order': 1296, 'image': None, 'label': '1296.2922.2a', 'multiplicity': 1, 'nt': [3, 2], 'qdim': 2, 'qvalues': [2, 2, 0, 0, 2, 0, 2, -1, 2, 2, -1, -1, -1, 2, 0, 2, 2, 2, 0, 2, 2, -1, -1, -1, 0, 0, 0, 0, -1, -1, -1, 0, 2, 2, 0, 0, -1, -1, -1, 0, 0, 2, 2, 2, -1, -1, -1, 2, 2, -1, -1, -1, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 5445478
    {'cdim': 2, 'counter': 10, 'faithful': False, 'group': '1296.2922', 'group_order': 1296, 'image': None, 'label': '1296.2922.2b', 'multiplicity': 1, 'nt': [3, 2], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 0, 0, 2, 2, 2, 2, 2, 2, 2, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 2, 2, 0, 0, 0, 0, 0, -1, -1, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1], 'schur_index': 1}
  • id: 5445479
    {'cdim': 2, 'counter': 11, 'faithful': False, 'group': '1296.2922', 'group_order': 1296, 'image': None, 'label': '1296.2922.2c', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, 2, -2, -2, 0, 0, 2, 2, 2, 2, 2, 2, 2, 0, 0, 2, 2, 2, -2, 2, 2, 2, 2, 2, -2, -2, -2, -2, 2, 2, 2, -2, 0, 0, -2, -2, 0, 0, 0, 0, 0, -1, -1, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1], 'schur_index': 1}
  • id: 5445480
    {'cdim': 2, 'counter': 12, 'faithful': False, 'group': '1296.2922', 'group_order': 1296, 'image': None, 'label': '1296.2922.2d', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, 2, 0, 0, -2, 0, 2, -1, 2, 2, -1, -1, -1, -2, 0, 2, 2, 2, 0, 2, 2, -1, -1, -1, 0, 0, 0, 0, -1, -1, -1, 0, -2, -2, 0, 0, 1, 1, 1, 0, 0, 2, 2, 2, -1, -1, -1, -2, -2, 1, 1, 1, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 5445485
    {'cdim': 3, 'counter': 17, 'faithful': False, 'group': '1296.2922', 'group_order': 1296, 'image': None, 'label': '1296.2922.3a', 'multiplicity': 1, 'nt': [4, 5], 'qdim': 3, 'qvalues': [3, -1, 3, -1, 1, 1, 3, 3, 3, 3, 3, 3, 3, -1, -1, -1, -1, -1, 3, -1, -1, -1, -1, -1, 3, -1, 3, -1, -1, -1, -1, -1, 1, 1, -1, -1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, -1, -1, -1, -1, -1, -1, -1, 0, 0, 0], 'schur_index': 1}
  • id: 5445486
    {'cdim': 3, 'counter': 18, 'faithful': False, 'group': '1296.2922', 'group_order': 1296, 'image': None, 'label': '1296.2922.3b', 'multiplicity': 1, 'nt': [6, 8], 'qdim': 3, 'qvalues': [3, -1, 3, -1, -1, -1, 3, 3, 3, 3, 3, 3, 3, 1, 1, -1, -1, -1, 3, -1, -1, -1, -1, -1, 3, -1, 3, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0], 'schur_index': 1}
  • id: 5445487
    {'cdim': 3, 'counter': 19, 'faithful': False, 'group': '1296.2922', 'group_order': 1296, 'image': None, 'label': '1296.2922.3c', 'multiplicity': 1, 'nt': [6, 11], 'qdim': 3, 'qvalues': [3, -1, -3, 1, -1, 1, 3, 3, 3, 3, 3, 3, 3, 1, -1, -1, -1, -1, -3, -1, -1, -1, -1, -1, -3, 1, -3, 1, -1, -1, -1, 1, -1, -1, 1, 1, -1, -1, -1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, -1, -1, 0, 0, 0], 'schur_index': 1}
  • id: 5445489
    {'cdim': 3, 'counter': 20, 'faithful': False, 'group': '1296.2922', 'group_order': 1296, 'image': None, 'label': '1296.2922.3d', 'multiplicity': 1, 'nt': [6, 11], 'qdim': 3, 'qvalues': [3, -1, -3, 1, 1, -1, 3, 3, 3, 3, 3, 3, 3, -1, 1, -1, -1, -1, -3, -1, -1, -1, -1, -1, -3, 1, -3, 1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 0, 0, 0, 0, 0, 0, -1, -1, -1, -1, -1, 1, 1, 0, 0, 0], 'schur_index': 1}
  • id: 5445481
    {'cdim': 2, 'counter': 13, 'faithful': False, 'group': '1296.2922', 'group_order': 1296, 'image': None, 'label': '1296.2922.2e', 'multiplicity': 2, 'nt': [6, 5], 'qdim': 4, 'qvalues': [4, 4, 0, 0, 4, 0, 4, -2, -2, -2, -2, 1, 1, 4, 0, -2, -2, -2, 0, 4, -2, 1, 1, -2, 0, 0, 0, 0, -2, 1, 1, 0, -2, -2, 0, 0, 1, 1, -2, 0, 0, 4, -2, -2, 1, 1, -2, -2, -2, 1, -2, 1, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 5445482
    {'cdim': 2, 'counter': 14, 'faithful': False, 'group': '1296.2922', 'group_order': 1296, 'image': None, 'label': '1296.2922.2f', 'multiplicity': 2, 'nt': [6, 5], 'qdim': 4, 'qvalues': [4, 4, 4, 4, 0, 0, 4, 4, -2, -2, 4, -2, -2, 0, 0, -2, -2, -2, 4, 4, -2, -2, -2, 4, -2, -2, -2, -2, 4, -2, -2, 4, 0, 0, -2, -2, 0, 0, 0, 0, 0, -2, 1, 1, 1, 1, -2, 0, 0, 0, 0, 0, 0, 0, -2, 1, 1], 'schur_index': 1}
  • id: 5445483
    {'cdim': 2, 'counter': 15, 'faithful': False, 'group': '1296.2922', 'group_order': 1296, 'image': None, 'label': '1296.2922.2g', 'multiplicity': 2, 'nt': [12, 18], 'qdim': 4, 'qvalues': [4, 4, -4, -4, 0, 0, 4, 4, -2, -2, 4, -2, -2, 0, 0, -2, -2, -2, -4, 4, -2, -2, -2, 4, 2, 2, 2, 2, 4, -2, -2, -4, 0, 0, 2, 2, 0, 0, 0, 0, 0, -2, 1, 1, 1, 1, -2, 0, 0, 0, 0, 0, 0, 0, 2, -1, -1], 'schur_index': 1}
  • id: 5445484
    {'cdim': 2, 'counter': 16, 'faithful': False, 'group': '1296.2922', 'group_order': 1296, 'image': None, 'label': '1296.2922.2h', 'multiplicity': 2, 'nt': [12, 18], 'qdim': 4, 'qvalues': [4, 4, 0, 0, -4, 0, 4, -2, -2, -2, -2, 1, 1, -4, 0, -2, -2, -2, 0, 4, -2, 1, 1, -2, 0, 0, 0, 0, -2, 1, 1, 0, 2, 2, 0, 0, -1, -1, 2, 0, 0, 4, -2, -2, 1, 1, -2, 2, 2, -1, 2, -1, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 5445494
    {'cdim': 4, 'counter': 25, 'faithful': False, 'group': '1296.2922', 'group_order': 1296, 'image': None, 'label': '1296.2922.4a', 'multiplicity': 1, 'nt': [6, 9], 'qdim': 4, 'qvalues': [4, 4, 0, 0, 0, 0, 4, -2, 4, 4, -2, -2, -2, 0, 0, 4, 4, 4, 0, 4, 4, -2, -2, -2, 0, 0, 0, 0, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 5445490
    {'cdim': 3, 'counter': 21, 'faithful': False, 'group': '1296.2922', 'group_order': 1296, 'image': None, 'label': '1296.2922.3e', 'multiplicity': 2, 'nt': [12, 45], 'qdim': 6, 'qvalues': [6, -2, 6, -2, 2, 2, 6, 6, -3, -3, 6, -3, -3, -2, -2, 1, 1, 1, 6, -2, 1, 1, 1, -2, -3, 1, -3, 1, -2, 1, 1, -2, -1, -1, 1, 1, -1, -1, 2, -1, -1, 0, 0, 0, 0, 0, 0, 1, 1, 1, -2, 1, 1, 1, 0, 0, 0], 'schur_index': 1}
  • id: 5445491
    {'cdim': 3, 'counter': 22, 'faithful': False, 'group': '1296.2922', 'group_order': 1296, 'image': None, 'label': '1296.2922.3f', 'multiplicity': 2, 'nt': [18, 30], 'qdim': 6, 'qvalues': [6, -2, 6, -2, -2, -2, 6, 6, -3, -3, 6, -3, -3, 2, 2, 1, 1, 1, 6, -2, 1, 1, 1, -2, -3, 1, -3, 1, -2, 1, 1, -2, 1, 1, 1, 1, 1, 1, -2, 1, 1, 0, 0, 0, 0, 0, 0, -1, -1, -1, 2, -1, -1, -1, 0, 0, 0], 'schur_index': 1}
  • id: 5445492
    {'cdim': 3, 'counter': 23, 'faithful': False, 'group': '1296.2922', 'group_order': 1296, 'image': None, 'label': '1296.2922.3g', 'multiplicity': 2, 'nt': [18, 61], 'qdim': 6, 'qvalues': [6, -2, -6, 2, -2, 2, 6, 6, -3, -3, 6, -3, -3, 2, -2, 1, 1, 1, -6, -2, 1, 1, 1, -2, 3, -1, 3, -1, -2, 1, 1, 2, 1, 1, -1, -1, 1, 1, -2, -1, -1, 0, 0, 0, 0, 0, 0, -1, -1, -1, 2, -1, 1, 1, 0, 0, 0], 'schur_index': 1}
  • id: 5445493
    {'cdim': 3, 'counter': 24, 'faithful': False, 'group': '1296.2922', 'group_order': 1296, 'image': None, 'label': '1296.2922.3h', 'multiplicity': 2, 'nt': [18, 61], 'qdim': 6, 'qvalues': [6, -2, -6, 2, 2, -2, 6, 6, -3, -3, 6, -3, -3, -2, 2, 1, 1, 1, -6, -2, 1, 1, 1, -2, 3, -1, 3, -1, -2, 1, 1, 2, -1, -1, -1, -1, -1, -1, 2, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, -2, 1, -1, -1, 0, 0, 0], 'schur_index': 1}
  • id: 5445496
    {'cdim': 6, 'counter': 27, 'faithful': False, 'group': '1296.2922', 'group_order': 1296, 'image': None, 'label': '1296.2922.6a', 'multiplicity': 1, 'nt': [9, 10], 'qdim': 6, 'qvalues': [6, 6, 6, 6, 0, 0, -3, 6, 0, 0, -3, 0, 0, 0, 0, 0, 0, 0, -3, -3, 0, 0, 0, 6, 0, 0, 0, 0, -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, 0, 0, 0], 'schur_index': 1}
  • id: 5445497
    {'cdim': 6, 'counter': 28, 'faithful': False, 'group': '1296.2922', 'group_order': 1296, 'image': None, 'label': '1296.2922.6b', 'multiplicity': 1, 'nt': [12, 83], 'qdim': 6, 'qvalues': [6, -2, 0, 0, 2, 0, 6, -3, 6, 6, -3, -3, -3, -2, 0, -2, -2, -2, 0, -2, -2, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 0, 2, 2, 0, 0, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, 1, 1, 1, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 5445498
    {'cdim': 6, 'counter': 29, 'faithful': False, 'group': '1296.2922', 'group_order': 1296, 'image': None, 'label': '1296.2922.6c', 'multiplicity': 1, 'nt': [18, 45], 'qdim': 6, 'qvalues': [6, 6, -6, -6, 0, 0, -3, 6, 0, 0, -3, 0, 0, 0, 0, 0, 0, 0, 3, -3, 0, 0, 0, 6, 0, 0, 0, 0, -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, 0, 0, 0], 'schur_index': 1}
  • id: 5445500
    {'cdim': 6, 'counter': 30, 'faithful': False, 'group': '1296.2922', 'group_order': 1296, 'image': None, 'label': '1296.2922.6d', 'multiplicity': 1, 'nt': [18, 69], 'qdim': 6, 'qvalues': [6, -2, 0, 0, -2, 0, 6, -3, 6, 6, -3, -3, -3, 2, 0, -2, -2, -2, 0, -2, -2, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 0, -2, -2, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, -1, -1, -1, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 5445501
    {'cdim': 6, 'counter': 31, 'faithful': False, 'group': '1296.2922', 'group_order': 1296, 'image': None, 'label': '1296.2922.6e', 'multiplicity': 1, 'nt': [18, 98], 'qdim': 6, 'qvalues': [6, -2, 6, -2, 0, 0, -3, 6, 0, 0, -3, 0, 0, 0, 0, 4, 4, -2, -3, 1, -2, 4, 4, -2, 0, 4, 0, 4, 1, -2, -2, 1, 0, 0, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 5445502
    {'cdim': 6, 'counter': 32, 'faithful': False, 'group': '1296.2922', 'group_order': 1296, 'image': None, 'label': '1296.2922.6f', 'multiplicity': 1, 'nt': [18, 147], 'qdim': 6, 'qvalues': [6, -2, -6, 2, 0, 0, -3, 6, 0, 0, -3, 0, 0, 0, 0, 4, 4, -2, 3, 1, -2, 4, 4, -2, 0, -4, 0, -4, 1, -2, -2, -1, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 5445495
    {'cdim': 4, 'counter': 26, 'faithful': False, 'group': '1296.2922', 'group_order': 1296, 'image': None, 'label': '1296.2922.4b', 'multiplicity': 2, 'nt': [12, 70], 'qdim': 8, 'qvalues': [8, 8, 0, 0, 0, 0, 8, -4, -4, -4, -4, 2, 2, 0, 0, -4, -4, -4, 0, 8, -4, 2, 2, -4, 0, 0, 0, 0, -4, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 2, 2, -1, -1, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 5445503
    {'cdim': 6, 'counter': 33, 'faithful': False, 'group': '1296.2922', 'group_order': 1296, 'image': None, 'label': '1296.2922.6g', 'multiplicity': 2, 'nt': [24, 1328], 'qdim': 12, 'qvalues': [12, -4, 0, 0, 4, 0, 12, -6, -6, -6, -6, 3, 3, -4, 0, 2, 2, 2, 0, -4, 2, -1, -1, 2, 0, 0, 0, 0, 2, -1, -1, 0, -2, -2, 0, 0, 1, 1, -2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, -1, 2, -1, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 5445504
    {'cdim': 6, 'counter': 34, 'faithful': False, 'group': '1296.2922', 'group_order': 1296, 'image': None, 'label': '1296.2922.6h', 'multiplicity': 2, 'nt': [36, 186], 'qdim': 12, 'qvalues': [12, -4, 12, -4, 0, 0, -6, 12, 0, 0, -6, 0, 0, 0, 0, -4, -4, 2, -6, 2, 2, -4, -4, -4, 0, -4, 0, -4, 2, 2, 2, 2, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 5445505
    {'cdim': 6, 'counter': 35, 'faithful': False, 'group': '1296.2922', 'group_order': 1296, 'image': None, 'label': '1296.2922.6i', 'multiplicity': 2, 'nt': [36, 566], 'qdim': 12, 'qvalues': [12, -4, -12, 4, 0, 0, -6, 12, 0, 0, -6, 0, 0, 0, 0, -4, -4, 2, 6, 2, 2, -4, -4, -4, 0, 4, 0, 4, 2, 2, 2, -2, 0, 0, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 5445506
    {'cdim': 6, 'counter': 36, 'faithful': False, 'group': '1296.2922', 'group_order': 1296, 'image': None, 'label': '1296.2922.6j', 'multiplicity': 2, 'nt': [36, 598], 'qdim': 12, 'qvalues': [12, -4, 0, 0, -4, 0, 12, -6, -6, -6, -6, 3, 3, 4, 0, 2, 2, 2, 0, -4, 2, -1, -1, 2, 0, 0, 0, 0, 2, -1, -1, 0, 2, 2, 0, 0, -1, -1, 2, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, 1, -2, 1, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 5445507
    {'cdim': 12, 'counter': 37, 'faithful': False, 'group': '1296.2922', 'group_order': 1296, 'image': None, 'label': '1296.2922.12a', 'multiplicity': 1, 'nt': [18, 122], 'qdim': 12, 'qvalues': [12, 12, 0, 0, 0, 0, -6, -6, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, -6, 0, 0, 0, -6, 0, 0, 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, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 5445508
    {'cdim': 12, 'counter': 38, 'faithful': True, 'group': '1296.2922', 'group_order': 1296, 'image': None, 'label': '1296.2922.12b', 'multiplicity': 1, 'nt': [36, 1989], 'qdim': 12, 'qvalues': [12, -4, 0, 0, 0, 0, -6, -6, 0, 0, 3, 0, 0, 0, 0, 8, 8, -4, 0, 2, -4, -4, -4, 2, 0, 0, 0, 0, -1, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 5445509
    {'cdim': 12, 'counter': 39, 'faithful': True, 'group': '1296.2922', 'group_order': 1296, 'image': None, 'label': '1296.2922.12c', 'multiplicity': 2, 'nt': [72, 0], 'qdim': 24, 'qvalues': [24, -8, 0, 0, 0, 0, -12, -12, 0, 0, 6, 0, 0, 0, 0, -8, -8, 4, 0, 4, 4, 4, 4, 4, 0, 0, 0, 0, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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: 10615658
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 1296, 'counter': 1, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '1296.2922', 'group_counter': 2922, 'group_order': 1296, 'image': None, 'image_isoclass': '1.1', 'image_order': 1, 'indicator': 1, 'kernel': '1.a1.a1', 'kernel_order': 1296, 'label': '1296.2922.1a', '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]]]}
  • id: 10615669
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 1296, 'counter': 2, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '1296.2922', 'group_counter': 2922, 'group_order': 1296, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.c1.a1', 'kernel_order': 648, 'label': '1296.2922.1b', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 10615680
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 1296, 'counter': 3, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '1296.2922', 'group_counter': 2922, 'group_order': 1296, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.b1.a1', 'kernel_order': 648, 'label': '1296.2922.1c', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 10615691
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 1296, 'counter': 4, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '1296.2922', 'group_counter': 2922, 'group_order': 1296, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.a1.a1', 'kernel_order': 648, 'label': '1296.2922.1d', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 10615702
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 1296, 'counter': 5, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '1296.2922', 'group_counter': 2922, 'group_order': 1296, 'image': None, 'image_isoclass': '3.1', 'image_order': 3, 'indicator': 0, 'kernel': '3.a1.a1', 'kernel_order': 432, 'label': '1296.2922.1e1', 'nt': [3, 1], 'q_character': None, 'values': [[[1, 0]], [[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, 0]], [[1, 0]], [[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, -1]], [[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, -1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, -1]]]}
  • id: 10615711
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 1296, 'counter': 6, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '1296.2922', 'group_counter': 2922, 'group_order': 1296, 'image': None, 'image_isoclass': '3.1', 'image_order': 3, 'indicator': 0, 'kernel': '3.a1.a1', 'kernel_order': 432, 'label': '1296.2922.1e2', 'nt': [3, 2], 'q_character': None, 'values': [[[1, 0]], [[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, 0]], [[1, 0]], [[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, 1]], [[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, 1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 1]]]}
  • id: 10615712
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 1296, 'counter': 7, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '1296.2922', 'group_counter': 2922, 'group_order': 1296, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': '6.e1.a1', 'kernel_order': 216, 'label': '1296.2922.1f1', 'nt': [6, 1], 'q_character': None, 'values': [[[1, 0]], [[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, 0]], [[1, 0]], [[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, -1]], [[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, -1]], [[1, 0]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, 0]], [[-1, -1]], [[1, 1]], [[1, -1]], [[-1, 0]], [[-1, 1]], [[-1, -1]]]}
  • id: 10615713
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 1296, 'counter': 8, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '1296.2922', 'group_counter': 2922, 'group_order': 1296, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': '6.e1.a1', 'kernel_order': 216, 'label': '1296.2922.1f2', 'nt': [6, 2], 'q_character': None, 'values': [[[1, 0]], [[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, 0]], [[1, 0]], [[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, 1]], [[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, 1]], [[1, 0]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 0]], [[-1, 1]], [[1, -1]], [[1, 1]], [[-1, 0]], [[-1, -1]], [[-1, 1]]]}
  • id: 10615714
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 1296, 'counter': 9, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '1296.2922', 'group_counter': 2922, 'group_order': 1296, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': '6.c1.a1', 'kernel_order': 216, 'label': '1296.2922.1g1', 'nt': [6, 1], 'q_character': None, 'values': [[[1, 0]], [[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, 0]], [[-1, 0]], [[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, -1]], [[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, -1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 0]], [[-1, 1]], [[-1, -1]]]}
  • id: 10615659
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 1296, 'counter': 10, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '1296.2922', 'group_counter': 2922, 'group_order': 1296, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': '6.c1.a1', 'kernel_order': 216, 'label': '1296.2922.1g2', 'nt': [6, 2], 'q_character': None, 'values': [[[1, 0]], [[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, 0]], [[-1, 0]], [[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, 1]], [[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, 1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, 1]], [[-1, -1]], [[-1, 1]], [[-1, 0]], [[-1, -1]], [[-1, 1]]]}
  • id: 10615660
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 1296, 'counter': 11, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '1296.2922', 'group_counter': 2922, 'group_order': 1296, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': '6.b1.a1', 'kernel_order': 216, 'label': '1296.2922.1h1', 'nt': [6, 1], 'q_character': None, 'values': [[[1, 0]], [[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, 0]], [[-1, 0]], [[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, -1]], [[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, -1]], [[1, 0]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[1, 0]], [[1, 1]], [[1, -1]]]}
  • id: 10615661
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 1296, 'counter': 12, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '1296.2922', 'group_counter': 2922, 'group_order': 1296, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': '6.b1.a1', 'kernel_order': 216, 'label': '1296.2922.1h2', 'nt': [6, 2], 'q_character': None, 'values': [[[1, 0]], [[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, 0]], [[-1, 0]], [[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, 1]], [[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, 1]], [[1, 0]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[1, 0]], [[1, -1]], [[1, 1]]]}
  • id: 10615662
    {'center': '6.d1.a1', 'center_index': 6, 'center_order': 216, 'counter': 13, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '1296.2922', 'group_counter': 2922, 'group_order': 1296, 'image': None, 'image_isoclass': '6.1', 'image_order': 6, 'indicator': 1, 'kernel': '6.d1.a1', 'kernel_order': 216, 'label': '1296.2922.2a', 'nt': [3, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 10615663
    {'center': '6.a1.a1', 'center_index': 6, 'center_order': 216, 'counter': 14, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '1296.2922', 'group_counter': 2922, 'group_order': 1296, 'image': None, 'image_isoclass': '6.1', 'image_order': 6, 'indicator': 1, 'kernel': '6.a1.a1', 'kernel_order': 216, 'label': '1296.2922.2b', 'nt': [3, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 10615664
    {'center': '6.a1.a1', 'center_index': 6, 'center_order': 216, 'counter': 15, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '1296.2922', 'group_counter': 2922, 'group_order': 1296, 'image': None, 'image_isoclass': '12.4', 'image_order': 12, 'indicator': 1, 'kernel': '12.a1.a1', 'kernel_order': 108, 'label': '1296.2922.2c', 'nt': [6, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 10615665
    {'center': '6.d1.a1', 'center_index': 6, 'center_order': 216, 'counter': 16, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '1296.2922', 'group_counter': 2922, 'group_order': 1296, 'image': None, 'image_isoclass': '12.4', 'image_order': 12, 'indicator': 1, 'kernel': '12.c1.a1', 'kernel_order': 108, 'label': '1296.2922.2d', 'nt': [6, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 10615666
    {'center': '6.d1.a1', 'center_index': 6, 'center_order': 216, 'counter': 17, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '1296.2922', 'group_counter': 2922, 'group_order': 1296, 'image': None, 'image_isoclass': '18.3', 'image_order': 18, 'indicator': 0, 'kernel': '18.b1.a1', 'kernel_order': 72, 'label': '1296.2922.2e1', 'nt': [6, 5], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[-1, 0]], [[2, -1]], [[2, 1]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[2, 0]], [[0, 0]], [[2, 1]], [[2, -1]], [[2, -1]], [[0, 0]], [[2, 0]], [[2, 1]], [[-1, -1]], [[-1, 1]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[0, 0]], [[2, -1]], [[2, 1]], [[0, 0]], [[0, 0]], [[-1, -1]], [[-1, 1]], [[-1, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, -1]], [[2, 1]], [[-1, 1]], [[-1, -1]], [[-1, 0]], [[2, -1]], [[2, 1]], [[-1, 1]], [[-1, 0]], [[-1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 10615667
    {'center': '6.d1.a1', 'center_index': 6, 'center_order': 216, 'counter': 18, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '1296.2922', 'group_counter': 2922, 'group_order': 1296, 'image': None, 'image_isoclass': '18.3', 'image_order': 18, 'indicator': 0, 'kernel': '18.b1.a1', 'kernel_order': 72, 'label': '1296.2922.2e2', 'nt': [6, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[-1, 0]], [[2, 1]], [[2, -1]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[2, 0]], [[0, 0]], [[2, -1]], [[2, 1]], [[2, 1]], [[0, 0]], [[2, 0]], [[2, -1]], [[-1, 1]], [[-1, -1]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[0, 0]], [[2, 1]], [[2, -1]], [[0, 0]], [[0, 0]], [[-1, 1]], [[-1, -1]], [[-1, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 1]], [[2, -1]], [[-1, -1]], [[-1, 1]], [[-1, 0]], [[2, 1]], [[2, -1]], [[-1, -1]], [[-1, 0]], [[-1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 10615668
    {'center': '6.a1.a1', 'center_index': 6, 'center_order': 216, 'counter': 19, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '1296.2922', 'group_counter': 2922, 'group_order': 1296, 'image': None, 'image_isoclass': '18.3', 'image_order': 18, 'indicator': 0, 'kernel': '18.a1.a1', 'kernel_order': 72, 'label': '1296.2922.2f1', 'nt': [6, 5], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, -1]], [[2, 1]], [[2, 0]], [[2, -1]], [[2, 1]], [[0, 0]], [[0, 0]], [[2, 1]], [[2, -1]], [[2, -1]], [[2, 0]], [[2, 0]], [[2, 1]], [[2, -1]], [[2, 1]], [[2, 0]], [[2, -1]], [[2, 1]], [[2, 1]], [[2, -1]], [[2, 0]], [[2, 1]], [[2, -1]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 1]], [[2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 1]], [[-1, -1]]]}
  • id: 10615670
    {'center': '6.a1.a1', 'center_index': 6, 'center_order': 216, 'counter': 20, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '1296.2922', 'group_counter': 2922, 'group_order': 1296, 'image': None, 'image_isoclass': '18.3', 'image_order': 18, 'indicator': 0, 'kernel': '18.a1.a1', 'kernel_order': 72, 'label': '1296.2922.2f2', 'nt': [6, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 1]], [[2, -1]], [[2, 0]], [[2, 1]], [[2, -1]], [[0, 0]], [[0, 0]], [[2, -1]], [[2, 1]], [[2, 1]], [[2, 0]], [[2, 0]], [[2, -1]], [[2, 1]], [[2, -1]], [[2, 0]], [[2, 1]], [[2, -1]], [[2, -1]], [[2, 1]], [[2, 0]], [[2, -1]], [[2, 1]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, -1]], [[2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, -1]], [[-1, 1]]]}
  • id: 10615671
    {'center': '6.a1.a1', 'center_index': 6, 'center_order': 216, 'counter': 21, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '1296.2922', 'group_counter': 2922, 'group_order': 1296, 'image': None, 'image_isoclass': '36.12', 'image_order': 36, 'indicator': 0, 'kernel': '36.a1.a1', 'kernel_order': 36, 'label': '1296.2922.2g1', 'nt': [12, 18], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, -1]], [[2, 1]], [[2, 0]], [[2, -1]], [[2, 1]], [[0, 0]], [[0, 0]], [[2, 1]], [[2, -1]], [[2, -1]], [[-2, 0]], [[2, 0]], [[2, 1]], [[2, -1]], [[2, 1]], [[2, 0]], [[-2, -1]], [[-2, 1]], [[-2, 1]], [[-2, -1]], [[2, 0]], [[2, 1]], [[2, -1]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 1]], [[-2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 1]], [[1, -1]]]}
  • id: 10615672
    {'center': '6.a1.a1', 'center_index': 6, 'center_order': 216, 'counter': 22, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '1296.2922', 'group_counter': 2922, 'group_order': 1296, 'image': None, 'image_isoclass': '36.12', 'image_order': 36, 'indicator': 0, 'kernel': '36.a1.a1', 'kernel_order': 36, 'label': '1296.2922.2g2', 'nt': [12, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 1]], [[2, -1]], [[2, 0]], [[2, 1]], [[2, -1]], [[0, 0]], [[0, 0]], [[2, -1]], [[2, 1]], [[2, 1]], [[-2, 0]], [[2, 0]], [[2, -1]], [[2, 1]], [[2, -1]], [[2, 0]], [[-2, 1]], [[-2, -1]], [[-2, -1]], [[-2, 1]], [[2, 0]], [[2, -1]], [[2, 1]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, -1]], [[-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, -1]], [[1, 1]]]}
  • id: 10615673
    {'center': '6.d1.a1', 'center_index': 6, 'center_order': 216, 'counter': 23, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '1296.2922', 'group_counter': 2922, 'group_order': 1296, 'image': None, 'image_isoclass': '36.12', 'image_order': 36, 'indicator': 0, 'kernel': '36.c1.a1', 'kernel_order': 36, 'label': '1296.2922.2h1', 'nt': [12, 18], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[-1, 0]], [[2, -1]], [[2, 1]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[-2, 0]], [[0, 0]], [[2, 1]], [[2, -1]], [[2, -1]], [[0, 0]], [[2, 0]], [[2, 1]], [[-1, -1]], [[-1, 1]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[0, 0]], [[-2, -1]], [[-2, 1]], [[0, 0]], [[0, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, -1]], [[2, 1]], [[-1, 1]], [[-1, -1]], [[-1, 0]], [[-2, -1]], [[-2, 1]], [[1, 1]], [[1, 0]], [[1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 10615674
    {'center': '6.d1.a1', 'center_index': 6, 'center_order': 216, 'counter': 24, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '1296.2922', 'group_counter': 2922, 'group_order': 1296, 'image': None, 'image_isoclass': '36.12', 'image_order': 36, 'indicator': 0, 'kernel': '36.c1.a1', 'kernel_order': 36, 'label': '1296.2922.2h2', 'nt': [12, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[-1, 0]], [[2, 1]], [[2, -1]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[-2, 0]], [[0, 0]], [[2, -1]], [[2, 1]], [[2, 1]], [[0, 0]], [[2, 0]], [[2, -1]], [[-1, 1]], [[-1, -1]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[0, 0]], [[-2, 1]], [[-2, -1]], [[0, 0]], [[0, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 1]], [[2, -1]], [[-1, -1]], [[-1, 1]], [[-1, 0]], [[-2, 1]], [[-2, -1]], [[1, -1]], [[1, 0]], [[1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 10615675
    {'center': '24.a1.a1', 'center_index': 24, 'center_order': 54, 'counter': 25, 'cyclotomic_n': 1, 'dim': 3, 'faithful': False, 'field': [0, 1], 'group': '1296.2922', 'group_counter': 2922, 'group_order': 1296, 'image': None, 'image_isoclass': '24.12', 'image_order': 24, 'indicator': 1, 'kernel': '24.a1.a1', 'kernel_order': 54, 'label': '1296.2922.3a', 'nt': [4, 5], 'q_character': None, 'values': [[[3, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 10615676
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  • id: 10615677
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  • id: 10615678
    {'center': '24.a1.a1', 'center_index': 24, 'center_order': 54, 'counter': 28, 'cyclotomic_n': 1, 'dim': 3, 'faithful': False, 'field': [0, 1], 'group': '1296.2922', 'group_counter': 2922, 'group_order': 1296, 'image': None, 'image_isoclass': '48.48', 'image_order': 48, 'indicator': 1, 'kernel': '48.a1.a1', 'kernel_order': 27, 'label': '1296.2922.3d', 'nt': [6, 11], 'q_character': None, 'values': [[[3, 0]], [[-1, 0]], [[-3, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-3, 0]], [[1, 0]], [[-3, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 10615679
    {'center': '24.a1.a1', 'center_index': 24, 'center_order': 54, 'counter': 29, 'cyclotomic_n': 3, 'dim': 3, 'faithful': False, 'field': [1, -1, 1], 'group': '1296.2922', 'group_counter': 2922, 'group_order': 1296, 'image': None, 'image_isoclass': '72.42', 'image_order': 72, 'indicator': 0, 'kernel': '72.a1.a1', 'kernel_order': 18, 'label': '1296.2922.3e1', 'nt': [12, 45], 'q_character': None, 'values': [[[3, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[3, 0]], [[3, 0]], [[3, -1]], [[3, 1]], [[3, 0]], [[3, -1]], [[3, 1]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[3, 0]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, 0]], [[3, -1]], [[-1, 1]], [[3, 1]], [[-1, -1]], [[-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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 10615681
    {'center': '24.a1.a1', 'center_index': 24, 'center_order': 54, 'counter': 30, 'cyclotomic_n': 3, 'dim': 3, 'faithful': False, 'field': [1, -1, 1], 'group': '1296.2922', 'group_counter': 2922, 'group_order': 1296, 'image': None, 'image_isoclass': '72.42', 'image_order': 72, 'indicator': 0, 'kernel': '72.a1.a1', 'kernel_order': 18, 'label': '1296.2922.3e2', 'nt': [12, 2], 'q_character': None, 'values': [[[3, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[3, 0]], [[3, 0]], [[3, 1]], [[3, -1]], [[3, 0]], [[3, 1]], [[3, -1]], [[-1, 0]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[3, 0]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 0]], [[3, 1]], [[-1, -1]], [[3, -1]], [[-1, 1]], [[-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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 10615682
    {'center': '24.a1.a1', 'center_index': 24, 'center_order': 54, 'counter': 31, 'cyclotomic_n': 3, 'dim': 3, 'faithful': False, 'field': [1, -1, 1], 'group': '1296.2922', 'group_counter': 2922, 'group_order': 1296, 'image': None, 'image_isoclass': '72.42', 'image_order': 72, 'indicator': 0, 'kernel': '72.a1.a1', 'kernel_order': 18, 'label': '1296.2922.3f1', 'nt': [18, 30], 'q_character': None, 'values': [[[3, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[3, 0]], [[3, -1]], [[3, 1]], [[3, 0]], [[3, -1]], [[3, 1]], [[1, 0]], [[1, 0]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[3, 0]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, 0]], [[3, -1]], [[-1, 1]], [[3, 1]], [[-1, -1]], [[-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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 10615683
    {'center': '24.a1.a1', 'center_index': 24, 'center_order': 54, 'counter': 32, 'cyclotomic_n': 3, 'dim': 3, 'faithful': False, 'field': [1, -1, 1], 'group': '1296.2922', 'group_counter': 2922, 'group_order': 1296, 'image': None, 'image_isoclass': '72.42', 'image_order': 72, 'indicator': 0, 'kernel': '72.a1.a1', 'kernel_order': 18, 'label': '1296.2922.3f2', 'nt': [18, 2], 'q_character': None, 'values': [[[3, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[3, 0]], [[3, 1]], [[3, -1]], [[3, 0]], [[3, 1]], [[3, -1]], [[1, 0]], [[1, 0]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[3, 0]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 0]], [[3, 1]], [[-1, -1]], [[3, -1]], [[-1, 1]], [[-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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 10615684
    {'center': '24.a1.a1', 'center_index': 24, 'center_order': 54, 'counter': 33, 'cyclotomic_n': 3, 'dim': 3, 'faithful': False, 'field': [1, -1, 1], 'group': '1296.2922', 'group_counter': 2922, 'group_order': 1296, 'image': None, 'image_isoclass': '144.188', 'image_order': 144, 'indicator': 0, 'kernel': '144.a1.a1', 'kernel_order': 9, 'label': '1296.2922.3g1', 'nt': [18, 61], 'q_character': None, 'values': [[[3, 0]], [[-1, 0]], [[-3, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[3, 0]], [[3, 0]], [[3, -1]], [[3, 1]], [[3, 0]], [[3, -1]], [[3, 1]], [[1, 0]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-3, 0]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, 0]], [[-3, -1]], [[1, 1]], [[-3, 1]], [[1, -1]], [[-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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, -1]], [[-1, 1]], [[-1, -1]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 10615685
    {'center': '24.a1.a1', 'center_index': 24, 'center_order': 54, 'counter': 34, 'cyclotomic_n': 3, 'dim': 3, 'faithful': False, 'field': [1, -1, 1], 'group': '1296.2922', 'group_counter': 2922, 'group_order': 1296, 'image': None, 'image_isoclass': '144.188', 'image_order': 144, 'indicator': 0, 'kernel': '144.a1.a1', 'kernel_order': 9, 'label': '1296.2922.3g2', 'nt': [18, 2], 'q_character': None, 'values': [[[3, 0]], [[-1, 0]], [[-3, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[3, 0]], [[3, 0]], [[3, 1]], [[3, -1]], [[3, 0]], [[3, 1]], [[3, -1]], [[1, 0]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-3, 0]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 0]], [[-3, 1]], [[1, -1]], [[-3, -1]], [[1, 1]], [[-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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, 1]], [[-1, -1]], [[-1, 1]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 10615686
    {'center': '24.a1.a1', 'center_index': 24, 'center_order': 54, 'counter': 35, 'cyclotomic_n': 3, 'dim': 3, 'faithful': False, 'field': [1, -1, 1], 'group': '1296.2922', 'group_counter': 2922, 'group_order': 1296, 'image': None, 'image_isoclass': '144.188', 'image_order': 144, 'indicator': 0, 'kernel': '144.a1.a1', 'kernel_order': 9, 'label': '1296.2922.3h1', 'nt': [18, 61], 'q_character': None, 'values': [[[3, 0]], [[-1, 0]], [[-3, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[3, 0]], [[3, 0]], [[3, -1]], [[3, 1]], [[3, 0]], [[3, -1]], [[3, 1]], [[-1, 0]], [[1, 0]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-3, 0]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, 0]], [[-3, -1]], [[1, 1]], [[-3, 1]], [[1, -1]], [[-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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, 0]], [[-1, -1]], [[1, 1]], [[1, -1]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 10615687
    {'center': '24.a1.a1', 'center_index': 24, 'center_order': 54, 'counter': 36, 'cyclotomic_n': 3, 'dim': 3, 'faithful': False, 'field': [1, -1, 1], 'group': '1296.2922', 'group_counter': 2922, 'group_order': 1296, 'image': None, 'image_isoclass': '144.188', 'image_order': 144, 'indicator': 0, 'kernel': '144.a1.a1', 'kernel_order': 9, 'label': '1296.2922.3h2', 'nt': [18, 2], 'q_character': None, 'values': [[[3, 0]], [[-1, 0]], [[-3, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[3, 0]], [[3, 0]], [[3, 1]], [[3, -1]], [[3, 0]], [[3, 1]], [[3, -1]], [[-1, 0]], [[1, 0]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-3, 0]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 0]], [[-3, 1]], [[1, -1]], [[-3, -1]], [[1, 1]], [[-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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 0]], [[-1, 1]], [[1, -1]], [[1, 1]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 10615688
    {'center': '36.b1.a1', 'center_index': 36, 'center_order': 36, 'counter': 37, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '1296.2922', 'group_counter': 2922, 'group_order': 1296, 'image': None, 'image_isoclass': '36.10', 'image_order': 36, 'indicator': 1, 'kernel': '36.b1.a1', 'kernel_order': 36, 'label': '1296.2922.4a', 'nt': [6, 9], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[-2, 0]], [[4, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 10615689
    {'center': '36.b1.a1', 'center_index': 36, 'center_order': 36, 'counter': 38, 'cyclotomic_n': 3, 'dim': 4, 'faithful': False, 'field': [1, -1, 1], 'group': '1296.2922', 'group_counter': 2922, 'group_order': 1296, 'image': None, 'image_isoclass': '108.38', 'image_order': 108, 'indicator': 0, 'kernel': '108.a1.a1', 'kernel_order': 12, 'label': '1296.2922.4b1', 'nt': [12, 70], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[-2, 0]], [[4, -1]], [[4, 1]], [[-2, 0]], [[-2, -1]], [[-2, 1]], [[0, 0]], [[0, 0]], [[4, 1]], [[4, -1]], [[4, -1]], [[0, 0]], [[4, 0]], [[4, 1]], [[-2, -1]], [[-2, 1]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 1]], [[-2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, -1]], [[-2, 1]], [[1, 1]], [[1, -1]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 10615690
    {'center': '36.b1.a1', 'center_index': 36, 'center_order': 36, 'counter': 39, 'cyclotomic_n': 3, 'dim': 4, 'faithful': False, 'field': [1, -1, 1], 'group': '1296.2922', 'group_counter': 2922, 'group_order': 1296, 'image': None, 'image_isoclass': '108.38', 'image_order': 108, 'indicator': 0, 'kernel': '108.a1.a1', 'kernel_order': 12, 'label': '1296.2922.4b2', 'nt': [12, 2], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[-2, 0]], [[4, 1]], [[4, -1]], [[-2, 0]], [[-2, 1]], [[-2, -1]], [[0, 0]], [[0, 0]], [[4, -1]], [[4, 1]], [[4, 1]], [[0, 0]], [[4, 0]], [[4, -1]], [[-2, 1]], [[-2, -1]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, -1]], [[-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 1]], [[-2, -1]], [[1, -1]], [[1, 1]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 10615692
    {'center': '54.a1.a1', 'center_index': 54, 'center_order': 24, 'counter': 40, 'cyclotomic_n': 1, 'dim': 6, 'faithful': False, 'field': [0, 1], 'group': '1296.2922', 'group_counter': 2922, 'group_order': 1296, 'image': None, 'image_isoclass': '54.6', 'image_order': 54, 'indicator': 1, 'kernel': '54.a1.a1', 'kernel_order': 24, 'label': '1296.2922.6a', 'nt': [9, 10], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[6, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[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, 0]], [[0, 0]], [[0, 0]], [[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: 10615693
    {'center': '144.b1.a1', 'center_index': 144, 'center_order': 9, 'counter': 41, 'cyclotomic_n': 1, 'dim': 6, 'faithful': False, 'field': [0, 1], 'group': '1296.2922', 'group_counter': 2922, 'group_order': 1296, 'image': None, 'image_isoclass': '144.183', 'image_order': 144, 'indicator': 1, 'kernel': '144.b1.a1', 'kernel_order': 9, 'label': '1296.2922.6b', 'nt': [12, 83], 'q_character': None, 'values': [[[6, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[6, 0]], [[-3, 0]], [[6, 0]], [[6, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 10615694
    {'center': '54.a1.a1', 'center_index': 54, 'center_order': 24, 'counter': 42, 'cyclotomic_n': 1, 'dim': 6, 'faithful': False, 'field': [0, 1], 'group': '1296.2922', 'group_counter': 2922, 'group_order': 1296, 'image': None, 'image_isoclass': '108.26', 'image_order': 108, 'indicator': 1, 'kernel': '108.b1.a1', 'kernel_order': 12, 'label': '1296.2922.6c', 'nt': [18, 45], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[-6, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[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, 0]], [[0, 0]], [[0, 0]], [[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: 10615695
    {'center': '144.b1.a1', 'center_index': 144, 'center_order': 9, 'counter': 43, 'cyclotomic_n': 1, 'dim': 6, 'faithful': False, 'field': [0, 1], 'group': '1296.2922', 'group_counter': 2922, 'group_order': 1296, 'image': None, 'image_isoclass': '144.183', 'image_order': 144, 'indicator': 1, 'kernel': '144.b1.a1', 'kernel_order': 9, 'label': '1296.2922.6d', 'nt': [18, 69], 'q_character': None, 'values': [[[6, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[6, 0]], [[-3, 0]], [[6, 0]], [[6, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 10615696
    {'center': '216.a1.a1', 'center_index': 216, 'center_order': 6, 'counter': 44, 'cyclotomic_n': 1, 'dim': 6, 'faithful': False, 'field': [0, 1], 'group': '1296.2922', 'group_counter': 2922, 'group_order': 1296, 'image': None, 'image_isoclass': '216.90', 'image_order': 216, 'indicator': 1, 'kernel': '216.a1.a1', 'kernel_order': 6, 'label': '1296.2922.6e', 'nt': [18, 98], 'q_character': None, 'values': [[[6, 0]], [[-2, 0]], [[6, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[-2, 0]], [[-3, 0]], [[1, 0]], [[-2, 0]], [[4, 0]], [[4, 0]], [[-2, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[4, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 10615697
    {'center': '216.a1.a1', 'center_index': 216, 'center_order': 6, 'counter': 45, 'cyclotomic_n': 1, 'dim': 6, 'faithful': False, 'field': [0, 1], 'group': '1296.2922', 'group_counter': 2922, 'group_order': 1296, 'image': None, 'image_isoclass': '432.533', 'image_order': 432, 'indicator': 1, 'kernel': '432.b1.a1', 'kernel_order': 3, 'label': '1296.2922.6f', 'nt': [18, 147], 'q_character': None, 'values': [[[6, 0]], [[-2, 0]], [[-6, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[-2, 0]], [[3, 0]], [[1, 0]], [[-2, 0]], [[4, 0]], [[4, 0]], [[-2, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[-4, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 10615698
    {'center': '144.b1.a1', 'center_index': 144, 'center_order': 9, 'counter': 46, 'cyclotomic_n': 3, 'dim': 6, 'faithful': False, 'field': [1, -1, 1], 'group': '1296.2922', 'group_counter': 2922, 'group_order': 1296, 'image': None, 'image_isoclass': '432.745', 'image_order': 432, 'indicator': 0, 'kernel': '432.a1.a1', 'kernel_order': 3, 'label': '1296.2922.6g1', 'nt': [24, 1328], 'q_character': None, 'values': [[[6, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[6, 0]], [[-3, 0]], [[6, -1]], [[6, 1]], [[-3, 0]], [[-3, -1]], [[-3, 1]], [[-2, 0]], [[0, 0]], [[-2, 1]], [[-2, -1]], [[-2, -1]], [[0, 0]], [[-2, 0]], [[-2, 1]], [[1, -1]], [[1, 1]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[0, 0]], [[2, -1]], [[2, 1]], [[0, 0]], [[0, 0]], [[-1, -1]], [[-1, 1]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, -1]], [[-2, 1]], [[1, 1]], [[1, 0]], [[1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 10615699
    {'center': '144.b1.a1', 'center_index': 144, 'center_order': 9, 'counter': 47, 'cyclotomic_n': 3, 'dim': 6, 'faithful': False, 'field': [1, -1, 1], 'group': '1296.2922', 'group_counter': 2922, 'group_order': 1296, 'image': None, 'image_isoclass': '432.745', 'image_order': 432, 'indicator': 0, 'kernel': '432.a1.a1', 'kernel_order': 3, 'label': '1296.2922.6g2', 'nt': [24, 2], 'q_character': None, 'values': [[[6, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[6, 0]], [[-3, 0]], [[6, 1]], [[6, -1]], [[-3, 0]], [[-3, 1]], [[-3, -1]], [[-2, 0]], [[0, 0]], [[-2, -1]], [[-2, 1]], [[-2, 1]], [[0, 0]], [[-2, 0]], [[-2, -1]], [[1, 1]], [[1, -1]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[0, 0]], [[2, 1]], [[2, -1]], [[0, 0]], [[0, 0]], [[-1, 1]], [[-1, -1]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1]], [[-2, -1]], [[1, -1]], [[1, 0]], [[1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 10615700
    {'center': '216.a1.a1', 'center_index': 216, 'center_order': 6, 'counter': 48, 'cyclotomic_n': 3, 'dim': 6, 'faithful': False, 'field': [1, -1, 1], 'group': '1296.2922', 'group_counter': 2922, 'group_order': 1296, 'image': None, 'image_isoclass': '216.90', 'image_order': 216, 'indicator': 0, 'kernel': '216.a1.a1', 'kernel_order': 6, 'label': '1296.2922.6h1', 'nt': [36, 186], 'q_character': None, 'values': [[[6, 0]], [[-2, 0]], [[6, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, -1]], [[4, 1]], [[-2, 1]], [[-3, 0]], [[1, 0]], [[-2, -1]], [[4, 1]], [[4, -1]], [[-2, 0]], [[0, 0]], [[4, -1]], [[0, 0]], [[4, 1]], [[1, 0]], [[-2, -1]], [[-2, 1]], [[1, 0]], [[0, 0]], [[0, 0]], [[-2, -1]], [[-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 10615701
    {'center': '216.a1.a1', 'center_index': 216, 'center_order': 6, 'counter': 49, 'cyclotomic_n': 3, 'dim': 6, 'faithful': False, 'field': [1, -1, 1], 'group': '1296.2922', 'group_counter': 2922, 'group_order': 1296, 'image': None, 'image_isoclass': '216.90', 'image_order': 216, 'indicator': 0, 'kernel': '216.a1.a1', 'kernel_order': 6, 'label': '1296.2922.6h2', 'nt': [36, 2], 'q_character': None, 'values': [[[6, 0]], [[-2, 0]], [[6, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 1]], [[4, -1]], [[-2, -1]], [[-3, 0]], [[1, 0]], [[-2, 1]], [[4, -1]], [[4, 1]], [[-2, 0]], [[0, 0]], [[4, 1]], [[0, 0]], [[4, -1]], [[1, 0]], [[-2, 1]], [[-2, -1]], [[1, 0]], [[0, 0]], [[0, 0]], [[-2, 1]], [[-2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 10615703
    {'center': '216.a1.a1', 'center_index': 216, 'center_order': 6, 'counter': 50, 'cyclotomic_n': 3, 'dim': 6, 'faithful': False, 'field': [1, -1, 1], 'group': '1296.2922', 'group_counter': 2922, 'group_order': 1296, 'image': None, 'image_isoclass': '432.533', 'image_order': 432, 'indicator': 0, 'kernel': '432.b1.a1', 'kernel_order': 3, 'label': '1296.2922.6i1', 'nt': [36, 566], 'q_character': None, 'values': [[[6, 0]], [[-2, 0]], [[-6, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, -1]], [[4, 1]], [[-2, 1]], [[3, 0]], [[1, 0]], [[-2, -1]], [[4, 1]], [[4, -1]], [[-2, 0]], [[0, 0]], [[-4, -1]], [[0, 0]], [[-4, 1]], [[1, 0]], [[-2, -1]], [[-2, 1]], [[-1, 0]], [[0, 0]], [[0, 0]], [[2, -1]], [[2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 10615704
    {'center': '216.a1.a1', 'center_index': 216, 'center_order': 6, 'counter': 51, 'cyclotomic_n': 3, 'dim': 6, 'faithful': False, 'field': [1, -1, 1], 'group': '1296.2922', 'group_counter': 2922, 'group_order': 1296, 'image': None, 'image_isoclass': '432.533', 'image_order': 432, 'indicator': 0, 'kernel': '432.b1.a1', 'kernel_order': 3, 'label': '1296.2922.6i2', 'nt': [36, 2], 'q_character': None, 'values': [[[6, 0]], [[-2, 0]], [[-6, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 1]], [[4, -1]], [[-2, -1]], [[3, 0]], [[1, 0]], [[-2, 1]], [[4, -1]], [[4, 1]], [[-2, 0]], [[0, 0]], [[-4, 1]], [[0, 0]], [[-4, -1]], [[1, 0]], [[-2, 1]], [[-2, -1]], [[-1, 0]], [[0, 0]], [[0, 0]], [[2, 1]], [[2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 10615705
    {'center': '144.b1.a1', 'center_index': 144, 'center_order': 9, 'counter': 52, 'cyclotomic_n': 3, 'dim': 6, 'faithful': False, 'field': [1, -1, 1], 'group': '1296.2922', 'group_counter': 2922, 'group_order': 1296, 'image': None, 'image_isoclass': '432.745', 'image_order': 432, 'indicator': 0, 'kernel': '432.a1.a1', 'kernel_order': 3, 'label': '1296.2922.6j1', 'nt': [36, 598], 'q_character': None, 'values': [[[6, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[6, 0]], [[-3, 0]], [[6, -1]], [[6, 1]], [[-3, 0]], [[-3, -1]], [[-3, 1]], [[2, 0]], [[0, 0]], [[-2, 1]], [[-2, -1]], [[-2, -1]], [[0, 0]], [[-2, 0]], [[-2, 1]], [[1, -1]], [[1, 1]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[0, 0]], [[-2, -1]], [[-2, 1]], [[0, 0]], [[0, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, -1]], [[2, 1]], [[-1, 1]], [[-1, 0]], [[-1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 10615706
    {'center': '144.b1.a1', 'center_index': 144, 'center_order': 9, 'counter': 53, 'cyclotomic_n': 3, 'dim': 6, 'faithful': False, 'field': [1, -1, 1], 'group': '1296.2922', 'group_counter': 2922, 'group_order': 1296, 'image': None, 'image_isoclass': '432.745', 'image_order': 432, 'indicator': 0, 'kernel': '432.a1.a1', 'kernel_order': 3, 'label': '1296.2922.6j2', 'nt': [36, 2], 'q_character': None, 'values': [[[6, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[6, 0]], [[-3, 0]], [[6, 1]], [[6, -1]], [[-3, 0]], [[-3, 1]], [[-3, -1]], [[2, 0]], [[0, 0]], [[-2, -1]], [[-2, 1]], [[-2, 1]], [[0, 0]], [[-2, 0]], [[-2, -1]], [[1, 1]], [[1, -1]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[0, 0]], [[-2, 1]], [[-2, -1]], [[0, 0]], [[0, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1]], [[2, -1]], [[-1, -1]], [[-1, 0]], [[-1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 10615707
    {'center': '324.a1.a1', 'center_index': 324, 'center_order': 4, 'counter': 54, 'cyclotomic_n': 1, 'dim': 12, 'faithful': False, 'field': [0, 1], 'group': '1296.2922', 'group_counter': 2922, 'group_order': 1296, 'image': None, 'image_isoclass': '324.118', 'image_order': 324, 'indicator': 1, 'kernel': '324.a1.a1', 'kernel_order': 4, 'label': '1296.2922.12a', 'nt': [18, 122], 'q_character': None, 'values': [[[12, 0]], [[12, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-6, 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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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: 10615708
    {'center': '1296.a1.a1', 'center_index': 1296, 'center_order': 1, 'counter': 55, 'cyclotomic_n': 1, 'dim': 12, 'faithful': True, 'field': [0, 1], 'group': '1296.2922', 'group_counter': 2922, 'group_order': 1296, 'image': None, 'image_isoclass': '1296.2922', 'image_order': 1296, 'indicator': 1, 'kernel': '1296.a1.a1', 'kernel_order': 1, 'label': '1296.2922.12b', 'nt': [36, 1989], 'q_character': None, 'values': [[[12, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[8, 0]], [[8, 0]], [[-4, 0]], [[0, 0]], [[2, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 10615709
    {'center': '1296.a1.a1', 'center_index': 1296, 'center_order': 1, 'counter': 56, 'cyclotomic_n': 3, 'dim': 12, 'faithful': True, 'field': [1, -1, 1], 'group': '1296.2922', 'group_counter': 2922, 'group_order': 1296, 'image': None, 'image_isoclass': '1296.2922', 'image_order': 1296, 'indicator': 0, 'kernel': '1296.a1.a1', 'kernel_order': 1, 'label': '1296.2922.12c1', 'nt': [72, 0], 'q_character': None, 'values': [[[12, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[8, -1]], [[8, 1]], [[-4, 1]], [[0, 0]], [[2, 0]], [[-4, -1]], [[-4, 1]], [[-4, -1]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[2, -1]], [[2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 10615710
    {'center': '1296.a1.a1', 'center_index': 1296, 'center_order': 1, 'counter': 57, 'cyclotomic_n': 3, 'dim': 12, 'faithful': True, 'field': [1, -1, 1], 'group': '1296.2922', 'group_counter': 2922, 'group_order': 1296, 'image': None, 'image_isoclass': '1296.2922', 'image_order': 1296, 'indicator': 0, 'kernel': '1296.a1.a1', 'kernel_order': 1, 'label': '1296.2922.12c2', 'nt': [72, 2], 'q_character': None, 'values': [[[12, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[8, 1]], [[8, -1]], [[-4, -1]], [[0, 0]], [[2, 0]], [[-4, 1]], [[-4, -1]], [[-4, 1]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[2, 1]], [[2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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: 71006737
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': True, 'core_order': 1296, 'counter': 1, 'cyclic': False, 'direct': True, 'hall': 6, 'label': '1296.2922.1.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '1.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': False, 'quotient': '1.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 1, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_1', 'simple': False, 'solvable': True, 'special_labels': ['R', 'L0', 'D0', 'C0'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '1296.2922', 'subgroup_hash': 2922, 'subgroup_order': 1296, 'subgroup_tex': 'C_6^2.S_3^2', 'supersolvable': False, 'sylow': 0}
  • id: 71006848
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': True, 'core_order': 648, 'counter': 2, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1296.2922.2.a1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': ['C1'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '648.585', 'subgroup_hash': 585, 'subgroup_order': 648, 'subgroup_tex': 'S_3\\times C_3^2.A_4', 'supersolvable': False, 'sylow': 0}
  • id: 71006946
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': True, 'core_order': 648, 'counter': 3, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1296.2922.2.b1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '648.559', 'subgroup_hash': 559, 'subgroup_order': 648, 'subgroup_tex': 'C_3^3.S_4', 'supersolvable': False, 'sylow': 0}
  • id: 71006957
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': True, 'core_order': 648, 'counter': 4, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1296.2922.2.c1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '648.570', 'subgroup_hash': 570, 'subgroup_order': 648, 'subgroup_tex': 'C_3^3.S_4', 'supersolvable': False, 'sylow': 0}
  • id: 71006968
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': True, 'core_order': 432, 'counter': 5, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1296.2922.3.a1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '3.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '3.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 3, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '432.522', 'subgroup_hash': 522, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2.D_6', 'supersolvable': False, 'sylow': 0}
  • id: 71006979
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 216, 'counter': 6, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.2922.3.b1.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.533', 'subgroup_hash': 533, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2.D_6', 'supersolvable': False, 'sylow': 0}
  • id: 71006990
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 216, 'counter': 7, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.2922.3.c1.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.658', 'subgroup_hash': 658, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 71007001
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': True, 'core_order': 324, 'counter': 8, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1296.2922.4.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '324.134', 'subgroup_hash': 134, 'subgroup_order': 324, 'subgroup_tex': 'C_3^3.A_4', 'supersolvable': False, 'sylow': 0}
  • id: 71007012
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 54, 'counter': 9, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.2922.4.b1.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '324.118', 'subgroup_hash': 118, 'subgroup_order': 324, 'subgroup_tex': 'C_3^2.S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 71006738
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': True, 'core_order': 216, 'counter': 10, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1296.2922.6.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '6.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '6.1', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 6, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '216.174', 'subgroup_hash': 174, 'subgroup_order': 216, 'subgroup_tex': 'S_3\\times C_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 71006749
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': True, 'core_order': 216, 'counter': 11, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1296.2922.6.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '6.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '6.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 6, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6', 'simple': False, 'solvable': True, 'special_labels': ['C2'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '216.98', 'subgroup_hash': 98, 'subgroup_order': 216, 'subgroup_tex': 'C_6^2.C_6', 'supersolvable': False, 'sylow': 0}
  • id: 71006760
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': True, 'core_order': 216, 'counter': 12, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1296.2922.6.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '6.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '6.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 6, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '216.91', 'subgroup_hash': 91, 'subgroup_order': 216, 'subgroup_tex': 'C_3^2.S_4', 'supersolvable': False, 'sylow': 0}
  • id: 71006771
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': True, 'centralizer_order': 6, 'characteristic': True, 'core_order': 216, 'counter': 13, 'cyclic': False, 'direct': True, 'hall': 0, 'label': '1296.2922.6.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '6.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '6.1', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 6, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '216.90', 'subgroup_hash': 90, 'subgroup_order': 216, 'subgroup_tex': 'C_3^2.S_4', 'supersolvable': False, 'sylow': 0}
  • id: 71006782
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': True, 'core_order': 216, 'counter': 14, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1296.2922.6.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '6.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '6.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 6, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '216.94', 'subgroup_hash': 94, 'subgroup_order': 216, 'subgroup_tex': 'C_3^2.S_4', 'supersolvable': False, 'sylow': 0}
  • id: 71006793
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 54, 'counter': 15, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.2922.6.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.170', 'subgroup_hash': 170, 'subgroup_order': 216, 'subgroup_tex': 'C_6\\times S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 71006804
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 54, 'counter': 16, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.2922.6.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.119', 'subgroup_hash': 119, 'subgroup_order': 216, 'subgroup_tex': 'C_6.S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 71006815
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 27, 'counter': 17, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.2922.6.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.121', 'subgroup_hash': 121, 'subgroup_order': 216, 'subgroup_tex': 'C_3^3:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 71006826
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 27, 'counter': 18, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.2922.6.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.122', 'subgroup_hash': 122, 'subgroup_order': 216, 'subgroup_tex': 'C_3^2:D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 71006837
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 108, 'counter': 19, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.2922.6.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '216.106', 'subgroup_hash': 106, 'subgroup_order': 216, 'subgroup_tex': 'C_6^2.C_6', 'supersolvable': False, 'sylow': 0}
  • id: 71006849
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 72, 'counter': 20, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.2922.6.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '216.98', 'subgroup_hash': 98, 'subgroup_order': 216, 'subgroup_tex': 'C_6^2.C_6', 'supersolvable': False, 'sylow': 0}
  • id: 71006860
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 108, 'counter': 21, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.2922.6.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.l1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '216.139', 'subgroup_hash': 139, 'subgroup_order': 216, 'subgroup_tex': 'C_6^2:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 71006871
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 72, 'counter': 22, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.2922.6.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.m1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.90', 'subgroup_hash': 90, 'subgroup_order': 216, 'subgroup_tex': 'C_3^2.S_4', 'supersolvable': False, 'sylow': 0}
  • id: 71006882
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 108, 'counter': 23, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.2922.6.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.n1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.144', 'subgroup_hash': 144, 'subgroup_order': 216, 'subgroup_tex': 'C_6^2:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 71006893
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 108, 'counter': 24, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.2922.6.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.o1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.90', 'subgroup_hash': 90, 'subgroup_order': 216, 'subgroup_tex': 'C_3^2.S_4', 'supersolvable': False, 'sylow': 0}
  • id: 71006904
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 36, 'counter': 25, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.2922.6.p1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.p1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.90', 'subgroup_hash': 90, 'subgroup_order': 216, 'subgroup_tex': 'C_3^2.S_4', 'supersolvable': False, 'sylow': 0}
  • id: 71006915
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 54, 'counter': 26, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.2922.8.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, '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': '162.37', 'subgroup_hash': 37, 'subgroup_order': 162, 'subgroup_tex': 'C_3^3.C_6', 'supersolvable': True, 'sylow': 0}
  • id: 71006926
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 27, 'counter': 27, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.2922.8.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, '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': '162.36', 'subgroup_hash': 36, 'subgroup_order': 162, 'subgroup_tex': 'D_9:C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 71006937
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 27, 'counter': 28, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.2922.8.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, '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': '162.42', 'subgroup_hash': 42, 'subgroup_order': 162, 'subgroup_tex': 'C_3^3.S_3', 'supersolvable': True, 'sylow': 0}
  • id: 71006945
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 36, 'counter': 29, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.2922.9.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '9.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 9, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.167', 'subgroup_hash': 167, 'subgroup_order': 144, 'subgroup_tex': 'C_6^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 71006947
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 72, 'counter': 30, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.2922.9.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '9.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 9, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.109', 'subgroup_hash': 109, 'subgroup_order': 144, 'subgroup_tex': 'C_2^2:D_{18}', 'supersolvable': False, 'sylow': 0}
  • id: 71006948
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 24, 'counter': 31, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.2922.9.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '9.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '144.162', 'subgroup_hash': 162, 'subgroup_order': 144, 'subgroup_tex': 'C_{12}:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 71006949
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 72, 'counter': 32, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.2922.9.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '9.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '144.153', 'subgroup_hash': 153, 'subgroup_order': 144, 'subgroup_tex': 'D_6:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 71006950
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': True, 'core_order': 108, 'counter': 33, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1296.2922.12.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '12.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '12.4', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_6', 'simple': False, 'solvable': True, 'special_labels': ['F'], 'split': False, '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: 71006951
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': True, 'core_order': 108, 'counter': 34, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1296.2922.12.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '12.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '12.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_6', 'simple': False, 'solvable': True, 'special_labels': ['D', 'L1', 'D1', 'C3'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '108.20', 'subgroup_hash': 20, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2.A_4', 'supersolvable': False, 'sylow': 0}
  • id: 71006952
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': True, 'core_order': 108, 'counter': 35, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1296.2922.12.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '12.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '12.4', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': 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: 71006953
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 54, 'counter': 36, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.2922.12.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '108.42', 'subgroup_hash': 42, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 71006954
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 27, 'counter': 37, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.2922.12.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '108.42', 'subgroup_hash': 42, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 71006955
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 27, 'counter': 38, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.2922.12.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '108.42', 'subgroup_hash': 42, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 71006956
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 27, 'counter': 39, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.2922.12.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '108.43', 'subgroup_hash': 43, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 71006958
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 27, 'counter': 40, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.2922.12.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.32', 'subgroup_hash': 32, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 71006959
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 27, 'counter': 41, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.2922.12.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.33', 'subgroup_hash': 33, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 71006960
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 36, 'counter': 42, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.2922.12.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.20', 'subgroup_hash': 20, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2.A_4', 'supersolvable': False, 'sylow': 0}
  • id: 71006961
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 36, 'counter': 43, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.2922.12.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.21', 'subgroup_hash': 21, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2.A_4', 'supersolvable': False, 'sylow': 0}
  • id: 71006962
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 36, 'counter': 44, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.2922.12.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.l1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.21', 'subgroup_hash': 21, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2.A_4', 'supersolvable': False, 'sylow': 0}
  • id: 71006963
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 12, 'counter': 45, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.2922.12.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.m1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.21', 'subgroup_hash': 21, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2.A_4', 'supersolvable': False, 'sylow': 0}
  • id: 71006964
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 9, 'counter': 46, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.2922.12.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.n1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.26', 'subgroup_hash': 26, 'subgroup_order': 108, 'subgroup_tex': 'C_{18}:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 71006965
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 54, 'counter': 47, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.2922.12.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.o1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.38', 'subgroup_hash': 38, 'subgroup_order': 108, 'subgroup_tex': 'C_3\\times S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 71006966
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 18, 'counter': 48, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.2922.12.p1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.p1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.16', 'subgroup_hash': 16, 'subgroup_order': 108, 'subgroup_tex': 'S_3\\times D_9', 'supersolvable': True, 'sylow': 0}
  • id: 71006967
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 27, 'counter': 49, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.2922.12.q1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.q1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.38', 'subgroup_hash': 38, 'subgroup_order': 108, 'subgroup_tex': 'C_3\\times S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 71006969
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 27, 'counter': 50, 'cyclic': False, 'direct': None, 'hall': 3, 'label': '1296.2922.16.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, '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': 3}
  • id: 71006970
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': True, 'core_order': 72, 'counter': 51, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1296.2922.18.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '18.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '18.3', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 18, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3\\times S_3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '72.48', 'subgroup_hash': 48, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 71006971
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': True, 'core_order': 72, 'counter': 52, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1296.2922.18.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '18.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '18.3', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 18, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3\\times S_3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '72.15', 'subgroup_hash': 15, 'subgroup_order': 72, 'subgroup_tex': 'C_2^2:D_9', 'supersolvable': False, 'sylow': 0}
  • id: 71006972
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 9, 'counter': 53, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.2922.18.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.48', 'subgroup_hash': 48, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 71006973
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 9, 'counter': 54, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.2922.18.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.29', 'subgroup_hash': 29, 'subgroup_order': 72, 'subgroup_tex': 'C_6:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 71006974
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 6, 'counter': 55, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.2922.18.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.48', 'subgroup_hash': 48, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 71006975
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 18, 'counter': 56, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.2922.18.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.46', 'subgroup_hash': 46, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 71006976
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 18, 'counter': 57, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.2922.18.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.20', 'subgroup_hash': 20, 'subgroup_order': 72, 'subgroup_tex': 'C_6.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 71006977
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 6, 'counter': 58, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.2922.18.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.27', 'subgroup_hash': 27, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 71006978
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 9, 'counter': 59, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.2922.18.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '72.30', 'subgroup_hash': 30, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 71006980
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 9, 'counter': 60, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.2922.18.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '72.30', 'subgroup_hash': 30, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 71006981
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 61, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.2922.18.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '72.30', 'subgroup_hash': 30, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 71006982
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 9, 'counter': 62, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.2922.18.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.l1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '72.22', 'subgroup_hash': 22, 'subgroup_order': 72, 'subgroup_tex': 'D_6:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 71006983
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 63, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.2922.18.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.m1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.28', 'subgroup_hash': 28, 'subgroup_order': 72, 'subgroup_tex': 'C_3\\times D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 71006984
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 9, 'counter': 64, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.2922.18.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.n1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.23', 'subgroup_hash': 23, 'subgroup_order': 72, 'subgroup_tex': 'C_3:D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 71006985
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 36, 'counter': 65, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.2922.18.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '18.o1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.50', 'subgroup_hash': 50, 'subgroup_order': 72, 'subgroup_tex': 'C_2\\times C_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 71006986
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 36, 'counter': 66, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.2922.18.p1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.p1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.16', 'subgroup_hash': 16, 'subgroup_order': 72, 'subgroup_tex': 'C_2^2:C_{18}', 'supersolvable': False, 'sylow': 0}
  • id: 71006987
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 12, 'counter': 67, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.2922.18.q1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.q1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.16', 'subgroup_hash': 16, 'subgroup_order': 72, 'subgroup_tex': 'C_2^2:C_{18}', 'supersolvable': False, 'sylow': 0}
  • id: 71006988
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 24, 'counter': 68, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.2922.18.r1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.r1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.48', 'subgroup_hash': 48, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 71006989
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 12, 'counter': 69, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.2922.18.s1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '18.s1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.37', 'subgroup_hash': 37, 'subgroup_order': 72, 'subgroup_tex': 'D_4\\times C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 71006991
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 36, 'counter': 70, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.2922.18.t1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.t1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.30', 'subgroup_hash': 30, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 71006992
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 36, 'counter': 71, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.2922.18.u1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.u1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.30', 'subgroup_hash': 30, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 71006993
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 12, 'counter': 72, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.2922.18.v1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.v1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.30', 'subgroup_hash': 30, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 71006994
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 36, 'counter': 73, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.2922.18.w1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.w1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.30', 'subgroup_hash': 30, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 71006995
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 12, 'counter': 74, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.2922.18.x1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.x1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.30', 'subgroup_hash': 30, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 71006996
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 4, 'counter': 75, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.2922.18.y1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.y1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.30', 'subgroup_hash': 30, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 71006997
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 36, 'counter': 76, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.2922.18.z1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.z1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.35', 'subgroup_hash': 35, 'subgroup_order': 72, 'subgroup_tex': 'C_6^2:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 71006998
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 36, 'counter': 77, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.2922.18.ba1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.ba1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.15', 'subgroup_hash': 15, 'subgroup_order': 72, 'subgroup_tex': 'C_2^2:D_9', 'supersolvable': False, 'sylow': 0}
  • id: 71006999
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 12, 'counter': 78, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.2922.18.bb1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.bb1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.15', 'subgroup_hash': 15, 'subgroup_order': 72, 'subgroup_tex': 'C_2^2:D_9', 'supersolvable': False, 'sylow': 0}
  • id: 71007000
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': True, 'core_order': 54, 'counter': 79, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1296.2922.24.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '24.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '24.12', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 12, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'S_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '54.12', 'subgroup_hash': 12, 'subgroup_order': 54, 'subgroup_tex': 'S_3\\times C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 71007002
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 27, 'counter': 80, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.2922.24.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.15', 'subgroup_hash': 15, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 71007003
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 9, 'counter': 81, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.2922.24.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.11', 'subgroup_hash': 11, 'subgroup_order': 54, 'subgroup_tex': 'C_9:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 71007004
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 18, 'counter': 82, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.2922.24.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.4', 'subgroup_hash': 4, 'subgroup_order': 54, 'subgroup_tex': 'S_3\\times C_9', 'supersolvable': True, 'sylow': 0}
  • id: 71007005
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 18, 'counter': 83, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.2922.24.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.4', 'subgroup_hash': 4, 'subgroup_order': 54, 'subgroup_tex': 'S_3\\times C_9', 'supersolvable': True, 'sylow': 0}
  • id: 71007006
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 27, 'counter': 84, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.2922.24.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.12', 'subgroup_hash': 12, 'subgroup_order': 54, 'subgroup_tex': 'S_3\\times C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 71007007
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 27, 'counter': 85, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.2922.24.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.12', 'subgroup_hash': 12, 'subgroup_order': 54, 'subgroup_tex': 'S_3\\times C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 71007008
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 9, 'counter': 86, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.2922.24.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.3', 'subgroup_hash': 3, 'subgroup_order': 54, 'subgroup_tex': 'C_3\\times D_9', 'supersolvable': True, 'sylow': 0}
  • id: 71007009
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 9, 'counter': 87, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.2922.24.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.6', 'subgroup_hash': 6, 'subgroup_order': 54, 'subgroup_tex': 'C_9:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 71007010
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 3, 'counter': 88, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.2922.24.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.6', 'subgroup_hash': 6, 'subgroup_order': 54, 'subgroup_tex': 'C_9:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 71007011
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 27, 'counter': 89, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.2922.24.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.13', 'subgroup_hash': 13, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 71007013
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 9, 'counter': 90, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.2922.24.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.l1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.6', 'subgroup_hash': 6, 'subgroup_order': 54, 'subgroup_tex': 'C_9:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 71007014
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 9, 'counter': 91, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.2922.24.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.m1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.6', 'subgroup_hash': 6, 'subgroup_order': 54, 'subgroup_tex': 'C_9:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 71007015
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 9, 'counter': 92, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.2922.24.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.n1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.7', 'subgroup_hash': 7, 'subgroup_order': 54, 'subgroup_tex': 'C_3:D_9', 'supersolvable': True, 'sylow': 0}
  • id: 71007016
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 4, 'counter': 93, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.2922.27.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '27.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 27, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.45', 'subgroup_hash': 45, 'subgroup_order': 48, 'subgroup_tex': 'C_6\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 71007017
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 12, 'counter': 94, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.2922.27.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '27.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '48.43', 'subgroup_hash': 43, 'subgroup_order': 48, 'subgroup_tex': 'C_6:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 71007018
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 24, 'counter': 95, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.2922.27.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '27.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '48.38', 'subgroup_hash': 38, 'subgroup_order': 48, 'subgroup_tex': 'S_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 71007019
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': True, 'core_order': 36, 'counter': 96, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1296.2922.36.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '36.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '36.12', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 12, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 36, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6\\times S_3', 'simple': False, 'solvable': True, 'special_labels': ['S', 'C4'], '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: 71007020
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 216, 'characteristic': True, 'core_order': 36, 'counter': 97, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1296.2922.36.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '36.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '36.10', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 10, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 36, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': 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: 71007021
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': True, 'core_order': 36, 'counter': 98, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1296.2922.36.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '36.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '36.12', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 12, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 36, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6\\times S_3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, '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: 71007022
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 9, 'counter': 99, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.2922.36.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.14', 'subgroup_hash': 14, 'subgroup_order': 36, 'subgroup_tex': 'C_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 71006739
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 18, 'counter': 100, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.2922.36.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 71006740
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 6, 'counter': 101, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.2922.36.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 71006741
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 6, 'counter': 102, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.2922.36.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 71006742
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 9, 'counter': 103, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.2922.36.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.14', 'subgroup_hash': 14, 'subgroup_order': 36, 'subgroup_tex': 'C_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 71006743
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 9, 'counter': 104, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.2922.36.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 71006744
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 3, 'counter': 105, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.2922.36.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 71006745
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 3, 'counter': 106, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.2922.36.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 71006746
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 3, 'counter': 107, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.2922.36.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.l1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '36.14', 'subgroup_hash': 14, 'subgroup_order': 36, 'subgroup_tex': 'C_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 71006747
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 9, 'counter': 108, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.2922.36.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.m1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 71006748
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 9, 'counter': 109, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.2922.36.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.n1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 71006750
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 3, 'counter': 110, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.2922.36.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.o1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 71006751
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 9, 'counter': 111, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.2922.36.p1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.p1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 71006752
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 112, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.2922.36.q1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.q1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 71006753
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 113, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.2922.36.r1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.r1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 71006754
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 9, 'counter': 114, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.2922.36.s1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.s1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.13', 'subgroup_hash': 13, 'subgroup_order': 36, 'subgroup_tex': 'C_6:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 71006755
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 9, 'counter': 115, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.2922.36.t1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.t1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.6', 'subgroup_hash': 6, 'subgroup_order': 36, 'subgroup_tex': 'C_3:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 71006756
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 9, 'counter': 116, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.2922.36.u1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.u1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.7', 'subgroup_hash': 7, 'subgroup_order': 36, 'subgroup_tex': 'C_3^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 71006757
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 9, 'counter': 117, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.2922.36.v1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.v1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.6', 'subgroup_hash': 6, 'subgroup_order': 36, 'subgroup_tex': 'C_3:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 71006758
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 9, 'counter': 118, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.2922.36.w1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.w1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.6', 'subgroup_hash': 6, 'subgroup_order': 36, 'subgroup_tex': 'C_3:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 71006759
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 3, 'counter': 119, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.2922.36.x1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.x1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.6', 'subgroup_hash': 6, 'subgroup_order': 36, 'subgroup_tex': 'C_3:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 71006761
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 3, 'counter': 120, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.2922.36.y1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.y1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.8', 'subgroup_hash': 8, 'subgroup_order': 36, 'subgroup_tex': 'C_3\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 71006762
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 121, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.2922.36.z1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.z1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.6', 'subgroup_hash': 6, 'subgroup_order': 36, 'subgroup_tex': 'C_3:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 71006763
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 122, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.2922.36.ba1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.ba1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.6', 'subgroup_hash': 6, 'subgroup_order': 36, 'subgroup_tex': 'C_3:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 71006764
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 12, 'counter': 123, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.2922.36.bb1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.bb1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.14', 'subgroup_hash': 14, 'subgroup_order': 36, 'subgroup_tex': 'C_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 71006765
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 12, 'counter': 124, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.2922.36.bc1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.bc1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.3', 'subgroup_hash': 3, 'subgroup_order': 36, 'subgroup_tex': 'C_2^2:C_9', 'supersolvable': False, 'sylow': 0}
  • id: 71006766
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 12, 'counter': 125, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.2922.36.bd1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.bd1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.3', 'subgroup_hash': 3, 'subgroup_order': 36, 'subgroup_tex': 'C_2^2:C_9', 'supersolvable': False, 'sylow': 0}
  • id: 71006767
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 12, 'counter': 126, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.2922.36.be1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.be1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.3', 'subgroup_hash': 3, 'subgroup_order': 36, 'subgroup_tex': 'C_2^2:C_9', 'supersolvable': False, 'sylow': 0}
  • id: 71006768
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 12, 'counter': 127, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.2922.36.bf1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.bf1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.14', 'subgroup_hash': 14, 'subgroup_order': 36, 'subgroup_tex': 'C_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 71006769
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 4, 'counter': 128, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.2922.36.bg1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.bg1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.14', 'subgroup_hash': 14, 'subgroup_order': 36, 'subgroup_tex': 'C_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 71006770
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 9, 'counter': 129, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.2922.36.bh1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.bh1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 71006772
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 3, 'counter': 130, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.2922.36.bi1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.bi1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.4', 'subgroup_hash': 4, 'subgroup_order': 36, 'subgroup_tex': 'D_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 71006773
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 6, 'counter': 131, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.2922.36.bj1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.bj1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 71006774
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 18, 'counter': 132, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.2922.36.bk1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.bk1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 71006775
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 9, 'counter': 133, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.2922.36.bl1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.bl1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 71006776
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 134, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.2922.36.bm1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.bm1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 71006777
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 9, 'counter': 135, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.2922.36.bn1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.bn1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 71006778
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': True, 'core_order': 27, 'counter': 136, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1296.2922.48.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '48.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '48.48', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 48, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 48, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_2\\times S_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 71006779
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 9, 'counter': 137, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.2922.48.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.2', 'subgroup_hash': 2, 'subgroup_order': 27, 'subgroup_tex': 'C_3\\times C_9', 'supersolvable': True, 'sylow': 0}
  • id: 71006780
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 9, 'counter': 138, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.2922.48.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.2', 'subgroup_hash': 2, 'subgroup_order': 27, 'subgroup_tex': 'C_3\\times C_9', 'supersolvable': True, 'sylow': 0}
  • id: 71006781
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 9, 'counter': 139, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.2922.48.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.4', 'subgroup_hash': 4, 'subgroup_order': 27, 'subgroup_tex': 'C_9:C_3', 'supersolvable': True, 'sylow': 0}
  • id: 71006783
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 9, 'counter': 140, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.2922.48.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.4', 'subgroup_hash': 4, 'subgroup_order': 27, 'subgroup_tex': 'C_9:C_3', 'supersolvable': True, 'sylow': 0}
  • id: 71006784
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 3, 'counter': 141, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.2922.48.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.4', 'subgroup_hash': 4, 'subgroup_order': 27, 'subgroup_tex': 'C_9:C_3', 'supersolvable': True, 'sylow': 0}
  • id: 71006785
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 3, 'counter': 142, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.2922.48.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '27.4', 'subgroup_hash': 4, 'subgroup_order': 27, 'subgroup_tex': 'C_9:C_3', 'supersolvable': True, 'sylow': 0}
  • id: 71006786
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': True, 'core_order': 24, 'counter': 143, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1296.2922.54.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '54.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '54.6', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 6, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 54, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_9:C_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 71006787
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 144, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.2922.54.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '54.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.15', 'subgroup_hash': 15, 'subgroup_order': 24, 'subgroup_tex': 'C_2^2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 71006788
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 145, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.2922.54.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 71006789
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 146, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.2922.54.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.7', 'subgroup_hash': 7, 'subgroup_order': 24, 'subgroup_tex': 'C_6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 71006790
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 147, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.2922.54.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '54.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '24.9', 'subgroup_hash': 9, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 71006791
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 6, 'counter': 148, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.2922.54.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 71006792
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 6, 'counter': 149, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.2922.54.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '24.5', 'subgroup_hash': 5, 'subgroup_order': 24, 'subgroup_tex': 'C_4\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 71006794
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 150, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.2922.54.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '54.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '24.10', 'subgroup_hash': 10, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 71006795
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 151, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.2922.54.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '24.8', 'subgroup_hash': 8, 'subgroup_order': 24, 'subgroup_tex': 'C_3:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 71006796
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 152, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.2922.54.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '54.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '24.10', 'subgroup_hash': 10, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 71006797
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 153, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.2922.54.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '24.8', 'subgroup_hash': 8, 'subgroup_order': 24, 'subgroup_tex': 'C_3:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 71006798
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 154, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.2922.54.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.l1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '24.8', 'subgroup_hash': 8, 'subgroup_order': 24, 'subgroup_tex': 'C_3:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 71006799
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 155, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.2922.54.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.m1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.6', 'subgroup_hash': 6, 'subgroup_order': 24, 'subgroup_tex': 'D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 71006800
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 12, 'counter': 156, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.2922.54.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '54.n1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.15', 'subgroup_hash': 15, 'subgroup_order': 24, 'subgroup_tex': 'C_2^2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 71006801
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 4, 'counter': 157, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.2922.54.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '54.o1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.15', 'subgroup_hash': 15, 'subgroup_order': 24, 'subgroup_tex': 'C_2^2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 71006802
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 12, 'counter': 158, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.2922.54.p1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '54.p1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.10', 'subgroup_hash': 10, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 71006803
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 4, 'counter': 159, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.2922.54.q1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '54.q1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.10', 'subgroup_hash': 10, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 71006805
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 4, 'counter': 160, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.2922.54.r1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '54.r1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.10', 'subgroup_hash': 10, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 71006806
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 12, 'counter': 161, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.2922.54.s1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.s1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.8', 'subgroup_hash': 8, 'subgroup_order': 24, 'subgroup_tex': 'C_3:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 71006807
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 4, 'counter': 162, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.2922.54.t1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '54.t1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.10', 'subgroup_hash': 10, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 71006808
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 12, 'counter': 163, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.2922.54.u1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.u1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.8', 'subgroup_hash': 8, 'subgroup_order': 24, 'subgroup_tex': 'C_3:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 71006809
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 12, 'counter': 164, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.2922.54.v1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.v1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.8', 'subgroup_hash': 8, 'subgroup_order': 24, 'subgroup_tex': 'C_3:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 71006810
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 4, 'counter': 165, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.2922.54.w1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.w1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.8', 'subgroup_hash': 8, 'subgroup_order': 24, 'subgroup_tex': 'C_3:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 71006811
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': True, 'core_order': 18, 'counter': 166, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1296.2922.72.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '72.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '72.42', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 42, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 72, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_3\\times S_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 71006812
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 9, 'counter': 167, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.2922.72.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 71006813
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 216, 'characteristic': False, 'core_order': 9, 'counter': 168, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.2922.72.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 71006814
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 3, 'counter': 169, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.2922.72.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 71006816
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 216, 'characteristic': False, 'core_order': 3, 'counter': 170, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.2922.72.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 71006817
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 3, 'counter': 171, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.2922.72.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 71006818
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 1, 'counter': 172, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.2922.72.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 71006819
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 1, 'counter': 173, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.2922.72.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 71006820
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 9, 'counter': 174, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.2922.72.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 71006821
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 3, 'counter': 175, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1296.2922.72.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.2', 'subgroup_hash': 2, 'subgroup_order': 18, 'subgroup_tex': 'C_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 71006822
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 3, 'counter': 176, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1296.2922.72.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.2', 'subgroup_hash': 2, 'subgroup_order': 18, 'subgroup_tex': 'C_{18}', 'supersolvable': True, 'sylow': 0}
  • id: 71006823
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 6, 'counter': 177, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.2922.72.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.l1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 71006824
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 9, 'counter': 178, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.2922.72.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.m1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 71006825
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 9, 'counter': 179, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.2922.72.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.n1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 71006827
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 3, 'counter': 180, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.2922.72.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.o1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 71006828
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 3, 'counter': 181, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.2922.72.p1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.p1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 71006829
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 3, 'counter': 182, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.2922.72.q1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.q1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 71006830
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 9, 'counter': 183, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.2922.72.r1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.r1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 71006831
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 9, 'counter': 184, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.2922.72.s1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.s1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 71006832
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 3, 'counter': 185, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.2922.72.t1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.t1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 71006833
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 186, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.2922.72.u1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.u1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.1', 'subgroup_hash': 1, 'subgroup_order': 18, 'subgroup_tex': 'D_9', 'supersolvable': True, 'sylow': 0}
  • id: 71006834
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 9, 'counter': 187, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.2922.72.v1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.v1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 71006835
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 188, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.2922.72.w1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.w1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 71006836
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 189, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.2922.72.x1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.x1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 71006838
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 9, 'counter': 190, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.2922.72.y1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.y1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.4', 'subgroup_hash': 4, 'subgroup_order': 18, 'subgroup_tex': 'C_3:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 71006839
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 3, 'counter': 191, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.2922.72.z1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.z1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.1', 'subgroup_hash': 1, 'subgroup_order': 18, 'subgroup_tex': 'D_9', 'supersolvable': True, 'sylow': 0}
  • id: 71006840
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 3, 'counter': 192, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.2922.72.ba1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ba1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.1', 'subgroup_hash': 1, 'subgroup_order': 18, 'subgroup_tex': 'D_9', 'supersolvable': True, 'sylow': 0}
  • id: 71006841
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 4, 'counter': 193, 'cyclic': False, 'direct': None, 'hall': 2, 'label': '1296.2922.81.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '81.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 2}
  • id: 71006842
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 216, 'characteristic': True, 'core_order': 12, 'counter': 194, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1296.2922.108.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '108.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '108.38', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 38, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 108, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3\\times S_3^2', 'simple': False, 'solvable': True, 'special_labels': [], '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: 71006843
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': True, 'core_order': 12, 'counter': 195, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1296.2922.108.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '108.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '108.26', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 26, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 108, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{18}:C_6', 'simple': False, 'solvable': True, 'special_labels': ['C5'], 'split': True, '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: 71006844
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 3, 'counter': 196, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.2922.108.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 71006845
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 1, 'counter': 197, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.2922.108.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 71006846
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 1, 'counter': 198, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.2922.108.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 71006847
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 6, 'counter': 199, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.2922.108.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 71006850
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 3, 'counter': 200, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.2922.108.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 71006851
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 1, 'counter': 201, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.2922.108.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 71006852
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 1, 'counter': 202, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.2922.108.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 71006853
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 3, 'counter': 203, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.2922.108.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 71006854
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 3, 'counter': 204, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.2922.108.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 71006855
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 1, 'counter': 205, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.2922.108.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.l1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 71006856
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1, 'counter': 206, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.2922.108.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.m1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 71006857
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 3, 'counter': 207, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.2922.108.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.n1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 71006858
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 208, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.2922.108.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.o1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 71006859
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 209, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.2922.108.p1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.p1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 71006861
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 210, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.2922.108.q1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.q1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 71006862
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 211, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.2922.108.r1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.r1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 71006863
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 3, 'counter': 212, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.2922.108.s1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.s1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.1', 'subgroup_hash': 1, 'subgroup_order': 12, 'subgroup_tex': 'C_3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 71006864
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 213, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.2922.108.t1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.t1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.1', 'subgroup_hash': 1, 'subgroup_order': 12, 'subgroup_tex': 'C_3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 71006865
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 3, 'counter': 214, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1296.2922.108.u1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.u1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 71006866
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 215, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.2922.108.v1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.v1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.1', 'subgroup_hash': 1, 'subgroup_order': 12, 'subgroup_tex': 'C_3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 71006867
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 1, 'counter': 216, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1296.2922.108.w1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.w1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 71006868
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 217, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1296.2922.108.x1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.x1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 71006869
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 218, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.2922.108.y1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.y1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.1', 'subgroup_hash': 1, 'subgroup_order': 12, 'subgroup_tex': 'C_3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 71006870
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1, 'counter': 219, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1296.2922.108.z1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.z1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 71006872
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 216, 'characteristic': False, 'core_order': 4, 'counter': 220, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.2922.108.ba1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.ba1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 71006873
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 4, 'counter': 221, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.2922.108.bb1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.bb1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 71006874
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 4, 'counter': 222, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.2922.108.bc1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.bc1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 71006875
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 223, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.2922.108.bd1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.bd1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 71006876
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 224, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.2922.108.be1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.be1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 71006877
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 6, 'counter': 225, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.2922.108.bf1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.bf1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 71006878
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 226, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.2922.108.bg1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.bg1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 71006879
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 227, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.2922.108.bh1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.bh1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 71006880
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 228, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.2922.108.bi1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.bi1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 71006881
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 324, 'characteristic': True, 'core_order': 9, 'counter': 229, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1296.2922.144.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '144.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '144.188', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 188, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 144, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_6\\times S_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 71006883
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 216, 'characteristic': True, 'core_order': 9, 'counter': 230, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1296.2922.144.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '144.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '144.183', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 183, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 144, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'S_3\\times S_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 71006884
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 3, 'counter': 231, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.2922.144.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, '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: 71006885
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 3, 'counter': 232, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1296.2922.144.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, '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: 71006886
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 3, 'counter': 233, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1296.2922.144.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, '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: 71006887
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 3, 'counter': 234, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1296.2922.144.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, '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: 71006888
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 3, 'counter': 235, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1296.2922.144.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, '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: 71006889
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 216, 'characteristic': False, 'core_order': 3, 'counter': 236, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.2922.144.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, '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: 71006890
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 1, 'counter': 237, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.2922.144.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, '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: 71006891
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 238, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.2922.162.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '162.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 71006892
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 239, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.2922.162.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '162.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 71006894
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 240, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.2922.162.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '162.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 71006895
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 241, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.2922.162.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '162.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 71006896
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 4, 'counter': 242, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.2922.162.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '162.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 71006897
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 4, 'counter': 243, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.2922.162.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '162.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 71006898
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 4, 'counter': 244, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.2922.162.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '162.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 71006899
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': True, 'centralizer_order': 216, 'characteristic': True, 'core_order': 6, 'counter': 245, 'cyclic': False, 'direct': True, 'hall': 0, 'label': '1296.2922.216.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '216.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '216.90', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 90, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 216, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_3^2.S_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
  • id: 71006900
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 216, 'characteristic': False, 'core_order': 3, 'counter': 246, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1296.2922.216.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, '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: 71006901
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 216, 'characteristic': False, 'core_order': 3, 'counter': 247, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1296.2922.216.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 71006902
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 432, 'characteristic': False, 'core_order': 1, 'counter': 248, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1296.2922.216.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, '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: 71006903
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 216, 'characteristic': False, 'core_order': 1, 'counter': 249, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1296.2922.216.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, '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: 71006905
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 1, 'counter': 250, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1296.2922.216.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, '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: 71006906
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 216, 'characteristic': False, 'core_order': 1, 'counter': 251, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1296.2922.216.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, '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: 71006907
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 1, 'counter': 252, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1296.2922.216.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, '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: 71006908
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 216, 'characteristic': False, 'core_order': 3, 'counter': 253, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1296.2922.216.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, '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: 71006909
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 1, 'counter': 254, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1296.2922.216.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, '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: 71006910
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 3, 'counter': 255, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1296.2922.216.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, '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: 71006911
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 1, 'counter': 256, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1296.2922.216.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.l1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, '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: 71006912
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 1, 'counter': 257, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1296.2922.216.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.m1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 71006913
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 3, 'counter': 258, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.2922.216.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.n1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
  • id: 71006914
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 3, 'counter': 259, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1296.2922.216.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.o1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 71006916
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 1, 'counter': 260, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1296.2922.216.p1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.p1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 71006917
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1, 'counter': 261, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1296.2922.216.q1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.q1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 71006918
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 3, 'counter': 262, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.2922.216.r1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.r1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
  • id: 71006919
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 263, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1296.2922.216.s1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.s1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 71006920
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 264, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.2922.216.t1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.t1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
  • id: 71006921
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 265, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.2922.216.u1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.u1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
  • id: 71006922
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 266, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.2922.216.v1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.v1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
  • id: 71006923
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 216, 'characteristic': True, 'core_order': 4, 'counter': 267, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1296.2922.324.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '324.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '324.118', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 118, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 324, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3^2.S_3^2', 'simple': False, 'solvable': True, 'special_labels': ['D2'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 71006924
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 1, 'counter': 268, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.2922.324.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '324.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 71006925
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 1, 'counter': 269, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.2922.324.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '324.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 71006927
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 1, 'counter': 270, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.2922.324.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '324.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 71006928
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 271, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.2922.324.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '324.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 71006929
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 1, 'counter': 272, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1296.2922.324.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '324.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 71006930
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 273, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1296.2922.324.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '324.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 71006931
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 274, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.2922.324.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '324.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 71006932
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 275, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.2922.324.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '324.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 71006933
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 648, 'characteristic': True, 'core_order': 3, 'counter': 276, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '1296.2922.432.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '432.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '432.745', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 745, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 432, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_6^2:D_6', 'simple': True, 'solvable': True, 'special_labels': ['Phi'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '3.1', 'subgroup_hash': 1, 'subgroup_order': 3, 'subgroup_tex': 'C_3', 'supersolvable': True, 'sylow': 0}
  • id: 71006934
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 648, 'characteristic': True, 'core_order': 3, 'counter': 277, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '1296.2922.432.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '432.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '432.533', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 533, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 432, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_6^2.D_6', 'simple': True, 'solvable': True, 'special_labels': ['C6'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '3.1', 'subgroup_hash': 1, 'subgroup_order': 3, 'subgroup_tex': 'C_3', 'supersolvable': True, 'sylow': 0}
  • id: 71006935
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 432, 'characteristic': False, 'core_order': 1, 'counter': 278, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1296.2922.432.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, '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: 71006936
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 324, 'characteristic': False, 'core_order': 1, 'counter': 279, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1296.2922.432.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, '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: 71006938
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 216, 'characteristic': False, 'core_order': 1, 'counter': 280, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1296.2922.432.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, '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: 71006939
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 432, 'characteristic': False, 'core_order': 1, 'counter': 281, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1296.2922.648.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, '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: 71006940
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 432, 'characteristic': False, 'core_order': 1, 'counter': 282, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1296.2922.648.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, '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: 71006941
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 1, 'counter': 283, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1296.2922.648.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, '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: 71006942
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 1, 'counter': 284, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1296.2922.648.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, '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: 71006943
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 285, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1296.2922.648.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 648, '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: 71006944
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1296.2922', 'ambient_counter': 2922, 'ambient_order': 1296, 'ambient_tex': 'C_6^2.S_3^2', 'central': True, 'central_factor': False, 'centralizer_order': 1296, 'characteristic': True, 'core_order': 1, 'counter': 286, 'cyclic': True, 'direct': True, 'hall': 1, 'label': '1296.2922.1296.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '1296.a1.a1', 'outer_equivalence': False, 'perfect': True, 'proper': False, 'quotient': '1296.2922', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 2922, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 1296, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_6^2.S_3^2', 'simple': False, 'solvable': True, 'special_labels': ['Z', 'PC', 'U0', 'D3', 'C7'], 'split': True, 'standard_generators': False, 'stem': True, 'subgroup': '1.1', 'subgroup_hash': 1, 'subgroup_order': 1, 'subgroup_tex': 'C_1', 'supersolvable': True, 'sylow': 1}
• gps_subgroup_data •

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

  
  
  • id: 71006737
    {'ambient': '1296.2922', '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': '1296.a1.a1', 'complements': ['1296.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': [], 'contains': ['2.a1.a1', '2.b1.a1', '2.c1.a1', '3.a1.a1', '3.b1.a1', '3.c1.a1', '4.b1.a1'], 'core': '1.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1707, 4170, 1258, 4212, 2303, 4875, 2283, 5124], 'generators': [3, 432, 36, 54, 48, 648, 108, 2], 'label': '1296.2922.1.a1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '1.a1.a1', 'normal_contained_in': [], 'normal_contains': ['2.a1.a1', '2.b1.a1', '2.c1.a1', '3.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '1.a1.a1', 'projective_image': '1296.2922', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1296.2922'}
  • id: 71006738
    {'ambient': '1296.2922', 'aut_centralizer_order': 36, 'aut_label': '6.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '36.10', 'aut_weyl_index': 36, 'centralizer': '36.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '3.c1.a1'], 'contains': ['12.a1.a1', '12.d1.a1', '12.e1.a1', '18.a1.a1', '18.o1.a1', '18.r1.a1'], 'core': '6.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5758, 9380, 6329, 9475, 4760, 9202, 5178, 798], 'generators': [54, 432, 36, 108, 648, 2], 'label': '1296.2922.6.a1.a1', 'mobius_quo': 0, 'mobius_sub': 3, 'normal_closure': '6.a1.a1', 'normal_contained_in': ['2.a1.a1'], 'normal_contains': ['12.a1.a1', '18.a1.a1', '24.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '6.a1.a1', 'projective_image': '1296.2922', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.a1.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 71006739
    {'ambient': '1296.2922', 'aut_centralizer_order': 36, 'aut_label': '36.e1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '12.4', 'aut_weyl_index': 108, 'centralizer': '36.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.d1.a1', '18.a1.a1', '18.f1.a1', '18.g1.a1'], 'contains': ['72.a1.a1', '72.b1.a1', '72.n1.a1', '108.c1.a1', '108.f1.a1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4294, -1, 4325, -1, 4224, -1, 4022, -1], 'generators': [54, 108, 36, 432], 'label': '1296.2922.36.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1.a1', 'old_label': '36.e1.a1', 'projective_image': '1296.2922', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.e1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 71006740
    {'ambient': '1296.2922', 'aut_centralizer_order': 72, 'aut_label': '36.f1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '6.1', 'aut_weyl_index': 216, 'centralizer': '18.u1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.d1.a1', '18.e1.a1', '18.h1.a1', '18.r1.a1'], 'contains': ['72.e1.a1', '72.l1.a1', '72.o1.a1', '108.d1.a1', '108.f1.a1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8918, -1, 8902, -1, 7659, -1, 7738, -1], 'generators': [54, 648, 2, 432], 'label': '1296.2922.36.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1.a1', 'old_label': '36.f1.a1', 'projective_image': '1296.2922', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.f1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 71006741
    {'ambient': '1296.2922', 'aut_centralizer_order': 36, 'aut_label': '36.g1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '6.1', 'aut_weyl_index': 216, 'centralizer': '36.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.d1.a1', '18.r1.a1'], 'contains': ['72.f1.a1', '72.l1.a1', '72.p1.a1', '108.e1.a1', '108.f1.a1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [9489, -1, 9515, -1, 7531, -1, 7609, -1], 'generators': [54, 108, 2, 432], 'label': '1296.2922.36.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.a1', 'old_label': '36.g1.a1', 'projective_image': '1296.2922', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.g1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 71006742
    {'ambient': '1296.2922', 'aut_centralizer_order': 72, 'aut_label': '36.h1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '2.1', 'aut_weyl_index': 648, 'centralizer': '18.o1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.e1.a1', '18.i1.a1', '18.j1.a1', '18.o1.a1'], 'contains': ['72.c1.a1', '72.m1.a1', '108.g1.a1', '108.h1.a1', '108.i1.a1'], 'core': '144.b1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [7212, -1, 6605, -1, 6611, -1, 6468, -1], 'generators': [702, 108, 2, 36], 'label': '1296.2922.36.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '36.h1.a1', 'projective_image': '1296.2922', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.h1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 71006743
    {'ambient': '1296.2922', 'aut_centralizer_order': 36, 'aut_label': '36.i1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '12.4', 'aut_weyl_index': 108, 'centralizer': '36.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.e1.a1', '18.a1.a1', '18.l1.a1', '18.n1.a1'], 'contains': ['72.b1.a1', '72.n1.a1', '108.g1.a1', '108.j1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5350, -1, 5008, -1, 5128, -1, 4709, -1], 'generators': [702, 108, 36, 432], 'label': '1296.2922.36.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1.a1', 'old_label': '36.i1.a1', 'projective_image': '1296.2922', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.i1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 71006744
    {'ambient': '1296.2922', 'aut_centralizer_order': 36, 'aut_label': '36.j1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '12.4', 'aut_weyl_index': 108, 'centralizer': '36.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.e1.a1', '18.k1.a1', '18.m1.a1', '18.r1.a1'], 'contains': ['72.e1.a1', '72.p1.a1', '108.h1.a1', '108.j1.a1'], 'core': '432.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [9666, -1, 9825, -1, 8777, -1, 8997, -1], 'generators': [162, 648, 2, 432], 'label': '1296.2922.36.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1.a1', 'old_label': '36.j1.a1', 'projective_image': '1296.2922', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.j1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 71006745
    {'ambient': '1296.2922', 'aut_centralizer_order': 36, 'aut_label': '36.k1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '6.1', 'aut_weyl_index': 216, 'centralizer': '36.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.e1.a1', '18.r1.a1'], 'contains': ['72.f1.a1', '72.o1.a1', '72.p1.a1', '108.i1.a1', '108.j1.a1'], 'core': '432.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [9968, -1, 9677, -1, 7789, -1, 8087, -1], 'generators': [702, 108, 2, 432], 'label': '1296.2922.36.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.a1', 'old_label': '36.k1.a1', 'projective_image': '1296.2922', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.k1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 71006746
    {'ambient': '1296.2922', 'aut_centralizer_order': 36, 'aut_label': '36.l1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '4.2', 'aut_weyl_index': 324, 'centralizer': '36.l1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.f1.a1', '18.e1.a1', '18.k1.a1', '18.s1.a1'], 'contains': ['72.e1.a1', '72.q1.a1', '108.k1.a1', '108.l1.a1', '108.m1.a1'], 'core': '432.b1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [8023, -1, 7849, -1, 7167, -1, 7294, -1], 'generators': [3, 648, 2, 432], 'label': '1296.2922.36.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1.a1', 'old_label': '36.l1.a1', 'projective_image': '1296.2922', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.l1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 71006747
    {'ambient': '1296.2922', 'aut_centralizer_order': 18, 'aut_label': '36.m1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '24.14', 'aut_weyl_index': 54, 'centralizer': '72.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.f1.a1', '18.f1.a1', '18.l1.a1', '18.t1.a1'], 'contains': ['72.b1.a1', '72.r1.a1', '108.k1.a1', '108.n1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4149, -1, 4009, -1, 3611, -1, 3508, -1], 'generators': [3, 648, 432, 36], 'label': '1296.2922.36.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1.a1', 'old_label': '36.m1.a1', 'projective_image': '1296.2922', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.m1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 71006748
    {'ambient': '1296.2922', 'aut_centralizer_order': 36, 'aut_label': '36.n1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '12.4', 'aut_weyl_index': 108, 'centralizer': '36.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.f1.a1', '18.c1.a1', '18.i1.a1', '18.u1.a1'], 'contains': ['72.c1.a1', '72.s1.a1', '108.l1.a1', '108.n1.a1'], 'core': '144.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5966, -1, 5427, -1, 4353, -1, 4430, -1], 'generators': [3, 648, 2, 36], 'label': '1296.2922.36.n1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1.a1', 'old_label': '36.n1.a1', 'projective_image': '1296.2922', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.n1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 71006749
    {'ambient': '1296.2922', 'aut_centralizer_order': 3, 'aut_label': '6.b1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '432.745', 'aut_weyl_index': 3, 'centralizer': '432.a1.a1', 'complements': ['216.p1.a1', '216.q1.a1', '216.s1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '3.a1.a1'], 'contains': ['12.b1.a1', '18.a1.a1', '18.p1.a1', '24.d1.a1'], 'core': '6.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1409, 7478, 1988, 7553, 2116, 7488, 2596, 2512], 'generators': [54, 432, 648, 84, 36, 756], 'label': '1296.2922.6.b1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '6.b1.a1', 'normal_contained_in': ['2.a1.a1', '3.a1.a1'], 'normal_contains': ['12.b1.a1', '18.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '6.b1.a1', 'projective_image': '1296.2922', 'quotient_action_image': '6.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '6.b1.a1', 'subgroup_fusion': None, 'weyl_group': '432.745'}
  • id: 71006750
    {'ambient': '1296.2922', 'aut_centralizer_order': 18, 'aut_label': '36.o1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '12.4', 'aut_weyl_index': 108, 'centralizer': '72.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.f1.a1', '18.v1.a1'], 'contains': ['72.d1.a1', '72.t1.a1', '108.m1.a1', '108.n1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [3902, -1, 2946, -1, 3402, -1, 3141, -1], 'generators': [3, 648, 434, 36], 'label': '1296.2922.36.o1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.l1.a1', 'old_label': '36.o1.a1', 'projective_image': '1296.2922', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.o1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 71006751
    {'ambient': '1296.2922', 'aut_centralizer_order': 12, 'aut_label': '36.p1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '12.4', 'aut_weyl_index': 108, 'centralizer': '108.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.g1.a1', '18.c1.a1', '18.j1.a1', '18.w1.a1'], 'contains': ['72.c1.a1', '72.v1.a1', '108.o1.a1', '108.p1.a1'], 'core': '144.b1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [6784, -1, 6331, -1, 4482, -1, 3804, -1], 'generators': [81, 756, 2, 36], 'label': '1296.2922.36.p1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '36.p1.a1', 'projective_image': '1296.2922', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.p1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 71006752
    {'ambient': '1296.2922', 'aut_centralizer_order': 12, 'aut_label': '36.q1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '12.4', 'aut_weyl_index': 108, 'centralizer': '108.l1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.g1.a1', '18.e1.a1', '18.m1.a1', '18.x1.a1'], 'contains': ['72.e1.a1', '72.w1.a1', '108.o1.a1', '108.q1.a1'], 'core': '432.b1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [7835, -1, 8213, -1, 7401, -1, 7191, -1], 'generators': [81, 756, 38, 432], 'label': '1296.2922.36.q1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1.a1', 'old_label': '36.q1.a1', 'projective_image': '1296.2922', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.q1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 71006753
    {'ambient': '1296.2922', 'aut_centralizer_order': 6, 'aut_label': '36.r1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '12.4', 'aut_weyl_index': 108, 'centralizer': '216.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.g1.a1', '18.y1.a1'], 'contains': ['72.g1.a1', '72.x1.a1', '108.o1.a1', '108.r1.a1'], 'core': '1296.a1.a1', 'coset_action_label': '36T1990', 'count': 18, 'diagramx': [4408, -1, 7298, -1, 4920, -1, 4151, -1], 'generators': [81, 756, 434, 900], 'label': '1296.2922.36.r1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.y1.a1', 'old_label': '36.r1.a1', 'projective_image': '1296.2922', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.r1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 71006754
    {'ambient': '1296.2922', 'aut_centralizer_order': 6, 'aut_label': '36.s1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '72.46', 'aut_weyl_index': 18, 'centralizer': '216.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.g1.a1', '18.f1.a1', '18.n1.a1', '18.z1.a1'], 'contains': ['72.b1.a1', '72.y1.a1', '108.p1.a1', '108.q1.a1', '108.r1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5013, -1, 4879, -1, 4626, -1, 3364, -1], 'generators': [81, 756, 36, 432], 'label': '1296.2922.36.s1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1.a1', 'old_label': '36.s1.a1', 'projective_image': '1296.2922', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.s1.a1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 71006755
    {'ambient': '1296.2922', 'aut_centralizer_order': 18, 'aut_label': '36.t1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '24.14', 'aut_weyl_index': 54, 'centralizer': '72.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.h1.a1', '18.g1.a1', '18.n1.a1', '18.t1.a1'], 'contains': ['72.b1.a1', '108.s1.a1', '108.u1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5680, -1, 5169, -1, 5925, -1, 5833, -1], 'generators': [111, 432, 648, 36], 'label': '1296.2922.36.t1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1.a1', 'old_label': '36.t1.a1', 'projective_image': '1296.2922', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.t1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 71006756
    {'ambient': '1296.2922', 'aut_centralizer_order': 6, 'aut_label': '36.u1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '72.46', 'aut_weyl_index': 18, 'centralizer': '216.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.i1.a1', '18.g1.a1', '18.l1.a1', '18.z1.a1'], 'contains': ['72.b1.a1', '108.t1.a1', '108.v1.a1', '108.y1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4717, -1, 4430, -1, 6218, -1, 6375, -1], 'generators': [729, 756, 36, 432], 'label': '1296.2922.36.u1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1.a1', 'old_label': '36.u1.a1', 'projective_image': '1296.2922', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.u1.a1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 71006757
    {'ambient': '1296.2922', 'aut_centralizer_order': 36, 'aut_label': '36.v1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '12.4', 'aut_weyl_index': 108, 'centralizer': '36.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.h1.a1', '18.d1.a1', '18.j1.a1', '18.u1.a1'], 'contains': ['72.c1.a1', '108.s1.a1', '108.w1.a1'], 'core': '144.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7349, -1, 6711, -1, 6729, -1, 6081, -1], 'generators': [111, 2, 648, 36], 'label': '1296.2922.36.v1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1.a1', 'old_label': '36.v1.a1', 'projective_image': '1296.2922', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.v1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 71006758
    {'ambient': '1296.2922', 'aut_centralizer_order': 12, 'aut_label': '36.w1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '12.4', 'aut_weyl_index': 108, 'centralizer': '108.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.i1.a1', '18.d1.a1', '18.i1.a1', '18.w1.a1'], 'contains': ['72.c1.a1', '108.t1.a1', '108.x1.a1'], 'core': '144.b1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [6592, -1, 5852, -1, 6889, -1, 6587, -1], 'generators': [729, 2, 756, 36], 'label': '1296.2922.36.w1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '36.w1.a1', 'projective_image': '1296.2922', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.w1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 71006759
    {'ambient': '1296.2922', 'aut_centralizer_order': 18, 'aut_label': '36.x1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '12.4', 'aut_weyl_index': 108, 'centralizer': '72.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.h1.a1', '18.v1.a1'], 'contains': ['72.d1.a1', '108.s1.a1', '108.z1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [4567, -1, 3783, -1, 5422, -1, 5429, -1], 'generators': [111, 434, 648, 36], 'label': '1296.2922.36.x1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.l1.a1', 'old_label': '36.x1.a1', 'projective_image': '1296.2922', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.x1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 71006870
    {'ambient': '1296.2922', 'aut_centralizer_order': 36, 'aut_label': '108.z1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '2.1', 'aut_weyl_index': 648, 'centralizer': '36.y1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.x1.a1', '36.y1.a1', '54.r1.a1'], 'contains': ['216.g1.a1', '324.f1.a1'], 'core': '1296.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [5265, -1, 3441, -1, 7715, -1, 7387, -1], 'generators': [111, 434, 648], 'label': '1296.2922.108.z1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.s1.a1', 'old_label': '108.z1.a1', 'projective_image': '1296.2922', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.z1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 71006760
    {'ambient': '1296.2922', 'aut_centralizer_order': 3, 'aut_label': '6.c1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '432.533', 'aut_weyl_index': 3, 'centralizer': '432.b1.a1', 'complements': ['216.j1.a1', '216.m1.a1', '216.l1.a1', '216.s1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '3.a1.a1'], 'contains': ['12.b1.a1', '18.b1.a1', '18.t1.a1', '24.h1.a1'], 'core': '6.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1251, 2179, 930, 2201, 2402, 1964, 2202, 8035], 'generators': [3, 648, 108, 432, 48, 36], 'label': '1296.2922.6.c1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '6.c1.a1', 'normal_contained_in': ['2.b1.a1', '3.a1.a1'], 'normal_contains': ['12.b1.a1', '18.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '6.c1.a1', 'projective_image': '1296.2922', 'quotient_action_image': '6.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '6.c1.a1', 'subgroup_fusion': None, 'weyl_group': '432.533'}
  • id: 71006761
    {'ambient': '1296.2922', 'aut_centralizer_order': 36, 'aut_label': '36.y1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '4.2', 'aut_weyl_index': 324, 'centralizer': '36.y1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.h1.a1', '18.h1.a1', '18.m1.a1', '18.s1.a1'], 'contains': ['72.e1.a1', '108.u1.a1', '108.w1.a1', '108.z1.a1'], 'core': '432.b1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [9122, -1, 9236, -1, 9486, -1, 8726, -1], 'generators': [111, 2, 432, 648], 'label': '1296.2922.36.y1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1.a1', 'old_label': '36.y1.a1', 'projective_image': '1296.2922', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.y1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 71006762
    {'ambient': '1296.2922', 'aut_centralizer_order': 12, 'aut_label': '36.z1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '12.4', 'aut_weyl_index': 108, 'centralizer': '108.w1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.i1.a1', '18.h1.a1', '18.k1.a1', '18.x1.a1'], 'contains': ['72.e1.a1', '108.v1.a1', '108.x1.a1'], 'core': '432.b1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [8663, -1, 8440, -1, 9800, -1, 9230, -1], 'generators': [729, 38, 756, 432], 'label': '1296.2922.36.z1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1.a1', 'old_label': '36.z1.a1', 'projective_image': '1296.2922', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.z1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 71006763
    {'ambient': '1296.2922', 'aut_centralizer_order': 6, 'aut_label': '36.ba1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '12.4', 'aut_weyl_index': 108, 'centralizer': '216.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.i1.a1', '18.y1.a1'], 'contains': ['72.g1.a1', '108.x1.a1', '108.y1.a1'], 'core': '1296.a1.a1', 'coset_action_label': '36T1989', 'count': 18, 'diagramx': [5477, -1, 8020, -1, 7048, -1, 6746, -1], 'generators': [729, 434, 756, 900], 'label': '1296.2922.36.ba1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.y1.a1', 'old_label': '36.ba1.a1', 'projective_image': '1296.2922', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.ba1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 71006764
    {'ambient': '1296.2922', 'aut_centralizer_order': 108, 'aut_label': '36.bb1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '6.1', 'aut_weyl_index': 216, 'centralizer': '12.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.a1.a1', '12.l1.a1', '12.m1.a1', '18.v1.a1'], 'contains': ['72.d1.a1', '108.a1.a1', '108.bc1.a1'], 'core': '108.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2341, -1, 2105, -1, 3507, -1, 3246, -1], 'generators': [108, 648, 434, 36], 'label': '1296.2922.36.bb1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '36.bb1.a1', 'projective_image': '1296.2922', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.bb1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 71006765
    {'ambient': '1296.2922', 'aut_centralizer_order': 18, 'aut_label': '36.bc1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '36.11', 'aut_weyl_index': 36, 'centralizer': '72.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.c1.a1', '12.j1.a1', '12.m1.a1', '18.q1.a1'], 'contains': ['108.a1.a1', '144.e1.a1'], 'core': '108.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2523, -1, 2419, -1, 1535, -1, 2667, -1], 'generators': [86, 36, 108, 648], 'label': '1296.2922.36.bc1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '36.bc1.a1', 'projective_image': '1296.2922', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.bc1.a1', 'subgroup_fusion': None, 'weyl_group': '36.11'}
  • id: 71006766
    {'ambient': '1296.2922', 'aut_centralizer_order': 9, 'aut_label': '36.bd1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '72.42', 'aut_weyl_index': 18, 'centralizer': '144.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.b1.a1', '12.k1.a1', '12.m1.a1', '18.bb1.a1'], 'contains': ['108.a1.a1', '144.f1.a1'], 'core': '108.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [549, -1, 2290, -1, 1751, -1, 2343, -1], 'generators': [516, 36, 108, 648], 'label': '1296.2922.36.bd1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '36.bd1.a1', 'projective_image': '1296.2922', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.bd1.a1', 'subgroup_fusion': None, 'weyl_group': '72.42'}
  • id: 71006767
    {'ambient': '1296.2922', 'aut_centralizer_order': 9, 'aut_label': '36.be1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '36.11', 'aut_weyl_index': 36, 'centralizer': '144.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.j1.a1', '12.k1.a1', '12.l1.a1', '12.m1.a1'], 'contains': ['108.a1.a1', '144.g1.a1'], 'core': '108.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [1820, -1, 2516, -1, 1643, -1, 2451, -1], 'generators': [518, 36, 108, 648], 'label': '1296.2922.36.be1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '36.be1.a1', 'projective_image': '1296.2922', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.be1.a1', 'subgroup_fusion': None, 'weyl_group': '36.11'}
  • id: 71006768
    {'ambient': '1296.2922', 'aut_centralizer_order': 108, 'aut_label': '36.bf1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '4.2', 'aut_weyl_index': 324, 'centralizer': '12.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.a1.a1', '18.r1.a1', '18.s1.a1', '18.x1.a1'], 'contains': ['72.e1.a1', '72.f1.a1', '108.b1.a1', '108.ba1.a1', '108.bc1.a1'], 'core': '108.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7745, -1, 7488, -1, 7892, -1, 7505, -1], 'generators': [108, 648, 2, 432], 'label': '1296.2922.36.bf1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1.a1', 'old_label': '36.bf1.a1', 'projective_image': '1296.2922', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.bf1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 71006769
    {'ambient': '1296.2922', 'aut_centralizer_order': 108, 'aut_label': '36.bg1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '2.1', 'aut_weyl_index': 648, 'centralizer': '12.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.a1.a1', '18.y1.a1'], 'contains': ['72.g1.a1', '72.h1.a1', '108.ba1.a1', '108.bb1.a1', '108.bc1.a1'], 'core': '324.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [3523, -1, 7011, -1, 5717, -1, 5636, -1], 'generators': [108, 648, 2, 468], 'label': '1296.2922.36.bg1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.n1.a1', 'old_label': '36.bg1.a1', 'projective_image': '1296.2922', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.bg1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 71006770
    {'ambient': '1296.2922', 'aut_centralizer_order': 12, 'aut_label': '36.bh1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '6.1', 'aut_weyl_index': 216, 'centralizer': '108.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.n1.a1', '12.o1.a1', '18.c1.a1'], 'contains': ['72.i1.a1', '72.s1.a1', '72.v1.a1', '108.bd1.a1', '108.be1.a1'], 'core': '144.b1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [2185, -1, 1947, -1, 2124, -1, 1767, -1], 'generators': [3, 54, 2, 36], 'label': '1296.2922.36.bh1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.c1.a1', 'old_label': '36.bh1.a1', 'projective_image': '1296.2922', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.bh1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 71006771
    {'ambient': '1296.2922', 'aut_centralizer_order': 6, 'aut_label': '6.d1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '216.90', 'aut_weyl_index': 6, 'centralizer': '216.a1.a1', 'complements': ['216.a1.a1', '216.n1.a1', '216.u1.a1', '216.v1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '3.b1.a1'], 'contains': ['12.c1.a1', '18.b1.a1', '18.u1.a1', '24.i1.a1'], 'core': '6.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2650, 520, 803, 525, 2259, 469, 2453, 9531], 'generators': [3, 648, 108, 2, 48, 36], 'label': '1296.2922.6.d1.a1', 'mobius_quo': 0, 'mobius_sub': 3, 'normal_closure': '6.d1.a1', 'normal_contained_in': ['2.b1.a1'], 'normal_contains': ['12.c1.a1', '18.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '6.d1.a1', 'projective_image': '1296.2922', 'quotient_action_image': '1.1', 'quotient_action_kernel': '6.1', 'quotient_action_kernel_order': 6, 'quotient_fusion': None, 'short_label': '6.d1.a1', 'subgroup_fusion': None, 'weyl_group': '216.90'}
  • id: 71006772
    {'ambient': '1296.2922', 'aut_centralizer_order': 2, 'aut_label': '36.bi1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '54.6', 'aut_weyl_index': 24, 'centralizer': '648.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['9.b1.a1', '12.n1.a1', '12.p1.a1'], 'contains': ['72.j1.a1', '72.u1.a1', '72.z1.a1', '108.be1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [825, -1, 93, -1, 1174, -1, 946, -1], 'generators': [3, 54, 48, 36], 'label': '1296.2922.36.bi1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.n1.a1', 'old_label': '36.bi1.a1', 'projective_image': '1296.2922', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.bi1.a1', 'subgroup_fusion': None, 'weyl_group': '54.6'}
  • id: 71006773
    {'ambient': '1296.2922', 'aut_centralizer_order': 12, 'aut_label': '36.bj1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '6.1', 'aut_weyl_index': 216, 'centralizer': '108.l1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.o1.a1', '18.e1.a1'], 'contains': ['72.l1.a1', '72.q1.a1', '72.w1.a1', '108.bd1.a1', '108.bf1.a1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [4854, -1, 4569, -1, 2995, -1, 4927, -1], 'generators': [3, 54, 2, 432], 'label': '1296.2922.36.bj1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1.a1', 'old_label': '36.bj1.a1', 'projective_image': '1296.2922', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.bj1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 71006774
    {'ambient': '1296.2922', 'aut_centralizer_order': 6, 'aut_label': '36.bk1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '36.10', 'aut_weyl_index': 36, 'centralizer': '216.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.o1.a1', '12.p1.a1', '18.f1.a1'], 'contains': ['72.a1.a1', '72.r1.a1', '72.y1.a1', '108.be1.a1', '108.bf1.a1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2095, -1, 1855, -1, 2227, -1, 1663, -1], 'generators': [3, 54, 36, 432], 'label': '1296.2922.36.bk1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1.a1', 'old_label': '36.bk1.a1', 'projective_image': '1296.2922', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.bk1.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 71006775
    {'ambient': '1296.2922', 'aut_centralizer_order': 12, 'aut_label': '36.bl1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '6.1', 'aut_weyl_index': 216, 'centralizer': '108.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.q1.a1', '18.c1.a1'], 'contains': ['72.m1.a1', '72.s1.a1', '72.v1.a1', '108.bg1.a1', '108.bh1.a1'], 'core': '144.b1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [5140, -1, 4751, -1, 2788, -1, 2862, -1], 'generators': [3, 702, 2, 36], 'label': '1296.2922.36.bl1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.c1.a1', 'old_label': '36.bl1.a1', 'projective_image': '1296.2922', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.bl1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 71006776
    {'ambient': '1296.2922', 'aut_centralizer_order': 12, 'aut_label': '36.bm1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '6.1', 'aut_weyl_index': 216, 'centralizer': '108.l1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.q1.a1', '18.e1.a1'], 'contains': ['72.o1.a1', '72.q1.a1', '72.w1.a1', '108.bg1.a1', '108.bi1.a1'], 'core': '432.b1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [7026, -1, 6513, -1, 3124, -1, 5284, -1], 'generators': [3, 702, 2, 432], 'label': '1296.2922.36.bm1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1.a1', 'old_label': '36.bm1.a1', 'projective_image': '1296.2922', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.bm1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 71006777
    {'ambient': '1296.2922', 'aut_centralizer_order': 6, 'aut_label': '36.bn1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '36.10', 'aut_weyl_index': 36, 'centralizer': '216.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.q1.a1', '18.f1.a1'], 'contains': ['72.n1.a1', '72.r1.a1', '72.y1.a1', '108.bh1.a1', '108.bi1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [3993, -1, 4134, -1, 2891, -1, 2759, -1], 'generators': [3, 702, 36, 432], 'label': '1296.2922.36.bn1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1.a1', 'old_label': '36.bn1.a1', 'projective_image': '1296.2922', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.bn1.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 71006778
    {'ambient': '1296.2922', 'aut_centralizer_order': 108, 'aut_label': '48.a1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '12.4', 'aut_weyl_index': 108, 'centralizer': '12.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '24.a1.a1', '24.b1.a1', '24.f1.a1', '24.g1.a1', '24.k1.a1'], 'contains': ['144.a1.a1', '144.b1.a1', '144.c1.a1', '144.h1.a1', '144.i1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2968, 6382, 3409, 7721, 2974, 6301, 2774, 3699], 'generators': [2, 36, 432], 'label': '1296.2922.48.a1.a1', 'mobius_quo': 0, 'mobius_sub': 24, 'normal_closure': '48.a1.a1', 'normal_contained_in': ['12.a1.a1', '24.a1.a1'], 'normal_contains': ['144.a1.a1', '144.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '48.a1.a1', 'projective_image': '1296.2922', 'quotient_action_image': '12.4', 'quotient_action_kernel': '4.2', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '48.a1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 71006779
    {'ambient': '1296.2922', 'aut_centralizer_order': 27, 'aut_label': '48.b1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '12.5', 'aut_weyl_index': 108, 'centralizer': '48.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.b1.a1', '16.a1.a1', '24.d1.a1', '24.h1.a1', '24.n1.a1'], 'contains': ['144.a1.a1', '144.d1.a1', '144.f1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [201, -1, 531, -1, 992, -1, 822, -1], 'generators': [84, 432], 'label': '1296.2922.48.b1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '12.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.a1', 'old_label': '48.b1.a1', 'projective_image': '1296.2922', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.b1.a1', 'subgroup_fusion': None, 'weyl_group': '12.5'}
  • id: 71006780
    {'ambient': '1296.2922', 'aut_centralizer_order': 27, 'aut_label': '48.c1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '6.2', 'aut_weyl_index': 216, 'centralizer': '48.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.j1.a1', '16.a1.a1', '24.e1.a1'], 'contains': ['144.a1.a1', '144.e1.a1', '144.g1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [1407, -1, 1401, -1, 300, -1, 1045, -1], 'generators': [86, 432], 'label': '1296.2922.48.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.a1.a1', 'old_label': '48.c1.a1', 'projective_image': '1296.2922', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.c1.a1', 'subgroup_fusion': None, 'weyl_group': '6.2'}
  • id: 71006781
    {'ambient': '1296.2922', 'aut_centralizer_order': 18, 'aut_label': '48.d1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '18.3', 'aut_weyl_index': 72, 'centralizer': '72.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.c1.a1', '16.a1.a1', '24.c1.a1', '24.i1.a1', '24.l1.a1'], 'contains': ['144.b1.a1', '144.d1.a1', '144.e1.a1'], 'core': '144.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [1008, -1, 661, -1, 883, -1, 1154, -1], 'generators': [2, 84], 'label': '1296.2922.48.d1.a1', 'mobius_quo': None, 'mobius_sub': 6, 'normal_closure': '12.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.a1', 'old_label': '48.d1.a1', 'projective_image': '1296.2922', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.d1.a1', 'subgroup_fusion': None, 'weyl_group': '18.3'}
  • id: 71006782
    {'ambient': '1296.2922', 'aut_centralizer_order': 1, 'aut_label': '6.e1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '1296.2922', 'aut_weyl_index': 1, 'centralizer': '1296.a1.a1', 'complements': ['216.j1.a1', '216.m1.a1', '216.l1.a1', '216.p1.a1', '216.q1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1', '3.a1.a1'], 'contains': ['12.b1.a1', '18.z1.a1', '18.ba1.a1', '18.bb1.a1', '24.n1.a1'], 'core': '6.e1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [853, 4204, 1540, 4246, 2971, 5663, 1741, 4337], 'generators': [81, 648, 756, 48, 432, 36], 'label': '1296.2922.6.e1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '6.e1.a1', 'normal_contained_in': ['2.c1.a1', '3.a1.a1'], 'normal_contains': ['12.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '6.e1.a1', 'projective_image': '1296.2922', 'quotient_action_image': '6.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '6.e1.a1', 'subgroup_fusion': None, 'weyl_group': '1296.2922'}
  • id: 71006783
    {'ambient': '1296.2922', 'aut_centralizer_order': 9, 'aut_label': '48.e1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '18.3', 'aut_weyl_index': 72, 'centralizer': '144.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.k1.a1', '16.a1.a1', '24.m1.a1'], 'contains': ['144.b1.a1', '144.f1.a1', '144.g1.a1'], 'core': '144.b1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [398, -1, 902, -1, 1101, -1, 397, -1], 'generators': [2, 516], 'label': '1296.2922.48.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.c1.a1', 'old_label': '48.e1.a1', 'projective_image': '1296.2922', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.e1.a1', 'subgroup_fusion': None, 'weyl_group': '18.3'}
  • id: 71006784
    {'ambient': '1296.2922', 'aut_centralizer_order': 9, 'aut_label': '48.f1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '18.3', 'aut_weyl_index': 72, 'centralizer': '144.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.l1.a1', '16.a1.a1', '24.j1.a1'], 'contains': ['144.c1.a1', '144.d1.a1', '144.g1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [667, -1, 305, -1, 795, -1, 713, -1], 'generators': [434, 84], 'label': '1296.2922.48.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.b1.a1', 'old_label': '48.f1.a1', 'projective_image': '1296.2922', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.f1.a1', 'subgroup_fusion': None, 'weyl_group': '18.3'}
  • id: 71006785
    {'ambient': '1296.2922', 'aut_centralizer_order': 9, 'aut_label': '48.g1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '9.2', 'aut_weyl_index': 144, 'centralizer': '144.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.m1.a1', '16.a1.a1'], 'contains': ['144.c1.a1', '144.e1.a1', '144.f1.a1', '144.g1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [1213, -1, 980, -1, 707, -1, 625, -1], 'generators': [434, 516], 'label': '1296.2922.48.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.a1.a1', 'old_label': '48.g1.a1', 'projective_image': '1296.2922', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.g1.a1', 'subgroup_fusion': None, 'weyl_group': '9.2'}
  • id: 71006786
    {'ambient': '1296.2922', 'aut_centralizer_order': 36, 'aut_label': '54.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '36.10', 'aut_weyl_index': 36, 'centralizer': '36.b1.a1', 'complements': ['24.i1.a1', '24.j1.a1', '24.l1.a1', '24.m1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['18.a1.a1', '18.r1.a1', '27.c1.a1'], 'contains': ['108.b1.a1', '108.f1.a1', '108.j1.a1', '162.e1.a1'], 'core': '54.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7008, 7555, 7053, 5911, 8638, 7488, 8226, 2512], 'generators': [54, 108, 648, 432], 'label': '1296.2922.54.a1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '54.a1.a1', 'normal_contained_in': ['18.a1.a1'], 'normal_contains': ['108.b1.a1', '216.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '54.a1.a1', 'projective_image': '1296.2922', 'quotient_action_image': '6.1', 'quotient_action_kernel': '9.2', 'quotient_action_kernel_order': 9, 'quotient_fusion': None, 'short_label': '54.a1.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 71006787
    {'ambient': '1296.2922', 'aut_centralizer_order': 24, 'aut_label': '54.b1', 'aut_quo_index': None, 'aut_stab_index': 27, 'aut_weyl_group': '2.1', 'aut_weyl_index': 648, 'centralizer': '54.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.c1.a1', '18.e1.a1', '27.a1.a1'], 'contains': ['108.d1.a1', '108.l1.a1', '108.o1.a1', '108.bd1.a1', '108.bg1.a1', '162.a1.a1'], 'core': '1296.a1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [8201, -1, 7673, -1, 6347, -1, 7051, -1], 'generators': [3, 54, 648, 2], 'label': '1296.2922.54.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1.a1', 'old_label': '54.b1.a1', 'projective_image': '1296.2922', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.b1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 71006788
    {'ambient': '1296.2922', 'aut_centralizer_order': 12, 'aut_label': '54.c1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '12.4', 'aut_weyl_index': 108, 'centralizer': '108.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.c1.a1', '18.f1.a1', '27.b1.a1'], 'contains': ['108.c1.a1', '108.n1.a1', '108.p1.a1', '108.be1.a1', '108.bh1.a1', '162.a1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [3574, -1, 3312, -1, 3263, -1, 3002, -1], 'generators': [3, 54, 648, 36], 'label': '1296.2922.54.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '54.c1.a1', 'projective_image': '1296.2922', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.c1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 71006789
    {'ambient': '1296.2922', 'aut_centralizer_order': 12, 'aut_label': '54.d1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '12.4', 'aut_weyl_index': 108, 'centralizer': '108.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.d1.a1', '18.g1.a1', '27.b1.a1'], 'contains': ['108.c1.a1', '108.s1.a1', '108.t1.a1', '162.b1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [5265, -1, 5180, -1, 6084, -1, 6241, -1], 'generators': [111, 54, 648, 36], 'label': '1296.2922.54.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '54.d1.a1', 'projective_image': '1296.2922', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.d1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 71006790
    {'ambient': '1296.2922', 'aut_centralizer_order': 24, 'aut_label': '54.e1', 'aut_quo_index': None, 'aut_stab_index': 27, 'aut_weyl_group': '2.1', 'aut_weyl_index': 648, 'centralizer': '54.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.d1.a1', '18.h1.a1', '27.a1.a1'], 'contains': ['108.d1.a1', '108.w1.a1', '108.x1.a1', '162.b1.a1'], 'core': '1296.a1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [8728, -1, 8251, -1, 9642, -1, 9800, -1], 'generators': [111, 54, 2, 648], 'label': '1296.2922.54.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1.a1', 'old_label': '54.e1.a1', 'projective_image': '1296.2922', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.e1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 71006791
    {'ambient': '1296.2922', 'aut_centralizer_order': 12, 'aut_label': '54.f1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '12.4', 'aut_weyl_index': 108, 'centralizer': '108.l1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.e1.a1', '18.f1.a1', '27.c1.a1'], 'contains': ['108.f1.a1', '108.k1.a1', '108.q1.a1', '108.bf1.a1', '108.bi1.a1', '162.a1.a1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [6322, -1, 6064, -1, 6497, -1, 6901, -1], 'generators': [3, 54, 648, 432], 'label': '1296.2922.54.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1.a1', 'old_label': '54.f1.a1', 'projective_image': '1296.2922', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.f1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 71006792
    {'ambient': '1296.2922', 'aut_centralizer_order': 12, 'aut_label': '54.g1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '12.4', 'aut_weyl_index': 108, 'centralizer': '108.w1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.g1.a1', '18.h1.a1', '27.c1.a1'], 'contains': ['108.f1.a1', '108.u1.a1', '108.v1.a1', '162.b1.a1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [6810, -1, 6896, -1, 9944, -1, 8868, -1], 'generators': [111, 54, 648, 432], 'label': '1296.2922.54.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1.a1', 'old_label': '54.g1.a1', 'projective_image': '1296.2922', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.g1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 71006793
    {'ambient': '1296.2922', 'aut_centralizer_order': 6, 'aut_label': '6.f1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '72.46', 'aut_weyl_index': 18, 'centralizer': '216.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.c1.a1'], 'contains': ['12.d1.a1', '12.f1.a1', '12.g1.a1', '12.o1.a1', '12.q1.a1', '18.c1.a1', '18.e1.a1', '18.f1.a1'], 'core': '24.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5392, -1, 4521, -1, 3600, -1, 3623, -1], 'generators': [3, 432, 36, 54, 648, 2], 'label': '1296.2922.6.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1.a1', 'old_label': '6.f1.a1', 'projective_image': '1296.2922', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.f1.a1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 71006794
    {'ambient': '1296.2922', 'aut_centralizer_order': 12, 'aut_label': '54.h1', 'aut_quo_index': None, 'aut_stab_index': 27, 'aut_weyl_group': '4.2', 'aut_weyl_index': 324, 'centralizer': '108.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.i1.a1', '18.k1.a1', '27.a1.a1'], 'contains': ['108.h1.a1', '108.l1.a1', '108.x1.a1', '162.c1.a1'], 'core': '1296.a1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [8389, -1, 8090, -1, 9038, -1, 9943, -1], 'generators': [3, 162, 2, 648], 'label': '1296.2922.54.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1.a1', 'old_label': '54.h1.a1', 'projective_image': '1296.2922', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.h1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 71006795
    {'ambient': '1296.2922', 'aut_centralizer_order': 12, 'aut_label': '54.i1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '12.4', 'aut_weyl_index': 108, 'centralizer': '108.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.i1.a1', '18.l1.a1', '27.b1.a1'], 'contains': ['108.g1.a1', '108.n1.a1', '108.t1.a1', '162.c1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [4434, -1, 3729, -1, 5546, -1, 5957, -1], 'generators': [3, 162, 648, 36], 'label': '1296.2922.54.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '54.i1.a1', 'projective_image': '1296.2922', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.i1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 71006796
    {'ambient': '1296.2922', 'aut_centralizer_order': 12, 'aut_label': '54.j1', 'aut_quo_index': None, 'aut_stab_index': 27, 'aut_weyl_group': '4.2', 'aut_weyl_index': 324, 'centralizer': '108.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.j1.a1', '18.m1.a1', '27.a1.a1'], 'contains': ['108.h1.a1', '108.o1.a1', '108.w1.a1', '162.d1.a1'], 'core': '1296.a1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [8569, -1, 8695, -1, 9169, -1, 9657, -1], 'generators': [111, 162, 2, 648], 'label': '1296.2922.54.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1.a1', 'old_label': '54.j1.a1', 'projective_image': '1296.2922', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.j1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 71006797
    {'ambient': '1296.2922', 'aut_centralizer_order': 12, 'aut_label': '54.k1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '12.4', 'aut_weyl_index': 108, 'centralizer': '108.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.j1.a1', '18.n1.a1', '27.b1.a1'], 'contains': ['108.g1.a1', '108.p1.a1', '108.s1.a1', '162.d1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [5884, -1, 5388, -1, 5634, -1, 4818, -1], 'generators': [111, 162, 648, 36], 'label': '1296.2922.54.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '54.k1.a1', 'projective_image': '1296.2922', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.k1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 71006798
    {'ambient': '1296.2922', 'aut_centralizer_order': 6, 'aut_label': '54.l1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '24.14', 'aut_weyl_index': 54, 'centralizer': '216.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.k1.a1', '18.l1.a1', '27.c1.a1'], 'contains': ['108.j1.a1', '108.k1.a1', '108.v1.a1', '162.c1.a1'], 'core': '432.b1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [6598, -1, 6235, -1, 9279, -1, 9106, -1], 'generators': [3, 162, 648, 432], 'label': '1296.2922.54.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1.a1', 'old_label': '54.l1.a1', 'projective_image': '1296.2922', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.l1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 71006799
    {'ambient': '1296.2922', 'aut_centralizer_order': 6, 'aut_label': '54.m1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '24.14', 'aut_weyl_index': 54, 'centralizer': '216.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.m1.a1', '18.n1.a1', '27.c1.a1'], 'contains': ['108.j1.a1', '108.q1.a1', '108.u1.a1', '162.d1.a1'], 'core': '432.b1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [6905, -1, 7190, -1, 9366, -1, 8606, -1], 'generators': [111, 162, 648, 432], 'label': '1296.2922.54.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1.a1', 'old_label': '54.m1.a1', 'projective_image': '1296.2922', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.m1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 71006800
    {'ambient': '1296.2922', 'aut_centralizer_order': 72, 'aut_label': '54.n1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '6.1', 'aut_weyl_index': 216, 'centralizer': '18.o1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.a1.a1', '18.o1.a1', '18.p1.a1', '18.q1.a1', '27.b1.a1'], 'contains': ['108.a1.a1', '108.c1.a1', '108.g1.a1', '162.e1.a1'], 'core': '108.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [2994, -1, 2419, -1, 3830, -1, 4291, -1], 'generators': [54, 108, 648, 36], 'label': '1296.2922.54.n1.a1', 'mobius_quo': None, 'mobius_sub': 3, 'normal_closure': '18.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '54.n1.a1', 'projective_image': '1296.2922', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.n1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 71006801
    {'ambient': '1296.2922', 'aut_centralizer_order': 72, 'aut_label': '54.o1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '2.1', 'aut_weyl_index': 648, 'centralizer': '18.o1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.o1.a1', '18.r1.a1', '27.a1.a1'], 'contains': ['108.d1.a1', '108.e1.a1', '108.h1.a1', '108.i1.a1', '108.ba1.a1', '162.e1.a1'], 'core': '324.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [9278, -1, 8387, -1, 8007, -1, 9516, -1], 'generators': [54, 108, 648, 2], 'label': '1296.2922.54.o1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '54.o1.a1', 'projective_image': '1296.2922', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.o1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 71006802
    {'ambient': '1296.2922', 'aut_centralizer_order': 18, 'aut_label': '54.p1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '8.5', 'aut_weyl_index': 162, 'centralizer': '72.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.s1.a1', '18.t1.a1', '27.c1.a1'], 'contains': ['108.b1.a1', '108.k1.a1', '108.u1.a1', '162.f1.a1'], 'core': '108.b1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [6695, -1, 5939, -1, 8410, -1, 7868, -1], 'generators': [3, 108, 432, 648], 'label': '1296.2922.54.p1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1.a1', 'old_label': '54.p1.a1', 'projective_image': '1296.2922', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.p1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 71006803
    {'ambient': '1296.2922', 'aut_centralizer_order': 36, 'aut_label': '54.q1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '4.2', 'aut_weyl_index': 324, 'centralizer': '36.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.s1.a1', '18.u1.a1', '27.a1.a1'], 'contains': ['108.l1.a1', '108.w1.a1', '108.ba1.a1', '162.f1.a1'], 'core': '324.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [7980, -1, 7481, -1, 8148, -1, 8498, -1], 'generators': [3, 108, 2, 648], 'label': '1296.2922.54.q1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1.a1', 'old_label': '54.q1.a1', 'projective_image': '1296.2922', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.q1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 71006804
    {'ambient': '1296.2922', 'aut_centralizer_order': 6, 'aut_label': '6.g1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '72.46', 'aut_weyl_index': 18, 'centralizer': '216.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.c1.a1'], 'contains': ['12.d1.a1', '12.h1.a1', '12.i1.a1', '18.d1.a1', '18.g1.a1', '18.h1.a1'], 'core': '24.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6412, -1, 6727, -1, 6470, -1, 6493, -1], 'generators': [111, 432, 36, 54, 2, 648], 'label': '1296.2922.6.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1.a1', 'old_label': '6.g1.a1', 'projective_image': '1296.2922', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.g1.a1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 71006805
    {'ambient': '1296.2922', 'aut_centralizer_order': 18, 'aut_label': '54.r1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '4.2', 'aut_weyl_index': 324, 'centralizer': '72.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.s1.a1', '18.v1.a1'], 'contains': ['108.m1.a1', '108.z1.a1', '108.bc1.a1', '162.f1.a1'], 'core': '324.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [4977, -1, 3567, -1, 7272, -1, 7400, -1], 'generators': [3, 108, 434, 648], 'label': '1296.2922.54.r1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.s1.a1', 'old_label': '54.r1.a1', 'projective_image': '1296.2922', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.r1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 71006806
    {'ambient': '1296.2922', 'aut_centralizer_order': 36, 'aut_label': '54.s1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '12.4', 'aut_weyl_index': 108, 'centralizer': '36.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.b1.a1', '18.t1.a1', '18.u1.a1', '18.v1.a1', '27.b1.a1'], 'contains': ['108.a1.a1', '108.n1.a1', '108.s1.a1', '162.f1.a1'], 'core': '108.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [2365, -1, 2215, -1, 3949, -1, 3913, -1], 'generators': [3, 108, 648, 36], 'label': '1296.2922.54.s1.a1', 'mobius_quo': None, 'mobius_sub': 3, 'normal_closure': '18.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1.a1', 'old_label': '54.s1.a1', 'projective_image': '1296.2922', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.s1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 71006807
    {'ambient': '1296.2922', 'aut_centralizer_order': 12, 'aut_label': '54.t1', 'aut_quo_index': None, 'aut_stab_index': 27, 'aut_weyl_group': '4.2', 'aut_weyl_index': 324, 'centralizer': '108.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.w1.a1', '18.x1.a1', '18.y1.a1', '27.a1.a1'], 'contains': ['108.o1.a1', '108.x1.a1', '108.ba1.a1', '162.g1.a1'], 'core': '324.a1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [4145, -1, 8513, -1, 8278, -1, 8366, -1], 'generators': [81, 648, 38, 756], 'label': '1296.2922.54.t1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1.a1', 'old_label': '54.t1.a1', 'projective_image': '1296.2922', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.t1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 71006808
    {'ambient': '1296.2922', 'aut_centralizer_order': 12, 'aut_label': '54.u1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '12.4', 'aut_weyl_index': 108, 'centralizer': '108.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.w1.a1', '18.z1.a1', '18.ba1.a1', '18.bb1.a1', '27.b1.a1'], 'contains': ['108.a1.a1', '108.p1.a1', '108.t1.a1', '162.g1.a1'], 'core': '108.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [2209, -1, 2526, -1, 4115, -1, 3696, -1], 'generators': [81, 648, 756, 36], 'label': '1296.2922.54.u1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '6.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '54.u1.a1', 'projective_image': '1296.2922', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.u1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 71006809
    {'ambient': '1296.2922', 'aut_centralizer_order': 6, 'aut_label': '54.v1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '24.14', 'aut_weyl_index': 54, 'centralizer': '216.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.x1.a1', '18.z1.a1', '27.c1.a1'], 'contains': ['108.b1.a1', '108.q1.a1', '108.v1.a1', '162.g1.a1'], 'core': '108.b1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [6425, -1, 6799, -1, 8519, -1, 7978, -1], 'generators': [81, 648, 756, 432], 'label': '1296.2922.54.v1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1.a1', 'old_label': '54.v1.a1', 'projective_image': '1296.2922', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.v1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 71006810
    {'ambient': '1296.2922', 'aut_centralizer_order': 6, 'aut_label': '54.w1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '12.4', 'aut_weyl_index': 108, 'centralizer': '216.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.y1.a1', '18.z1.a1'], 'contains': ['108.r1.a1', '108.y1.a1', '108.bb1.a1', '162.g1.a1'], 'core': '324.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [2730, -1, 4941, -1, 5800, -1, 5553, -1], 'generators': [81, 648, 756, 468], 'label': '1296.2922.54.w1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.y1.a1', 'old_label': '54.w1.a1', 'projective_image': '1296.2922', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.w1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 71006811
    {'ambient': '1296.2922', 'aut_centralizer_order': 108, 'aut_label': '72.a1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '12.4', 'aut_weyl_index': 108, 'centralizer': '12.c1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['24.a1.a1', '24.d1.a1', '24.e1.a1', '36.e1.a1', '36.bk1.a1'], 'contains': ['144.a1.a1', '216.a1.a1', '216.i1.a1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1460, 8628, 1385, 8815, 2137, 8943, 2412, 1057], 'generators': [54, 36, 432], 'label': '1296.2922.72.a1.a1', 'mobius_quo': 0, 'mobius_sub': 12, 'normal_closure': '72.a1.a1', 'normal_contained_in': ['18.a1.a1', '24.a1.a1'], 'normal_contains': ['144.a1.a1', '216.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '72.a1.a1', 'projective_image': '1296.2922', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.a1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 71006812
    {'ambient': '1296.2922', 'aut_centralizer_order': 108, 'aut_label': '72.b1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '4.2', 'aut_weyl_index': 324, 'centralizer': '12.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.b1.a1', '36.a1.a1', '36.e1.a1', '36.i1.a1', '36.m1.a1', '36.s1.a1', '36.t1.a1', '36.u1.a1'], 'contains': ['144.a1.a1', '216.b1.a1', '216.c1.a1', '216.f1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4705, -1, 4340, -1, 4721, -1, 4323, -1], 'generators': [108, 36, 432], 'label': '1296.2922.72.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1.a1', 'old_label': '72.b1.a1', 'projective_image': '1296.2922', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.b1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 71006813
    {'ambient': '1296.2922', 'aut_centralizer_order': 216, 'aut_label': '72.c1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '2.1', 'aut_weyl_index': 648, 'centralizer': '6.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.b1.a1', '36.b1.a1', '36.d1.a1', '36.h1.a1', '36.n1.a1', '36.p1.a1', '36.v1.a1', '36.w1.a1'], 'contains': ['144.b1.a1', '216.b1.a1', '216.d1.a1', '216.e1.a1'], 'core': '144.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7513, -1, 6344, -1, 5569, -1, 5630, -1], 'generators': [108, 2, 36], 'label': '1296.2922.72.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1.a1', 'old_label': '72.c1.a1', 'projective_image': '1296.2922', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.c1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 71006814
    {'ambient': '1296.2922', 'aut_centralizer_order': 108, 'aut_label': '72.d1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '2.1', 'aut_weyl_index': 648, 'centralizer': '12.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.b1.a1', '36.o1.a1', '36.x1.a1', '36.bb1.a1'], 'contains': ['144.c1.a1', '216.b1.a1', '216.g1.a1', '216.h1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [3500, -1, 2793, -1, 4522, -1, 3995, -1], 'generators': [108, 434, 36], 'label': '1296.2922.72.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.l1.a1', 'old_label': '72.d1.a1', 'projective_image': '1296.2922', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.d1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 71006815
    {'ambient': '1296.2922', 'aut_centralizer_order': 6, 'aut_label': '6.h1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '72.46', 'aut_weyl_index': 18, 'centralizer': '216.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.c1.a1'], 'contains': ['12.e1.a1', '12.f1.a1', '12.i1.a1', '18.i1.a1', '18.k1.a1', '18.l1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5622, -1, 6191, -1, 6275, -1, 6298, -1], 'generators': [3, 432, 36, 162, 2, 648], 'label': '1296.2922.6.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1.a1', 'old_label': '6.h1.a1', 'projective_image': '1296.2922', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.h1.a1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 71006816
    {'ambient': '1296.2922', 'aut_centralizer_order': 216, 'aut_label': '72.e1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '2.1', 'aut_weyl_index': 648, 'centralizer': '6.l1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.b1.a1', '36.f1.a1', '36.j1.a1', '36.l1.a1', '36.q1.a1', '36.y1.a1', '36.z1.a1', '36.bf1.a1'], 'contains': ['144.h1.a1', '216.c1.a1', '216.d1.a1', '216.g1.a1'], 'core': '432.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [9054, -1, 9402, -1, 7960, -1, 7623, -1], 'generators': [648, 2, 432], 'label': '1296.2922.72.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1.a1', 'old_label': '72.e1.a1', 'projective_image': '1296.2922', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.e1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 71006817
    {'ambient': '1296.2922', 'aut_centralizer_order': 108, 'aut_label': '72.f1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '2.1', 'aut_weyl_index': 648, 'centralizer': '12.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.b1.a1', '36.g1.a1', '36.k1.a1', '36.bf1.a1'], 'contains': ['144.h1.a1', '216.c1.a1', '216.e1.a1', '216.h1.a1'], 'core': '432.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [9730, -1, 9861, -1, 7150, -1, 6951, -1], 'generators': [108, 2, 432], 'label': '1296.2922.72.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.a1', 'old_label': '72.f1.a1', 'projective_image': '1296.2922', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.f1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 71006818
    {'ambient': '1296.2922', 'aut_centralizer_order': 108, 'aut_label': '72.g1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '2.1', 'aut_weyl_index': 648, 'centralizer': '12.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.b1.a1', '36.r1.a1', '36.ba1.a1', '36.bg1.a1'], 'contains': ['144.i1.a1', '216.d1.a1', '216.f1.a1', '216.h1.a1'], 'core': '1296.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [5267, -1, 9138, -1, 5179, -1, 4453, -1], 'generators': [108, 434, 468], 'label': '1296.2922.72.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.n1.a1', 'old_label': '72.g1.a1', 'projective_image': '1296.2922', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.g1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 71006819
    {'ambient': '1296.2922', 'aut_centralizer_order': 108, 'aut_label': '72.h1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '1.1', 'aut_weyl_index': 1296, 'centralizer': '12.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.b1.a1', '36.bg1.a1'], 'contains': ['144.i1.a1', '216.e1.a1', '216.f1.a1', '216.g1.a1', '216.h1.a1'], 'core': '1296.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [5445, -1, 7597, -1, 5309, -1, 4782, -1], 'generators': [108, 2, 468], 'label': '1296.2922.72.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.a1.a1', 'old_label': '72.h1.a1', 'projective_image': '1296.2922', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.h1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 71006820
    {'ambient': '1296.2922', 'aut_centralizer_order': 72, 'aut_label': '72.i1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '6.1', 'aut_weyl_index': 216, 'centralizer': '18.o1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.a1.a1', '24.c1.a1', '36.d1.a1', '36.bh1.a1'], 'contains': ['144.b1.a1', '216.i1.a1', '216.j1.a1'], 'core': '144.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [1606, -1, 1536, -1, 2267, -1, 2878, -1], 'generators': [54, 2, 36], 'label': '1296.2922.72.i1.a1', 'mobius_quo': None, 'mobius_sub': 12, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '72.i1.a1', 'projective_image': '1296.2922', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.i1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 71006821
    {'ambient': '1296.2922', 'aut_centralizer_order': 18, 'aut_label': '72.j1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '6.2', 'aut_weyl_index': 216, 'centralizer': '72.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.p1.a1', '24.c1.a1', '24.d1.a1', '36.bi1.a1'], 'contains': ['144.d1.a1', '216.i1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [710, -1, 520, -1, 1187, -1, 1309, -1], 'generators': [54, 84, 36], 'label': '1296.2922.72.j1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '6.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.n1.a1', 'old_label': '72.j1.a1', 'projective_image': '1296.2922', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.j1.a1', 'subgroup_fusion': None, 'weyl_group': '6.2'}
  • id: 71006822
    {'ambient': '1296.2922', 'aut_centralizer_order': 18, 'aut_label': '72.k1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '3.1', 'aut_weyl_index': 432, 'centralizer': '72.k1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.q1.a1', '24.c1.a1', '24.e1.a1'], 'contains': ['144.e1.a1', '216.i1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [1269, -1, 1113, -1, 432, -1, 1414, -1], 'generators': [54, 86, 36], 'label': '1296.2922.72.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.c1.a1', 'old_label': '72.k1.a1', 'projective_image': '1296.2922', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.k1.a1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 71006823
    {'ambient': '1296.2922', 'aut_centralizer_order': 72, 'aut_label': '72.l1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '6.1', 'aut_weyl_index': 216, 'centralizer': '18.u1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.a1.a1', '36.f1.a1', '36.g1.a1', '36.bj1.a1'], 'contains': ['144.h1.a1', '216.a1.a1', '216.j1.a1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [9489, -1, 9286, -1, 4262, -1, 6492, -1], 'generators': [54, 2, 432], 'label': '1296.2922.72.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1.a1', 'old_label': '72.l1.a1', 'projective_image': '1296.2922', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.l1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 71006824
    {'ambient': '1296.2922', 'aut_centralizer_order': 72, 'aut_label': '72.m1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '2.1', 'aut_weyl_index': 648, 'centralizer': '18.o1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.f1.a1', '36.d1.a1', '36.h1.a1', '36.bl1.a1'], 'contains': ['144.b1.a1', '216.k1.a1', '216.l1.a1', '216.m1.a1'], 'core': '144.b1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [6076, -1, 5645, -1, 4851, -1, 5500, -1], 'generators': [162, 2, 36], 'label': '1296.2922.72.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '72.m1.a1', 'projective_image': '1296.2922', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.m1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 71006825
    {'ambient': '1296.2922', 'aut_centralizer_order': 36, 'aut_label': '72.n1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '12.4', 'aut_weyl_index': 108, 'centralizer': '36.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.f1.a1', '36.e1.a1', '36.i1.a1', '36.bn1.a1'], 'contains': ['144.a1.a1', '216.k1.a1', '216.n1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4272, -1, 4094, -1, 4133, -1, 3865, -1], 'generators': [162, 36, 432], 'label': '1296.2922.72.n1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1.a1', 'old_label': '72.n1.a1', 'projective_image': '1296.2922', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.n1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 71006826
    {'ambient': '1296.2922', 'aut_centralizer_order': 6, 'aut_label': '6.i1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '72.46', 'aut_weyl_index': 18, 'centralizer': '216.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.c1.a1'], 'contains': ['12.e1.a1', '12.g1.a1', '12.h1.a1', '18.j1.a1', '18.m1.a1', '18.n1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7160, -1, 6954, -1, 5915, -1, 5959, -1], 'generators': [111, 432, 36, 162, 2, 648], 'label': '1296.2922.6.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1.a1', 'old_label': '6.i1.a1', 'projective_image': '1296.2922', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.i1.a1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 71006827
    {'ambient': '1296.2922', 'aut_centralizer_order': 72, 'aut_label': '72.o1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '6.1', 'aut_weyl_index': 216, 'centralizer': '18.u1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.f1.a1', '36.f1.a1', '36.k1.a1', '36.bm1.a1'], 'contains': ['144.h1.a1', '216.l1.a1', '216.n1.a1'], 'core': '432.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [9845, -1, 9680, -1, 5875, -1, 7081, -1], 'generators': [702, 2, 432], 'label': '1296.2922.72.o1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1.a1', 'old_label': '72.o1.a1', 'projective_image': '1296.2922', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.o1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 71006828
    {'ambient': '1296.2922', 'aut_centralizer_order': 36, 'aut_label': '72.p1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '6.1', 'aut_weyl_index': 216, 'centralizer': '36.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.f1.a1', '36.g1.a1', '36.j1.a1', '36.k1.a1'], 'contains': ['144.h1.a1', '216.m1.a1', '216.n1.a1'], 'core': '432.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [9958, -1, 9977, -1, 6890, -1, 7753, -1], 'generators': [162, 2, 432], 'label': '1296.2922.72.p1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.a1', 'old_label': '72.p1.a1', 'projective_image': '1296.2922', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.p1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 71006829
    {'ambient': '1296.2922', 'aut_centralizer_order': 36, 'aut_label': '72.q1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '2.1', 'aut_weyl_index': 648, 'centralizer': '36.l1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.g1.a1', '36.l1.a1', '36.bj1.a1', '36.bm1.a1'], 'contains': ['144.h1.a1', '216.o1.a1', '216.p1.a1', '216.q1.a1'], 'core': '432.b1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [5752, -1, 4960, -1, 3476, -1, 5240, -1], 'generators': [3, 2, 432], 'label': '1296.2922.72.q1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1.a1', 'old_label': '72.q1.a1', 'projective_image': '1296.2922', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.q1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 71006830
    {'ambient': '1296.2922', 'aut_centralizer_order': 18, 'aut_label': '72.r1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '12.4', 'aut_weyl_index': 108, 'centralizer': '72.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.g1.a1', '24.h1.a1', '36.m1.a1', '36.bk1.a1', '36.bn1.a1'], 'contains': ['144.a1.a1', '216.o1.a1', '216.r1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2601, -1, 2516, -1, 2783, -1, 2540, -1], 'generators': [3, 432, 36], 'label': '1296.2922.72.r1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '6.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1.a1', 'old_label': '72.r1.a1', 'projective_image': '1296.2922', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.r1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 71006831
    {'ambient': '1296.2922', 'aut_centralizer_order': 36, 'aut_label': '72.s1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '6.1', 'aut_weyl_index': 216, 'centralizer': '36.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.g1.a1', '24.i1.a1', '36.n1.a1', '36.bh1.a1', '36.bl1.a1'], 'contains': ['144.b1.a1', '216.p1.a1', '216.r1.a1'], 'core': '144.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2938, -1, 3200, -1, 2525, -1, 2669, -1], 'generators': [3, 2, 36], 'label': '1296.2922.72.s1.a1', 'mobius_quo': None, 'mobius_sub': 6, 'normal_closure': '6.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1.a1', 'old_label': '72.s1.a1', 'projective_image': '1296.2922', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.s1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 71006832
    {'ambient': '1296.2922', 'aut_centralizer_order': 18, 'aut_label': '72.t1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '6.1', 'aut_weyl_index': 216, 'centralizer': '72.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.g1.a1', '24.j1.a1', '36.o1.a1'], 'contains': ['144.c1.a1', '216.q1.a1', '216.r1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [2487, -1, 2127, -1, 2396, -1, 2283, -1], 'generators': [3, 434, 36], 'label': '1296.2922.72.t1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.f1.a1', 'old_label': '72.t1.a1', 'projective_image': '1296.2922', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.t1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 71006833
    {'ambient': '1296.2922', 'aut_centralizer_order': 6, 'aut_label': '72.u1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '54.6', 'aut_weyl_index': 24, 'centralizer': '216.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.b1.a1', '24.h1.a1', '24.i1.a1', '24.j1.a1', '36.bi1.a1'], 'contains': ['144.d1.a1', '216.r1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [397, -1, 23, -1, 1263, -1, 1233, -1], 'generators': [3, 48, 36], 'label': '1296.2922.72.u1.a1', 'mobius_quo': None, 'mobius_sub': 3, 'normal_closure': '18.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.a1', 'old_label': '72.u1.a1', 'projective_image': '1296.2922', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.u1.a1', 'subgroup_fusion': None, 'weyl_group': '54.6'}
  • id: 71006834
    {'ambient': '1296.2922', 'aut_centralizer_order': 12, 'aut_label': '72.v1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '6.1', 'aut_weyl_index': 216, 'centralizer': '108.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.k1.a1', '24.l1.a1', '24.m1.a1', '36.p1.a1', '36.bh1.a1', '36.bl1.a1'], 'contains': ['144.b1.a1', '216.s1.a1', '216.t1.a1'], 'core': '144.b1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [2040, -1, 1716, -1, 2654, -1, 2154, -1], 'generators': [81, 2, 36], 'label': '1296.2922.72.v1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.c1.a1', 'old_label': '72.v1.a1', 'projective_image': '1296.2922', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.v1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 71006835
    {'ambient': '1296.2922', 'aut_centralizer_order': 12, 'aut_label': '72.w1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '6.1', 'aut_weyl_index': 216, 'centralizer': '108.l1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.k1.a1', '36.q1.a1', '36.bj1.a1', '36.bm1.a1'], 'contains': ['144.h1.a1', '216.s1.a1', '216.u1.a1'], 'core': '432.b1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [5930, -1, 5367, -1, 3736, -1, 5042, -1], 'generators': [81, 38, 432], 'label': '1296.2922.72.w1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1.a1', 'old_label': '72.w1.a1', 'projective_image': '1296.2922', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.w1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 71006836
    {'ambient': '1296.2922', 'aut_centralizer_order': 6, 'aut_label': '72.x1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '6.1', 'aut_weyl_index': 216, 'centralizer': '216.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.k1.a1', '36.r1.a1'], 'contains': ['144.i1.a1', '216.s1.a1', '216.v1.a1'], 'core': '1296.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [3614, -1, 4812, -1, 3079, -1, 3467, -1], 'generators': [81, 434, 900], 'label': '1296.2922.72.x1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.r1.a1', 'old_label': '72.x1.a1', 'projective_image': '1296.2922', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.x1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 71006837
    {'ambient': '1296.2922', 'aut_centralizer_order': 6, 'aut_label': '6.j1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '72.42', 'aut_weyl_index': 18, 'centralizer': '216.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '3.b1.a1'], 'contains': ['12.c1.a1', '18.o1.a1', '18.p1.a1', '18.q1.a1', '24.c1.a1'], 'core': '12.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [2815, -1, 1797, -1, 1829, -1, 3134, -1], 'generators': [54, 648, 108, 2, 84, 36], 'label': '1296.2922.6.j1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '6.j1.a1', 'projective_image': '1296.2922', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.j1.a1', 'subgroup_fusion': None, 'weyl_group': '72.42'}
  • id: 71006838
    {'ambient': '1296.2922', 'aut_centralizer_order': 6, 'aut_label': '72.y1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '36.10', 'aut_weyl_index': 36, 'centralizer': '216.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.k1.a1', '24.n1.a1', '36.s1.a1', '36.bk1.a1', '36.bn1.a1'], 'contains': ['144.a1.a1', '216.t1.a1', '216.u1.a1', '216.v1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2359, -1, 2419, -1, 2891, -1, 2046, -1], 'generators': [81, 36, 432], 'label': '1296.2922.72.y1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '6.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1.a1', 'old_label': '72.y1.a1', 'projective_image': '1296.2922', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.y1.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 71006839
    {'ambient': '1296.2922', 'aut_centralizer_order': 2, 'aut_label': '72.z1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '54.6', 'aut_weyl_index': 24, 'centralizer': '648.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.ba1.a1', '24.l1.a1', '24.n1.a1', '36.bi1.a1'], 'contains': ['144.d1.a1', '216.t1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [783, -1, 222, -1, 1369, -1, 946, -1], 'generators': [81, 48, 36], 'label': '1296.2922.72.z1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '6.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.n1.a1', 'old_label': '72.z1.a1', 'projective_image': '1296.2922', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.z1.a1', 'subgroup_fusion': None, 'weyl_group': '54.6'}
  • id: 71006840
    {'ambient': '1296.2922', 'aut_centralizer_order': 1, 'aut_label': '72.ba1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '54.6', 'aut_weyl_index': 24, 'centralizer': '1296.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.bb1.a1', '24.m1.a1', '24.n1.a1'], 'contains': ['144.f1.a1', '216.t1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [46, -1, 656, -1, 1474, -1, 160, -1], 'generators': [81, 480, 36], 'label': '1296.2922.72.ba1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.m1.a1', 'old_label': '72.ba1.a1', 'projective_image': '1296.2922', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ba1.a1', 'subgroup_fusion': None, 'weyl_group': '54.6'}
  • id: 71006841
    {'ambient': '1296.2922', 'aut_centralizer_order': 12, 'aut_label': '81.a1', 'aut_quo_index': None, 'aut_stab_index': 27, 'aut_weyl_group': '4.2', 'aut_weyl_index': 324, 'centralizer': '108.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['27.a1.a1', '27.b1.a1', '27.c1.a1'], 'contains': ['162.a1.a1', '162.b1.a1', '162.c1.a1', '162.d1.a1', '162.e1.a1', '162.f1.a1', '162.g1.a1'], 'core': '324.a1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [7714, -1, 7208, -1, 8907, -1, 9375, -1], 'generators': [3, 54, 108], 'label': '1296.2922.81.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1.a1', 'old_label': '81.a1.a1', 'projective_image': '1296.2922', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '81.a1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 71006842
    {'ambient': '1296.2922', 'aut_centralizer_order': 216, 'aut_label': '108.a1', 'aut_quo_index': 4, 'aut_stab_index': 1, 'aut_weyl_group': '6.1', 'aut_weyl_index': 216, 'centralizer': '6.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['36.a1.a1', '36.b1.a1', '36.c1.a1', '36.bb1.a1', '36.bc1.a1', '36.bd1.a1', '36.be1.a1', '54.n1.a1', '54.s1.a1', '54.u1.a1'], 'contains': ['216.b1.a1', '324.a1.a1'], 'core': '108.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1841, 3518, 1936, 3430, 3935, 3669, 3597, 6231], 'generators': [108, 648, 36], 'label': '1296.2922.108.a1.a1', 'mobius_quo': 1, 'mobius_sub': -18, 'normal_closure': '108.a1.a1', 'normal_contained_in': ['36.a1.a1', '36.b1.a1', '36.c1.a1'], 'normal_contains': ['324.a1.a1', '432.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '108.a1.a1', 'projective_image': '1296.2922', 'quotient_action_image': '6.1', 'quotient_action_kernel': '18.3', 'quotient_action_kernel_order': 18, 'quotient_fusion': None, 'short_label': '108.a1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 71006843
    {'ambient': '1296.2922', 'aut_centralizer_order': 108, 'aut_label': '108.b1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '12.4', 'aut_weyl_index': 108, 'centralizer': '12.a1.a1', 'complements': ['12.n1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['36.a1.a1', '36.bf1.a1', '54.a1.a1', '54.p1.a1', '54.v1.a1'], 'contains': ['216.c1.a1', '324.a1.a1'], 'core': '108.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6649, 5442, 6498, 5374, 8089, 5842, 7493, 4058], 'generators': [108, 648, 432], 'label': '1296.2922.108.b1.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '108.b1.a1', 'normal_contained_in': ['36.a1.a1', '54.a1.a1'], 'normal_contains': ['324.a1.a1', '432.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '108.b1.a1', 'projective_image': '1296.2922', 'quotient_action_image': '12.4', 'quotient_action_kernel': '9.2', 'quotient_action_kernel_order': 9, 'quotient_fusion': None, 'short_label': '108.b1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 71006844
    {'ambient': '1296.2922', 'aut_centralizer_order': 72, 'aut_label': '108.c1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '2.1', 'aut_weyl_index': 648, 'centralizer': '18.o1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.d1.a1', '36.e1.a1', '54.c1.a1', '54.d1.a1', '54.n1.a1'], 'contains': ['216.b1.a1', '216.i1.a1', '216.k1.a1', '324.b1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [3733, -1, 3294, -1, 4392, -1, 4193, -1], 'generators': [54, 108, 36], 'label': '1296.2922.108.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '108.c1.a1', 'projective_image': '1296.2922', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.c1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 71006845
    {'ambient': '1296.2922', 'aut_centralizer_order': 144, 'aut_label': '108.d1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '1.1', 'aut_weyl_index': 1296, 'centralizer': '9.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.d1.a1', '36.f1.a1', '54.b1.a1', '54.e1.a1', '54.o1.a1'], 'contains': ['216.d1.a1', '216.j1.a1', '216.l1.a1', '324.b1.a1'], 'core': '1296.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [9097, -1, 8365, -1, 7280, -1, 8281, -1], 'generators': [54, 648, 2], 'label': '1296.2922.108.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '108.d1.a1', 'projective_image': '1296.2922', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.d1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 71006846
    {'ambient': '1296.2922', 'aut_centralizer_order': 72, 'aut_label': '108.e1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '1.1', 'aut_weyl_index': 1296, 'centralizer': '18.o1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.d1.a1', '36.g1.a1', '54.o1.a1'], 'contains': ['216.e1.a1', '216.j1.a1', '216.m1.a1', '324.b1.a1'], 'core': '1296.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [9449, -1, 8942, -1, 7020, -1, 8151, -1], 'generators': [54, 108, 2], 'label': '1296.2922.108.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.o1.a1', 'old_label': '108.e1.a1', 'projective_image': '1296.2922', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.e1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 71006847
    {'ambient': '1296.2922', 'aut_centralizer_order': 72, 'aut_label': '108.f1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '6.1', 'aut_weyl_index': 216, 'centralizer': '18.u1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.e1.a1', '36.f1.a1', '36.g1.a1', '54.a1.a1', '54.f1.a1', '54.g1.a1'], 'contains': ['216.a1.a1', '216.c1.a1', '216.n1.a1', '324.b1.a1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6802, -1, 6749, -1, 7379, -1, 7180, -1], 'generators': [54, 108, 432], 'label': '1296.2922.108.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '54.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1.a1', 'old_label': '108.f1.a1', 'projective_image': '1296.2922', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.f1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 71006848
    {'ambient': '1296.2922', 'aut_centralizer_order': 3, 'aut_label': '2.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '432.745', 'aut_weyl_index': 3, 'centralizer': '432.a1.a1', 'complements': ['648.d1.a1', '648.e1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1', '6.a1.a1', '6.b1.a1', '6.j1.a1', '6.k1.a1', '8.a1.a1'], 'core': '2.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1963, 7268, 1950, 7341, 1829, 7776, 2641, 2223], 'generators': [54, 648, 756, 2, 432, 84, 36], 'label': '1296.2922.2.a1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.a1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.a1.a1', '6.a1.a1', '6.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.a1.a1', 'projective_image': '1296.2922', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.a1.a1', 'subgroup_fusion': None, 'weyl_group': '432.745'}
  • id: 71006849
    {'ambient': '1296.2922', 'aut_centralizer_order': 3, 'aut_label': '6.k1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '216.166', 'aut_weyl_index': 6, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1'], 'contains': ['12.j1.a1', '18.a1.a1', '18.q1.a1', '24.e1.a1'], 'core': '18.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3019, -1, 2914, -1, 1472, -1, 2955, -1], 'generators': [54, 432, 648, 86, 36, 756], 'label': '1296.2922.6.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '6.k1.a1', 'projective_image': '1296.2922', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.k1.a1', 'subgroup_fusion': None, 'weyl_group': '216.166'}
  • id: 71006850
    {'ambient': '1296.2922', 'aut_centralizer_order': 72, 'aut_label': '108.g1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '2.1', 'aut_weyl_index': 648, 'centralizer': '18.o1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.h1.a1', '36.i1.a1', '54.i1.a1', '54.k1.a1', '54.n1.a1'], 'contains': ['216.b1.a1', '216.k1.a1', '324.c1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [4733, -1, 4195, -1, 5050, -1, 4583, -1], 'generators': [702, 108, 36], 'label': '1296.2922.108.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '108.g1.a1', 'projective_image': '1296.2922', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.g1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 71006851
    {'ambient': '1296.2922', 'aut_centralizer_order': 72, 'aut_label': '108.h1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '2.1', 'aut_weyl_index': 648, 'centralizer': '18.o1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.h1.a1', '36.j1.a1', '54.h1.a1', '54.j1.a1', '54.o1.a1'], 'contains': ['216.d1.a1', '216.m1.a1', '324.c1.a1'], 'core': '1296.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [8983, -1, 9058, -1, 8298, -1, 9295, -1], 'generators': [162, 648, 2], 'label': '1296.2922.108.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '108.h1.a1', 'projective_image': '1296.2922', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.h1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 71006852
    {'ambient': '1296.2922', 'aut_centralizer_order': 72, 'aut_label': '108.i1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '1.1', 'aut_weyl_index': 1296, 'centralizer': '18.o1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.h1.a1', '36.k1.a1', '54.o1.a1'], 'contains': ['216.e1.a1', '216.l1.a1', '216.m1.a1', '324.c1.a1'], 'core': '1296.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [9335, -1, 9443, -1, 7478, -1, 8410, -1], 'generators': [702, 108, 2], 'label': '1296.2922.108.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.o1.a1', 'old_label': '108.i1.a1', 'projective_image': '1296.2922', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.i1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 71006853
    {'ambient': '1296.2922', 'aut_centralizer_order': 36, 'aut_label': '108.j1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '12.4', 'aut_weyl_index': 108, 'centralizer': '36.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.i1.a1', '36.j1.a1', '36.k1.a1', '54.a1.a1', '54.l1.a1', '54.m1.a1'], 'contains': ['216.c1.a1', '216.n1.a1', '324.c1.a1'], 'core': '432.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7224, -1, 7477, -1, 8397, -1, 8594, -1], 'generators': [702, 108, 432], 'label': '1296.2922.108.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '54.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1.a1', 'old_label': '108.j1.a1', 'projective_image': '1296.2922', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.j1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 71006854
    {'ambient': '1296.2922', 'aut_centralizer_order': 36, 'aut_label': '108.k1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '4.2', 'aut_weyl_index': 324, 'centralizer': '36.l1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.l1.a1', '36.m1.a1', '54.f1.a1', '54.l1.a1', '54.p1.a1'], 'contains': ['216.c1.a1', '216.o1.a1', '324.d1.a1'], 'core': '432.b1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [6391, -1, 5773, -1, 6691, -1, 6821, -1], 'generators': [3, 648, 432], 'label': '1296.2922.108.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1.a1', 'old_label': '108.k1.a1', 'projective_image': '1296.2922', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.k1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 71006855
    {'ambient': '1296.2922', 'aut_centralizer_order': 72, 'aut_label': '108.l1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '2.1', 'aut_weyl_index': 648, 'centralizer': '18.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.l1.a1', '36.n1.a1', '54.b1.a1', '54.h1.a1', '54.q1.a1'], 'contains': ['216.d1.a1', '216.p1.a1', '324.d1.a1'], 'core': '1296.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [8404, -1, 7846, -1, 6431, -1, 7279, -1], 'generators': [3, 648, 2], 'label': '1296.2922.108.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1.a1', 'old_label': '108.l1.a1', 'projective_image': '1296.2922', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.l1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 71006856
    {'ambient': '1296.2922', 'aut_centralizer_order': 36, 'aut_label': '108.m1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '2.1', 'aut_weyl_index': 648, 'centralizer': '36.l1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.l1.a1', '36.o1.a1', '54.r1.a1'], 'contains': ['216.g1.a1', '216.q1.a1', '324.d1.a1'], 'core': '1296.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [5075, -1, 2890, -1, 6093, -1, 6232, -1], 'generators': [3, 648, 434], 'label': '1296.2922.108.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.s1.a1', 'old_label': '108.m1.a1', 'projective_image': '1296.2922', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.m1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 71006857
    {'ambient': '1296.2922', 'aut_centralizer_order': 36, 'aut_label': '108.n1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '12.4', 'aut_weyl_index': 108, 'centralizer': '36.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.m1.a1', '36.n1.a1', '36.o1.a1', '54.c1.a1', '54.i1.a1', '54.s1.a1'], 'contains': ['216.b1.a1', '216.r1.a1', '324.d1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3199, -1, 2705, -1, 4034, -1, 3765, -1], 'generators': [3, 648, 36], 'label': '1296.2922.108.n1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1.a1', 'old_label': '108.n1.a1', 'projective_image': '1296.2922', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.n1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 71006858
    {'ambient': '1296.2922', 'aut_centralizer_order': 24, 'aut_label': '108.o1', 'aut_quo_index': None, 'aut_stab_index': 27, 'aut_weyl_group': '2.1', 'aut_weyl_index': 648, 'centralizer': '54.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.p1.a1', '36.q1.a1', '36.r1.a1', '54.b1.a1', '54.j1.a1', '54.t1.a1'], 'contains': ['216.d1.a1', '216.s1.a1', '324.e1.a1'], 'core': '1296.a1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [8139, -1, 8480, -1, 6561, -1, 6691, -1], 'generators': [81, 756, 38], 'label': '1296.2922.108.o1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1.a1', 'old_label': '108.o1.a1', 'projective_image': '1296.2922', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.o1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 71006859
    {'ambient': '1296.2922', 'aut_centralizer_order': 12, 'aut_label': '108.p1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '12.4', 'aut_weyl_index': 108, 'centralizer': '108.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.p1.a1', '36.s1.a1', '54.c1.a1', '54.k1.a1', '54.u1.a1'], 'contains': ['216.b1.a1', '216.t1.a1', '324.e1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [4475, -1, 4050, -1, 4622, -1, 3696, -1], 'generators': [81, 756, 36], 'label': '1296.2922.108.p1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '108.p1.a1', 'projective_image': '1296.2922', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.p1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 71006860
    {'ambient': '1296.2922', 'aut_centralizer_order': 18, 'aut_label': '6.l1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '24.14', 'aut_weyl_index': 54, 'centralizer': '72.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '3.c1.a1'], 'contains': ['12.a1.a1', '12.f1.a1', '12.h1.a1', '18.s1.a1', '18.t1.a1', '18.u1.a1', '18.v1.a1'], 'core': '12.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5076, -1, 3781, -1, 4297, -1, 4592, -1], 'generators': [3, 36, 648, 108, 2, 432], 'label': '1296.2922.6.l1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1.a1', 'old_label': '6.l1.a1', 'projective_image': '1296.2922', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.l1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 71006861
    {'ambient': '1296.2922', 'aut_centralizer_order': 12, 'aut_label': '108.q1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '12.4', 'aut_weyl_index': 108, 'centralizer': '108.l1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.q1.a1', '36.s1.a1', '54.f1.a1', '54.m1.a1', '54.v1.a1'], 'contains': ['216.c1.a1', '216.u1.a1', '324.e1.a1'], 'core': '432.b1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [6302, -1, 6315, -1, 6790, -1, 6591, -1], 'generators': [81, 756, 432], 'label': '1296.2922.108.q1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1.a1', 'old_label': '108.q1.a1', 'projective_image': '1296.2922', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.q1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 71006862
    {'ambient': '1296.2922', 'aut_centralizer_order': 6, 'aut_label': '108.r1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '12.4', 'aut_weyl_index': 108, 'centralizer': '216.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.r1.a1', '36.s1.a1', '54.w1.a1'], 'contains': ['216.f1.a1', '216.v1.a1', '324.e1.a1'], 'core': '1296.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [3980, -1, 5088, -1, 4950, -1, 4094, -1], 'generators': [81, 756, 468], 'label': '1296.2922.108.r1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.y1.a1', 'old_label': '108.r1.a1', 'projective_image': '1296.2922', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.r1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 71006863
    {'ambient': '1296.2922', 'aut_centralizer_order': 36, 'aut_label': '108.s1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '12.4', 'aut_weyl_index': 108, 'centralizer': '36.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.t1.a1', '36.v1.a1', '36.x1.a1', '54.d1.a1', '54.k1.a1', '54.s1.a1'], 'contains': ['216.b1.a1', '324.f1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5483, -1, 4986, -1, 5678, -1, 5869, -1], 'generators': [111, 648, 36], 'label': '1296.2922.108.s1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1.a1', 'old_label': '108.s1.a1', 'projective_image': '1296.2922', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.s1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 71006864
    {'ambient': '1296.2922', 'aut_centralizer_order': 12, 'aut_label': '108.t1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '12.4', 'aut_weyl_index': 108, 'centralizer': '108.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.u1.a1', '36.w1.a1', '54.d1.a1', '54.i1.a1', '54.u1.a1'], 'contains': ['216.b1.a1', '324.g1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [4320, -1, 3942, -1, 5766, -1, 5957, -1], 'generators': [729, 756, 36], 'label': '1296.2922.108.t1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '108.t1.a1', 'projective_image': '1296.2922', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.t1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 71006865
    {'ambient': '1296.2922', 'aut_centralizer_order': 36, 'aut_label': '108.u1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '4.2', 'aut_weyl_index': 324, 'centralizer': '36.y1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.t1.a1', '36.y1.a1', '54.g1.a1', '54.m1.a1', '54.p1.a1'], 'contains': ['216.c1.a1', '324.f1.a1'], 'core': '432.b1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [7093, -1, 6247, -1, 8779, -1, 8518, -1], 'generators': [111, 432, 648], 'label': '1296.2922.108.u1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1.a1', 'old_label': '108.u1.a1', 'projective_image': '1296.2922', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.u1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 71006866
    {'ambient': '1296.2922', 'aut_centralizer_order': 12, 'aut_label': '108.v1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '12.4', 'aut_weyl_index': 108, 'centralizer': '108.w1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.u1.a1', '36.z1.a1', '54.g1.a1', '54.l1.a1', '54.v1.a1'], 'contains': ['216.c1.a1', '324.g1.a1'], 'core': '432.b1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [6554, -1, 6170, -1, 8995, -1, 8672, -1], 'generators': [729, 756, 432], 'label': '1296.2922.108.v1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1.a1', 'old_label': '108.v1.a1', 'projective_image': '1296.2922', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.v1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 71006867
    {'ambient': '1296.2922', 'aut_centralizer_order': 72, 'aut_label': '108.w1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '2.1', 'aut_weyl_index': 648, 'centralizer': '18.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.v1.a1', '36.y1.a1', '54.e1.a1', '54.j1.a1', '54.q1.a1'], 'contains': ['216.d1.a1', '324.f1.a1'], 'core': '1296.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [8721, -1, 8576, -1, 8611, -1, 8906, -1], 'generators': [111, 2, 648], 'label': '1296.2922.108.w1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1.a1', 'old_label': '108.w1.a1', 'projective_image': '1296.2922', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.w1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 71006868
    {'ambient': '1296.2922', 'aut_centralizer_order': 24, 'aut_label': '108.x1', 'aut_quo_index': None, 'aut_stab_index': 27, 'aut_weyl_group': '2.1', 'aut_weyl_index': 648, 'centralizer': '54.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.w1.a1', '36.z1.a1', '36.ba1.a1', '54.e1.a1', '54.h1.a1', '54.t1.a1'], 'contains': ['216.d1.a1', '324.g1.a1'], 'core': '1296.a1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [8530, -1, 9153, -1, 8695, -1, 9119, -1], 'generators': [729, 38, 756], 'label': '1296.2922.108.x1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1.a1', 'old_label': '108.x1.a1', 'projective_image': '1296.2922', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.x1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 71006869
    {'ambient': '1296.2922', 'aut_centralizer_order': 6, 'aut_label': '108.y1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '12.4', 'aut_weyl_index': 108, 'centralizer': '216.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.u1.a1', '36.ba1.a1', '54.w1.a1'], 'contains': ['216.f1.a1', '324.g1.a1'], 'core': '1296.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [4582, -1, 5530, -1, 5984, -1, 6045, -1], 'generators': [729, 756, 468], 'label': '1296.2922.108.y1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.y1.a1', 'old_label': '108.y1.a1', 'projective_image': '1296.2922', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.y1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 71006871
    {'ambient': '1296.2922', 'aut_centralizer_order': 3, 'aut_label': '6.m1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '216.90', 'aut_weyl_index': 6, 'centralizer': '432.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1'], 'contains': ['12.l1.a1', '18.b1.a1', '18.v1.a1', '24.j1.a1'], 'core': '18.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1726, -1, 640, -1, 1972, -1, 2059, -1], 'generators': [3, 648, 108, 434, 48, 36], 'label': '1296.2922.6.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '6.m1.a1', 'projective_image': '1296.2922', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.m1.a1', 'subgroup_fusion': None, 'weyl_group': '216.90'}
  • id: 71006872
    {'ambient': '1296.2922', 'aut_centralizer_order': 216, 'aut_label': '108.ba1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '2.1', 'aut_weyl_index': 648, 'centralizer': '6.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.b1.a1', '36.bf1.a1', '36.bg1.a1', '54.o1.a1', '54.q1.a1', '54.t1.a1'], 'contains': ['216.d1.a1', '216.e1.a1', '324.a1.a1'], 'core': '324.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6055, -1, 7996, -1, 7608, -1, 8021, -1], 'generators': [108, 648, 2], 'label': '1296.2922.108.ba1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1.a1', 'old_label': '108.ba1.a1', 'projective_image': '1296.2922', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.ba1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 71006873
    {'ambient': '1296.2922', 'aut_centralizer_order': 108, 'aut_label': '108.bb1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '6.1', 'aut_weyl_index': 216, 'centralizer': '12.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.a1.a1', '36.bg1.a1', '54.w1.a1'], 'contains': ['216.f1.a1', '324.a1.a1'], 'core': '324.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2264, -1, 5177, -1, 5439, -1, 5370, -1], 'generators': [108, 648, 468], 'label': '1296.2922.108.bb1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '108.bb1.a1', 'projective_image': '1296.2922', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.bb1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 71006874
    {'ambient': '1296.2922', 'aut_centralizer_order': 108, 'aut_label': '108.bc1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '2.1', 'aut_weyl_index': 648, 'centralizer': '12.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.bb1.a1', '36.bf1.a1', '36.bg1.a1', '54.r1.a1'], 'contains': ['216.g1.a1', '216.h1.a1', '324.a1.a1'], 'core': '324.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2902, -1, 4760, -1, 6301, -1, 6362, -1], 'generators': [108, 648, 434], 'label': '1296.2922.108.bc1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.l1.a1', 'old_label': '108.bc1.a1', 'projective_image': '1296.2922', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.bc1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 71006875
    {'ambient': '1296.2922', 'aut_centralizer_order': 24, 'aut_label': '108.bd1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '1.1', 'aut_weyl_index': 1296, 'centralizer': '54.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.bh1.a1', '36.bj1.a1', '54.b1.a1'], 'contains': ['216.j1.a1', '216.p1.a1', '216.s1.a1', '324.h1.a1'], 'core': '1296.a1.a1', 'coset_action_label': None, 'count': 54, 'diagramx': [4160, -1, 3747, -1, 3277, -1, 4912, -1], 'generators': [3, 54, 2], 'label': '1296.2922.108.bd1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.b1.a1', 'old_label': '108.bd1.a1', 'projective_image': '1296.2922', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.bd1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 71006876
    {'ambient': '1296.2922', 'aut_centralizer_order': 12, 'aut_label': '108.be1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '6.1', 'aut_weyl_index': 216, 'centralizer': '108.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.bh1.a1', '36.bi1.a1', '36.bk1.a1', '54.c1.a1'], 'contains': ['216.i1.a1', '216.r1.a1', '216.t1.a1', '324.h1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [1138, -1, 836, -1, 2037, -1, 1967, -1], 'generators': [3, 54, 36], 'label': '1296.2922.108.be1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.c1.a1', 'old_label': '108.be1.a1', 'projective_image': '1296.2922', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.be1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 71006877
    {'ambient': '1296.2922', 'aut_centralizer_order': 12, 'aut_label': '108.bf1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '6.1', 'aut_weyl_index': 216, 'centralizer': '108.l1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.bj1.a1', '36.bk1.a1', '54.f1.a1'], 'contains': ['216.a1.a1', '216.o1.a1', '216.u1.a1', '324.h1.a1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [4041, -1, 3626, -1, 3377, -1, 4682, -1], 'generators': [3, 54, 432], 'label': '1296.2922.108.bf1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1.a1', 'old_label': '108.bf1.a1', 'projective_image': '1296.2922', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.bf1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 71006878
    {'ambient': '1296.2922', 'aut_centralizer_order': 24, 'aut_label': '108.bg1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '1.1', 'aut_weyl_index': 1296, 'centralizer': '54.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.bl1.a1', '36.bm1.a1', '54.b1.a1'], 'contains': ['216.l1.a1', '216.p1.a1', '216.s1.a1', '324.i1.a1'], 'core': '1296.a1.a1', 'coset_action_label': None, 'count': 54, 'diagramx': [7925, -1, 7284, -1, 3606, -1, 5760, -1], 'generators': [3, 702, 2], 'label': '1296.2922.108.bg1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.b1.a1', 'old_label': '108.bg1.a1', 'projective_image': '1296.2922', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.bg1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 71006879
    {'ambient': '1296.2922', 'aut_centralizer_order': 12, 'aut_label': '108.bh1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '6.1', 'aut_weyl_index': 216, 'centralizer': '108.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.bl1.a1', '36.bn1.a1', '54.c1.a1'], 'contains': ['216.k1.a1', '216.r1.a1', '216.t1.a1', '324.i1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [3496, -1, 3044, -1, 3178, -1, 2977, -1], 'generators': [3, 702, 36], 'label': '1296.2922.108.bh1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.c1.a1', 'old_label': '108.bh1.a1', 'projective_image': '1296.2922', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.bh1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 71006880
    {'ambient': '1296.2922', 'aut_centralizer_order': 12, 'aut_label': '108.bi1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '6.1', 'aut_weyl_index': 216, 'centralizer': '108.l1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.bm1.a1', '36.bn1.a1', '54.f1.a1'], 'contains': ['216.n1.a1', '216.o1.a1', '216.u1.a1', '324.i1.a1'], 'core': '432.b1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [5903, -1, 5363, -1, 3835, -1, 5141, -1], 'generators': [3, 702, 432], 'label': '1296.2922.108.bi1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1.a1', 'old_label': '108.bi1.a1', 'projective_image': '1296.2922', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.bi1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 71006881
    {'ambient': '1296.2922', 'aut_centralizer_order': 324, 'aut_label': '144.a1', 'aut_quo_index': 4, 'aut_stab_index': 1, 'aut_weyl_group': '4.2', 'aut_weyl_index': 324, 'centralizer': '4.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['48.a1.a1', '48.b1.a1', '48.c1.a1', '72.a1.a1', '72.b1.a1', '72.n1.a1', '72.r1.a1', '72.y1.a1'], 'contains': ['432.a1.a1', '432.b1.a1', '432.d1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2263, 6803, 2352, 7196, 2783, 6929, 2584, 2971], 'generators': [36, 432], 'label': '1296.2922.144.a1.a1', 'mobius_quo': 1, 'mobius_sub': -24, 'normal_closure': '144.a1.a1', 'normal_contained_in': ['36.a1.a1', '48.a1.a1', '72.a1.a1'], 'normal_contains': ['432.a1.a1', '432.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '144.a1.a1', 'projective_image': '1296.2922', 'quotient_action_image': '4.2', 'quotient_action_kernel': '36.11', 'quotient_action_kernel_order': 36, 'quotient_fusion': None, 'short_label': '144.a1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 71006882
    {'ambient': '1296.2922', 'aut_centralizer_order': 6, 'aut_label': '6.n1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '72.46', 'aut_weyl_index': 18, 'centralizer': '216.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1', '3.c1.a1'], 'contains': ['12.a1.a1', '12.g1.a1', '12.i1.a1', '18.w1.a1', '18.x1.a1', '18.y1.a1', '18.z1.a1'], 'core': '12.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4076, -1, 5347, -1, 5085, -1, 4932, -1], 'generators': [81, 432, 36, 648, 2, 756], 'label': '1296.2922.6.n1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1.a1', 'old_label': '6.n1.a1', 'projective_image': '1296.2922', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.n1.a1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 71006883
    {'ambient': '1296.2922', 'aut_centralizer_order': 216, 'aut_label': '144.b1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '6.1', 'aut_weyl_index': 216, 'centralizer': '6.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['48.a1.a1', '48.d1.a1', '48.e1.a1', '72.c1.a1', '72.i1.a1', '72.m1.a1', '72.s1.a1', '72.v1.a1'], 'contains': ['432.a1.a1', '432.c1.a1'], 'core': '144.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2427, 4214, 2038, 5062, 2862, 4756, 2722, 5144], 'generators': [2, 36], 'label': '1296.2922.144.b1.a1', 'mobius_quo': 0, 'mobius_sub': -72, 'normal_closure': '144.b1.a1', 'normal_contained_in': ['36.b1.a1', '48.a1.a1'], 'normal_contains': ['432.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '144.b1.a1', 'projective_image': '1296.2922', 'quotient_action_image': '6.1', 'quotient_action_kernel': '24.14', 'quotient_action_kernel_order': 24, 'quotient_fusion': None, 'short_label': '144.b1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 71006884
    {'ambient': '1296.2922', 'aut_centralizer_order': 108, 'aut_label': '144.c1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '6.1', 'aut_weyl_index': 216, 'centralizer': '12.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.a1.a1', '48.f1.a1', '48.g1.a1', '72.d1.a1', '72.t1.a1'], 'contains': ['432.a1.a1', '432.e1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2162, -1, 2205, -1, 2540, -1, 2353, -1], 'generators': [434, 36], 'label': '1296.2922.144.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '144.c1.a1', 'projective_image': '1296.2922', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.c1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 71006885
    {'ambient': '1296.2922', 'aut_centralizer_order': 54, 'aut_label': '144.d1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '6.2', 'aut_weyl_index': 216, 'centralizer': '24.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.c1.a1', '48.b1.a1', '48.d1.a1', '48.f1.a1', '72.j1.a1', '72.u1.a1', '72.z1.a1'], 'contains': ['432.a1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [652, -1, 391, -1, 1225, -1, 1193, -1], 'generators': [84], 'label': '1296.2922.144.d1.a1', 'mobius_quo': None, 'mobius_sub': -6, 'normal_closure': '36.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.a1', 'old_label': '144.d1.a1', 'projective_image': '1296.2922', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.d1.a1', 'subgroup_fusion': None, 'weyl_group': '6.2'}
  • id: 71006886
    {'ambient': '1296.2922', 'aut_centralizer_order': 54, 'aut_label': '144.e1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '3.1', 'aut_weyl_index': 432, 'centralizer': '24.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.bc1.a1', '48.c1.a1', '48.d1.a1', '48.g1.a1', '72.k1.a1'], 'contains': ['432.a1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [1491, -1, 1166, -1, 677, -1, 1338, -1], 'generators': [86], 'label': '1296.2922.144.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.a1.a1', 'old_label': '144.e1.a1', 'projective_image': '1296.2922', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.e1.a1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 71006887
    {'ambient': '1296.2922', 'aut_centralizer_order': 27, 'aut_label': '144.f1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '6.2', 'aut_weyl_index': 216, 'centralizer': '48.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.bd1.a1', '48.b1.a1', '48.e1.a1', '48.g1.a1', '72.ba1.a1'], 'contains': ['432.a1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [206, -1, 734, -1, 1384, -1, 594, -1], 'generators': [516], 'label': '1296.2922.144.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.c1.a1', 'old_label': '144.f1.a1', 'projective_image': '1296.2922', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.f1.a1', 'subgroup_fusion': None, 'weyl_group': '6.2'}
  • id: 71006888
    {'ambient': '1296.2922', 'aut_centralizer_order': 27, 'aut_label': '144.g1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '3.1', 'aut_weyl_index': 432, 'centralizer': '48.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.be1.a1', '48.c1.a1', '48.e1.a1', '48.f1.a1', '48.g1.a1'], 'contains': ['432.a1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [932, -1, 1063, -1, 948, -1, 891, -1], 'generators': [518], 'label': '1296.2922.144.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.a1.a1', 'old_label': '144.g1.a1', 'projective_image': '1296.2922', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.g1.a1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
  • id: 71006889
    {'ambient': '1296.2922', 'aut_centralizer_order': 216, 'aut_label': '144.h1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '2.1', 'aut_weyl_index': 648, 'centralizer': '6.l1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.a1.a1', '72.e1.a1', '72.f1.a1', '72.l1.a1', '72.o1.a1', '72.p1.a1', '72.q1.a1', '72.w1.a1'], 'contains': ['432.b1.a1', '432.c1.a1', '432.e1.a1'], 'core': '432.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [9577, -1, 9679, -1, 4596, -1, 6306, -1], 'generators': [2, 432], 'label': '1296.2922.144.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1.a1', 'old_label': '144.h1.a1', 'projective_image': '1296.2922', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.h1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 71006890
    {'ambient': '1296.2922', 'aut_centralizer_order': 108, 'aut_label': '144.i1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '2.1', 'aut_weyl_index': 648, 'centralizer': '12.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.a1.a1', '72.g1.a1', '72.h1.a1', '72.x1.a1'], 'contains': ['432.c1.a1', '432.d1.a1', '432.e1.a1'], 'core': '1296.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [4756, -1, 5777, -1, 3541, -1, 4181, -1], 'generators': [2, 468], 'label': '1296.2922.144.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.n1.a1', 'old_label': '144.i1.a1', 'projective_image': '1296.2922', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.i1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 71006891
    {'ambient': '1296.2922', 'aut_centralizer_order': 24, 'aut_label': '162.a1', 'aut_quo_index': None, 'aut_stab_index': 27, 'aut_weyl_group': '2.1', 'aut_weyl_index': 648, 'centralizer': '54.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['54.b1.a1', '54.c1.a1', '54.f1.a1', '81.a1.a1'], 'contains': ['324.b1.a1', '324.d1.a1', '324.e1.a1', '324.h1.a1', '324.i1.a1'], 'core': '1296.a1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [6785, -1, 5938, -1, 6197, -1, 6128, -1], 'generators': [3, 54, 648], 'label': '1296.2922.162.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1.a1', 'old_label': '162.a1.a1', 'projective_image': '1296.2922', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '162.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 71006892
    {'ambient': '1296.2922', 'aut_centralizer_order': 24, 'aut_label': '162.b1', 'aut_quo_index': None, 'aut_stab_index': 27, 'aut_weyl_group': '2.1', 'aut_weyl_index': 648, 'centralizer': '54.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['54.d1.a1', '54.e1.a1', '54.g1.a1', '81.a1.a1'], 'contains': ['324.b1.a1', '324.f1.a1', '324.g1.a1'], 'core': '1296.a1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [7258, -1, 6778, -1, 8886, -1, 9012, -1], 'generators': [111, 54], 'label': '1296.2922.162.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1.a1', 'old_label': '162.b1.a1', 'projective_image': '1296.2922', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '162.b1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 71006893
    {'ambient': '1296.2922', 'aut_centralizer_order': 2, 'aut_label': '6.o1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '216.90', 'aut_weyl_index': 6, 'centralizer': '648.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1', '3.b1.a1'], 'contains': ['12.c1.a1', '18.w1.a1', '18.ba1.a1', '24.l1.a1'], 'core': '12.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [1907, -1, 1345, -1, 2725, -1, 2346, -1], 'generators': [81, 648, 756, 2, 48, 36], 'label': '1296.2922.6.o1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '6.o1.a1', 'projective_image': '1296.2922', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.o1.a1', 'subgroup_fusion': None, 'weyl_group': '216.90'}
  • id: 71006894
    {'ambient': '1296.2922', 'aut_centralizer_order': 12, 'aut_label': '162.c1', 'aut_quo_index': None, 'aut_stab_index': 27, 'aut_weyl_group': '4.2', 'aut_weyl_index': 324, 'centralizer': '108.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['54.h1.a1', '54.i1.a1', '54.l1.a1', '81.a1.a1'], 'contains': ['324.c1.a1', '324.d1.a1', '324.g1.a1'], 'core': '1296.a1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [7007, -1, 6931, -1, 8466, -1, 9196, -1], 'generators': [3, 162], 'label': '1296.2922.162.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1.a1', 'old_label': '162.c1.a1', 'projective_image': '1296.2922', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '162.c1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 71006895
    {'ambient': '1296.2922', 'aut_centralizer_order': 12, 'aut_label': '162.d1', 'aut_quo_index': None, 'aut_stab_index': 27, 'aut_weyl_group': '4.2', 'aut_weyl_index': 324, 'centralizer': '108.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['54.j1.a1', '54.k1.a1', '54.m1.a1', '81.a1.a1'], 'contains': ['324.c1.a1', '324.e1.a1', '324.f1.a1'], 'core': '1296.a1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [7728, -1, 7236, -1, 8535, -1, 8829, -1], 'generators': [111, 162], 'label': '1296.2922.162.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1.a1', 'old_label': '162.d1.a1', 'projective_image': '1296.2922', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '162.d1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 71006896
    {'ambient': '1296.2922', 'aut_centralizer_order': 72, 'aut_label': '162.e1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '6.1', 'aut_weyl_index': 216, 'centralizer': '18.o1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['54.a1.a1', '54.n1.a1', '54.o1.a1', '81.a1.a1'], 'contains': ['324.a1.a1', '324.b1.a1', '324.c1.a1'], 'core': '324.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7960, -1, 7138, -1, 8194, -1, 8756, -1], 'generators': [54, 108, 648], 'label': '1296.2922.162.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '54.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '162.e1.a1', 'projective_image': '1296.2922', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '162.e1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 71006897
    {'ambient': '1296.2922', 'aut_centralizer_order': 36, 'aut_label': '162.f1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '4.2', 'aut_weyl_index': 324, 'centralizer': '36.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['54.p1.a1', '54.q1.a1', '54.r1.a1', '54.s1.a1', '81.a1.a1'], 'contains': ['324.a1.a1', '324.d1.a1', '324.f1.a1'], 'core': '324.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [6881, -1, 5409, -1, 7791, -1, 7921, -1], 'generators': [3, 108], 'label': '1296.2922.162.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1.a1', 'old_label': '162.f1.a1', 'projective_image': '1296.2922', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '162.f1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 71006898
    {'ambient': '1296.2922', 'aut_centralizer_order': 12, 'aut_label': '162.g1', 'aut_quo_index': None, 'aut_stab_index': 27, 'aut_weyl_group': '4.2', 'aut_weyl_index': 324, 'centralizer': '108.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['54.t1.a1', '54.u1.a1', '54.v1.a1', '54.w1.a1', '81.a1.a1'], 'contains': ['324.a1.a1', '324.e1.a1', '324.g1.a1'], 'core': '324.a1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [3534, -1, 6593, -1, 7860, -1, 7852, -1], 'generators': [81, 648], 'label': '1296.2922.162.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1.a1', 'old_label': '162.g1.a1', 'projective_image': '1296.2922', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '162.g1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 71006899
    {'ambient': '1296.2922', 'aut_centralizer_order': 216, 'aut_label': '216.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '6.1', 'aut_weyl_index': 216, 'centralizer': '6.d1.a1', 'complements': ['6.d1.a1', '6.m1.a1', '6.o1.a1', '6.p1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['72.a1.a1', '72.l1.a1', '108.f1.a1', '108.bf1.a1'], 'contains': ['432.b1.a1', '648.b1.a1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5683, 7665, 4617, 6949, 3968, 7697, 5460, 2203], 'generators': [54, 432], 'label': '1296.2922.216.a1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '216.a1.a1', 'normal_contained_in': ['54.a1.a1', '72.a1.a1'], 'normal_contains': ['432.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '216.a1.a1', 'projective_image': '1296.2922', 'quotient_action_image': '1.1', 'quotient_action_kernel': '216.90', 'quotient_action_kernel_order': 216, 'quotient_fusion': None, 'short_label': '216.a1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 71006900
    {'ambient': '1296.2922', 'aut_centralizer_order': 216, 'aut_label': '216.b1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '2.1', 'aut_weyl_index': 648, 'centralizer': '6.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.b1.a1', '72.c1.a1', '72.d1.a1', '108.a1.a1', '108.c1.a1', '108.g1.a1', '108.n1.a1', '108.p1.a1', '108.s1.a1', '108.t1.a1'], 'contains': ['432.a1.a1', '648.a1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3853, -1, 3611, -1, 4522, -1, 4323, -1], 'generators': [108, 36], 'label': '1296.2922.216.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '108.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1.a1', 'old_label': '216.b1.a1', 'projective_image': '1296.2922', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.b1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 71006901
    {'ambient': '1296.2922', 'aut_centralizer_order': 216, 'aut_label': '216.c1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '2.1', 'aut_weyl_index': 648, 'centralizer': '6.l1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.b1.a1', '72.e1.a1', '72.f1.a1', '108.b1.a1', '108.f1.a1', '108.j1.a1', '108.k1.a1', '108.q1.a1', '108.u1.a1', '108.v1.a1'], 'contains': ['432.b1.a1', '648.a1.a1'], 'core': '432.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6493, -1, 6264, -1, 7363, -1, 7127, -1], 'generators': [108, 432], 'label': '1296.2922.216.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '108.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1.a1', 'old_label': '216.c1.a1', 'projective_image': '1296.2922', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.c1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 71006902
    {'ambient': '1296.2922', 'aut_centralizer_order': 432, 'aut_label': '216.d1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '1.1', 'aut_weyl_index': 1296, 'centralizer': '3.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.c1.a1', '72.e1.a1', '72.g1.a1', '108.d1.a1', '108.h1.a1', '108.l1.a1', '108.o1.a1', '108.w1.a1', '108.x1.a1', '108.ba1.a1'], 'contains': ['432.c1.a1', '648.a1.a1'], 'core': '1296.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8530, -1, 8915, -1, 7280, -1, 7451, -1], 'generators': [648, 2], 'label': '1296.2922.216.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1.a1', 'old_label': '216.d1.a1', 'projective_image': '1296.2922', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.d1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 71006903
    {'ambient': '1296.2922', 'aut_centralizer_order': 216, 'aut_label': '216.e1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '1.1', 'aut_weyl_index': 1296, 'centralizer': '6.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.c1.a1', '72.f1.a1', '72.h1.a1', '108.e1.a1', '108.i1.a1', '108.ba1.a1'], 'contains': ['432.c1.a1', '648.a1.a1'], 'core': '1296.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [9040, -1, 7979, -1, 6951, -1, 6990, -1], 'generators': [108, 2], 'label': '1296.2922.216.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.a1', 'old_label': '216.e1.a1', 'projective_image': '1296.2922', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.e1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 71006904
    {'ambient': '1296.2922', 'aut_centralizer_order': 1, 'aut_label': '6.p1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '216.90', 'aut_weyl_index': 6, 'centralizer': '1296.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1'], 'contains': ['12.k1.a1', '18.w1.a1', '18.bb1.a1', '24.m1.a1'], 'core': '36.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [1093, -1, 2462, -1, 2832, -1, 1602, -1], 'generators': [81, 648, 756, 2, 480, 36], 'label': '1296.2922.6.p1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.p1.a1', 'old_label': '6.p1.a1', 'projective_image': '1296.2922', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.p1.a1', 'subgroup_fusion': None, 'weyl_group': '216.90'}
  • id: 71006905
    {'ambient': '1296.2922', 'aut_centralizer_order': 108, 'aut_label': '216.f1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '2.1', 'aut_weyl_index': 648, 'centralizer': '12.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.b1.a1', '72.g1.a1', '72.h1.a1', '108.r1.a1', '108.y1.a1', '108.bb1.a1'], 'contains': ['432.d1.a1', '648.a1.a1'], 'core': '1296.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [4611, -1, 5291, -1, 5210, -1, 4618, -1], 'generators': [108, 468], 'label': '1296.2922.216.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.n1.a1', 'old_label': '216.f1.a1', 'projective_image': '1296.2922', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.f1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 71006906
    {'ambient': '1296.2922', 'aut_centralizer_order': 216, 'aut_label': '216.g1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '1.1', 'aut_weyl_index': 1296, 'centralizer': '6.l1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.d1.a1', '72.e1.a1', '72.h1.a1', '108.m1.a1', '108.z1.a1', '108.bc1.a1'], 'contains': ['432.e1.a1', '648.a1.a1'], 'core': '1296.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [5091, -1, 3143, -1, 6197, -1, 6232, -1], 'generators': [648, 434], 'label': '1296.2922.216.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.l1.a1', 'old_label': '216.g1.a1', 'projective_image': '1296.2922', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.g1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 71006907
    {'ambient': '1296.2922', 'aut_centralizer_order': 108, 'aut_label': '216.h1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '1.1', 'aut_weyl_index': 1296, 'centralizer': '12.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.d1.a1', '72.f1.a1', '72.g1.a1', '72.h1.a1', '108.bc1.a1'], 'contains': ['432.e1.a1', '648.a1.a1'], 'core': '1296.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [5152, -1, 7704, -1, 5309, -1, 5391, -1], 'generators': [108, 434], 'label': '1296.2922.216.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.a1.a1', 'old_label': '216.h1.a1', 'projective_image': '1296.2922', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.h1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 71006908
    {'ambient': '1296.2922', 'aut_centralizer_order': 216, 'aut_label': '216.i1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '2.1', 'aut_weyl_index': 648, 'centralizer': '6.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.a1.a1', '72.i1.a1', '72.j1.a1', '72.k1.a1', '108.c1.a1', '108.be1.a1'], 'contains': ['432.a1.a1', '648.b1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [1085, -1, 1182, -1, 2202, -1, 2427, -1], 'generators': [54, 36], 'label': '1296.2922.216.i1.a1', 'mobius_quo': None, 'mobius_sub': -12, 'normal_closure': '72.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '216.i1.a1', 'projective_image': '1296.2922', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.i1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 71006909
    {'ambient': '1296.2922', 'aut_centralizer_order': 144, 'aut_label': '216.j1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '1.1', 'aut_weyl_index': 1296, 'centralizer': '9.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.i1.a1', '72.l1.a1', '108.d1.a1', '108.e1.a1', '108.bd1.a1'], 'contains': ['432.c1.a1', '648.b1.a1'], 'core': '1296.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [8927, -1, 7556, -1, 4262, -1, 6379, -1], 'generators': [54, 2], 'label': '1296.2922.216.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '216.j1.a1', 'projective_image': '1296.2922', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.j1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 71006910
    {'ambient': '1296.2922', 'aut_centralizer_order': 72, 'aut_label': '216.k1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '2.1', 'aut_weyl_index': 648, 'centralizer': '18.o1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.m1.a1', '72.n1.a1', '108.c1.a1', '108.g1.a1', '108.bh1.a1'], 'contains': ['432.a1.a1', '648.c1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [3931, -1, 3673, -1, 4193, -1, 4254, -1], 'generators': [162, 36], 'label': '1296.2922.216.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '216.k1.a1', 'projective_image': '1296.2922', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.k1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 71006911
    {'ambient': '1296.2922', 'aut_centralizer_order': 144, 'aut_label': '216.l1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '1.1', 'aut_weyl_index': 1296, 'centralizer': '9.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.m1.a1', '72.o1.a1', '108.d1.a1', '108.i1.a1', '108.bg1.a1'], 'contains': ['432.c1.a1', '648.c1.a1'], 'core': '1296.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [9101, -1, 7765, -1, 5806, -1, 7059, -1], 'generators': [702, 2], 'label': '1296.2922.216.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '216.l1.a1', 'projective_image': '1296.2922', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.l1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 71006912
    {'ambient': '1296.2922', 'aut_centralizer_order': 72, 'aut_label': '216.m1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '1.1', 'aut_weyl_index': 1296, 'centralizer': '18.o1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.m1.a1', '72.p1.a1', '108.e1.a1', '108.h1.a1', '108.i1.a1'], 'contains': ['432.c1.a1', '648.c1.a1'], 'core': '1296.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [9399, -1, 9535, -1, 6883, -1, 7753, -1], 'generators': [162, 2], 'label': '1296.2922.216.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.o1.a1', 'old_label': '216.m1.a1', 'projective_image': '1296.2922', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.m1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 71006913
    {'ambient': '1296.2922', 'aut_centralizer_order': 72, 'aut_label': '216.n1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '6.1', 'aut_weyl_index': 216, 'centralizer': '18.u1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.n1.a1', '72.o1.a1', '72.p1.a1', '108.f1.a1', '108.j1.a1', '108.bi1.a1'], 'contains': ['432.b1.a1', '648.c1.a1'], 'core': '432.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6568, -1, 7084, -1, 5875, -1, 6843, -1], 'generators': [162, 432], 'label': '1296.2922.216.n1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '54.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1.a1', 'old_label': '216.n1.a1', 'projective_image': '1296.2922', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.n1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 71006914
    {'ambient': '1296.2922', 'aut_centralizer_order': 36, 'aut_label': '216.o1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '2.1', 'aut_weyl_index': 648, 'centralizer': '36.l1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.q1.a1', '72.r1.a1', '108.k1.a1', '108.bf1.a1', '108.bi1.a1'], 'contains': ['432.b1.a1', '648.d1.a1'], 'core': '432.b1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [5361, -1, 4441, -1, 3752, -1, 5244, -1], 'generators': [3, 432], 'label': '1296.2922.216.o1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1.a1', 'old_label': '216.o1.a1', 'projective_image': '1296.2922', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.o1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 71006915
    {'ambient': '1296.2922', 'aut_centralizer_order': 3, 'aut_label': '8.a1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '108.38', 'aut_weyl_index': 12, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '4.b1.a1'], 'contains': ['16.a1.a1', '24.a1.a1', '24.c1.a1', '24.d1.a1', '24.e1.a1'], 'core': '24.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [1342, -1, 1221, -1, 323, -1, 1271, -1], 'generators': [54, 432, 2, 84, 36], 'label': '1296.2922.8.a1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.a1', 'old_label': '8.a1.a1', 'projective_image': '1296.2922', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.a1.a1', 'subgroup_fusion': None, 'weyl_group': '108.38'}
  • id: 71006916
    {'ambient': '1296.2922', 'aut_centralizer_order': 72, 'aut_label': '216.p1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '1.1', 'aut_weyl_index': 1296, 'centralizer': '18.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.q1.a1', '72.s1.a1', '108.l1.a1', '108.bd1.a1', '108.bg1.a1'], 'contains': ['432.c1.a1', '648.d1.a1'], 'core': '1296.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [5840, -1, 4711, -1, 3615, -1, 5529, -1], 'generators': [3, 2], 'label': '1296.2922.216.p1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1.a1', 'old_label': '216.p1.a1', 'projective_image': '1296.2922', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.p1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 71006917
    {'ambient': '1296.2922', 'aut_centralizer_order': 36, 'aut_label': '216.q1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '1.1', 'aut_weyl_index': 1296, 'centralizer': '36.l1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.q1.a1', '72.t1.a1', '108.m1.a1'], 'contains': ['432.e1.a1', '648.d1.a1'], 'core': '1296.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [4984, -1, 2787, -1, 3467, -1, 5175, -1], 'generators': [3, 434], 'label': '1296.2922.216.q1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.l1.a1', 'old_label': '216.q1.a1', 'projective_image': '1296.2922', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.q1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 71006918
    {'ambient': '1296.2922', 'aut_centralizer_order': 36, 'aut_label': '216.r1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '6.1', 'aut_weyl_index': 216, 'centralizer': '36.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.r1.a1', '72.s1.a1', '72.t1.a1', '72.u1.a1', '108.n1.a1', '108.be1.a1', '108.bh1.a1'], 'contains': ['432.a1.a1', '648.d1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2613, -1, 2258, -1, 2613, -1, 2511, -1], 'generators': [3, 36], 'label': '1296.2922.216.r1.a1', 'mobius_quo': None, 'mobius_sub': -6, 'normal_closure': '18.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1.a1', 'old_label': '216.r1.a1', 'projective_image': '1296.2922', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.r1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 71006919
    {'ambient': '1296.2922', 'aut_centralizer_order': 24, 'aut_label': '216.s1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '1.1', 'aut_weyl_index': 1296, 'centralizer': '54.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.v1.a1', '72.w1.a1', '72.x1.a1', '108.o1.a1', '108.bd1.a1', '108.bg1.a1'], 'contains': ['432.c1.a1', '648.e1.a1'], 'core': '1296.a1.a1', 'coset_action_label': None, 'count': 54, 'diagramx': [5744, -1, 4837, -1, 3683, -1, 5107, -1], 'generators': [81, 38], 'label': '1296.2922.216.s1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.b1.a1', 'old_label': '216.s1.a1', 'projective_image': '1296.2922', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.s1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 71006920
    {'ambient': '1296.2922', 'aut_centralizer_order': 12, 'aut_label': '216.t1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '6.1', 'aut_weyl_index': 216, 'centralizer': '108.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.v1.a1', '72.y1.a1', '72.z1.a1', '72.ba1.a1', '108.p1.a1', '108.be1.a1', '108.bh1.a1'], 'contains': ['432.a1.a1', '648.e1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [2111, -1, 1419, -1, 2682, -1, 2154, -1], 'generators': [81, 36], 'label': '1296.2922.216.t1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '6.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.c1.a1', 'old_label': '216.t1.a1', 'projective_image': '1296.2922', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.t1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 71006921
    {'ambient': '1296.2922', 'aut_centralizer_order': 12, 'aut_label': '216.u1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '6.1', 'aut_weyl_index': 216, 'centralizer': '108.l1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.w1.a1', '72.y1.a1', '108.q1.a1', '108.bf1.a1', '108.bi1.a1'], 'contains': ['432.b1.a1', '648.e1.a1'], 'core': '432.b1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [5453, -1, 4523, -1, 3821, -1, 5038, -1], 'generators': [81, 432], 'label': '1296.2922.216.u1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1.a1', 'old_label': '216.u1.a1', 'projective_image': '1296.2922', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.u1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 71006922
    {'ambient': '1296.2922', 'aut_centralizer_order': 6, 'aut_label': '216.v1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '6.1', 'aut_weyl_index': 216, 'centralizer': '216.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.x1.a1', '72.y1.a1', '108.r1.a1'], 'contains': ['432.d1.a1', '648.e1.a1'], 'core': '1296.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [2989, -1, 3966, -1, 3320, -1, 4094, -1], 'generators': [81, 468], 'label': '1296.2922.216.v1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.r1.a1', 'old_label': '216.v1.a1', 'projective_image': '1296.2922', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.v1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 71006923
    {'ambient': '1296.2922', 'aut_centralizer_order': 216, 'aut_label': '324.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '6.1', 'aut_weyl_index': 216, 'centralizer': '6.a1.a1', 'complements': ['4.b1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['108.a1.a1', '108.b1.a1', '108.ba1.a1', '108.bb1.a1', '108.bc1.a1', '162.e1.a1', '162.f1.a1', '162.g1.a1'], 'contains': ['648.a1.a1'], 'core': '324.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4823, 4967, 6064, 4391, 7206, 4167, 6916, 5453], 'generators': [108, 648], 'label': '1296.2922.324.a1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '324.a1.a1', 'normal_contained_in': ['108.a1.a1', '108.b1.a1'], 'normal_contains': ['1296.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '324.a1.a1', 'projective_image': '1296.2922', 'quotient_action_image': '6.1', 'quotient_action_kernel': '54.12', 'quotient_action_kernel_order': 54, 'quotient_fusion': None, 'short_label': '324.a1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 71006924
    {'ambient': '1296.2922', 'aut_centralizer_order': 144, 'aut_label': '324.b1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '1.1', 'aut_weyl_index': 1296, 'centralizer': '9.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.c1.a1', '108.d1.a1', '108.e1.a1', '108.f1.a1', '162.a1.a1', '162.b1.a1', '162.e1.a1'], 'contains': ['648.a1.a1', '648.b1.a1', '648.c1.a1'], 'core': '1296.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [7078, -1, 6940, -1, 7025, -1, 7201, -1], 'generators': [54, 108], 'label': '1296.2922.324.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '54.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '324.b1.a1', 'projective_image': '1296.2922', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.b1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 71006925
    {'ambient': '1296.2922', 'aut_centralizer_order': 72, 'aut_label': '324.c1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '2.1', 'aut_weyl_index': 648, 'centralizer': '18.o1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.g1.a1', '108.h1.a1', '108.i1.a1', '108.j1.a1', '162.c1.a1', '162.d1.a1', '162.e1.a1'], 'contains': ['648.a1.a1', '648.c1.a1'], 'core': '1296.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [7746, -1, 7131, -1, 8194, -1, 8594, -1], 'generators': [702, 108], 'label': '1296.2922.324.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '54.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '324.c1.a1', 'projective_image': '1296.2922', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.c1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 71006926
    {'ambient': '1296.2922', 'aut_centralizer_order': 3, 'aut_label': '8.b1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '108.26', 'aut_weyl_index': 12, 'centralizer': '432.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '4.b1.a1'], 'contains': ['16.a1.a1', '24.g1.a1', '24.h1.a1', '24.i1.a1', '24.j1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [687, -1, 262, -1, 627, -1, 641, -1], 'generators': [3, 36, 2, 432, 48], 'label': '1296.2922.8.b1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.a1', 'old_label': '8.b1.a1', 'projective_image': '1296.2922', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.b1.a1', 'subgroup_fusion': None, 'weyl_group': '108.26'}
  • id: 71006927
    {'ambient': '1296.2922', 'aut_centralizer_order': 72, 'aut_label': '324.d1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '2.1', 'aut_weyl_index': 648, 'centralizer': '18.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.k1.a1', '108.l1.a1', '108.m1.a1', '108.n1.a1', '162.a1.a1', '162.c1.a1', '162.f1.a1'], 'contains': ['648.a1.a1', '648.d1.a1'], 'core': '1296.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [6287, -1, 5787, -1, 6431, -1, 6769, -1], 'generators': [3, 648], 'label': '1296.2922.324.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1.a1', 'old_label': '324.d1.a1', 'projective_image': '1296.2922', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.d1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 71006928
    {'ambient': '1296.2922', 'aut_centralizer_order': 24, 'aut_label': '324.e1', 'aut_quo_index': None, 'aut_stab_index': 27, 'aut_weyl_group': '2.1', 'aut_weyl_index': 648, 'centralizer': '54.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.o1.a1', '108.p1.a1', '108.q1.a1', '108.r1.a1', '162.a1.a1', '162.d1.a1', '162.g1.a1'], 'contains': ['648.a1.a1', '648.e1.a1'], 'core': '1296.a1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [5931, -1, 6166, -1, 6561, -1, 6591, -1], 'generators': [81, 756], 'label': '1296.2922.324.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1.a1', 'old_label': '324.e1.a1', 'projective_image': '1296.2922', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.e1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 71006929
    {'ambient': '1296.2922', 'aut_centralizer_order': 72, 'aut_label': '324.f1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '2.1', 'aut_weyl_index': 648, 'centralizer': '18.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.s1.a1', '108.u1.a1', '108.w1.a1', '108.z1.a1', '162.b1.a1', '162.d1.a1', '162.f1.a1'], 'contains': ['648.a1.a1'], 'core': '1296.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [6981, -1, 5955, -1, 8332, -1, 8054, -1], 'generators': [111], 'label': '1296.2922.324.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1.a1', 'old_label': '324.f1.a1', 'projective_image': '1296.2922', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.f1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 71006930
    {'ambient': '1296.2922', 'aut_centralizer_order': 24, 'aut_label': '324.g1', 'aut_quo_index': None, 'aut_stab_index': 27, 'aut_weyl_group': '2.1', 'aut_weyl_index': 648, 'centralizer': '54.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.t1.a1', '108.v1.a1', '108.x1.a1', '108.y1.a1', '162.b1.a1', '162.c1.a1', '162.g1.a1'], 'contains': ['648.a1.a1'], 'core': '1296.a1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [6097, -1, 6746, -1, 8433, -1, 8255, -1], 'generators': [729], 'label': '1296.2922.324.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1.a1', 'old_label': '324.g1.a1', 'projective_image': '1296.2922', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.g1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 71006931
    {'ambient': '1296.2922', 'aut_centralizer_order': 24, 'aut_label': '324.h1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '1.1', 'aut_weyl_index': 1296, 'centralizer': '54.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.bd1.a1', '108.be1.a1', '108.bf1.a1', '162.a1.a1'], 'contains': ['648.b1.a1', '648.d1.a1', '648.e1.a1'], 'core': '1296.a1.a1', 'coset_action_label': None, 'count': 54, 'diagramx': [3645, -1, 4037, -1, 3394, -1, 4964, -1], 'generators': [3, 54], 'label': '1296.2922.324.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.b1.a1', 'old_label': '324.h1.a1', 'projective_image': '1296.2922', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.h1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 71006932
    {'ambient': '1296.2922', 'aut_centralizer_order': 24, 'aut_label': '324.i1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '1.1', 'aut_weyl_index': 1296, 'centralizer': '54.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.bg1.a1', '108.bh1.a1', '108.bi1.a1', '162.a1.a1'], 'contains': ['648.c1.a1', '648.d1.a1', '648.e1.a1'], 'core': '1296.a1.a1', 'coset_action_label': None, 'count': 54, 'diagramx': [6000, -1, 5890, -1, 3894, -1, 5318, -1], 'generators': [3, 702], 'label': '1296.2922.324.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.b1.a1', 'old_label': '324.i1.a1', 'projective_image': '1296.2922', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.i1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 71006933
    {'ambient': '1296.2922', 'aut_centralizer_order': 648, 'aut_label': '432.a1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 648, 'centralizer': '2.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['144.a1.a1', '144.b1.a1', '144.c1.a1', '144.d1.a1', '144.e1.a1', '144.f1.a1', '144.g1.a1', '216.b1.a1', '216.i1.a1', '216.k1.a1', '216.r1.a1', '216.t1.a1'], 'contains': ['1296.a1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2144, 4291, 1999, 5062, 2613, 4935, 2427, 4686], 'generators': [36], 'label': '1296.2922.432.a1.a1', 'mobius_quo': -1, 'mobius_sub': 72, 'normal_closure': '432.a1.a1', 'normal_contained_in': ['108.a1.a1', '144.a1.a1', '144.b1.a1'], 'normal_contains': ['1296.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '432.a1.a1', 'projective_image': '1296.2922', 'quotient_action_image': '2.1', 'quotient_action_kernel': '216.166', 'quotient_action_kernel_order': 216, 'quotient_fusion': None, 'short_label': '432.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 71006934
    {'ambient': '1296.2922', 'aut_centralizer_order': 648, 'aut_label': '432.b1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 648, 'centralizer': '2.b1.a1', 'complements': ['3.b1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['144.a1.a1', '144.h1.a1', '216.a1.a1', '216.c1.a1', '216.n1.a1', '216.o1.a1', '216.u1.a1'], 'contains': ['1296.a1.a1'], 'core': '432.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5630, 6404, 4625, 6123, 3968, 6381, 5458, 3509], 'generators': [432], 'label': '1296.2922.432.b1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '432.b1.a1', 'normal_contained_in': ['108.b1.a1', '144.a1.a1', '216.a1.a1'], 'normal_contains': ['1296.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '432.b1.a1', 'projective_image': '1296.2922', 'quotient_action_image': '2.1', 'quotient_action_kernel': '216.90', 'quotient_action_kernel_order': 216, 'quotient_fusion': None, 'short_label': '432.b1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 71006935
    {'ambient': '1296.2922', 'aut_centralizer_order': 432, 'aut_label': '432.c1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '1.1', 'aut_weyl_index': 1296, 'centralizer': '3.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.b1.a1', '144.h1.a1', '144.i1.a1', '216.d1.a1', '216.e1.a1', '216.j1.a1', '216.l1.a1', '216.m1.a1', '216.p1.a1', '216.s1.a1'], 'contains': ['1296.a1.a1'], 'core': '1296.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8888, -1, 7247, -1, 4262, -1, 6306, -1], 'generators': [2], 'label': '1296.2922.432.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '144.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1.a1', 'old_label': '432.c1.a1', 'projective_image': '1296.2922', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.c1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 71006936
    {'ambient': '1296.2922', 'aut_centralizer_order': 324, 'aut_label': '432.d1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '2.1', 'aut_weyl_index': 648, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.a1.a1', '144.i1.a1', '216.f1.a1', '216.v1.a1'], 'contains': ['1296.a1.a1'], 'core': '1296.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3562, -1, 4394, -1, 3541, -1, 4181, -1], 'generators': [468], 'label': '1296.2922.432.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '144.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '432.d1.a1', 'projective_image': '1296.2922', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.d1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 71006937
    {'ambient': '1296.2922', 'aut_centralizer_order': 1, 'aut_label': '8.c1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '324.118', 'aut_weyl_index': 4, 'centralizer': '1296.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1', '4.b1.a1'], 'contains': ['16.a1.a1', '24.k1.a1', '24.l1.a1', '24.m1.a1', '24.n1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [356, -1, 711, -1, 1188, -1, 369, -1], 'generators': [81, 36, 2, 48, 432], 'label': '1296.2922.8.c1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.a1', 'old_label': '8.c1.a1', 'projective_image': '1296.2922', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.c1.a1', 'subgroup_fusion': None, 'weyl_group': '324.118'}
  • id: 71006938
    {'ambient': '1296.2922', 'aut_centralizer_order': 216, 'aut_label': '432.e1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '1.1', 'aut_weyl_index': 1296, 'centralizer': '6.l1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.c1.a1', '144.h1.a1', '144.i1.a1', '216.g1.a1', '216.h1.a1', '216.q1.a1'], 'contains': ['1296.a1.a1'], 'core': '1296.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [5091, -1, 3986, -1, 3899, -1, 5249, -1], 'generators': [434], 'label': '1296.2922.432.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.l1.a1', 'old_label': '432.e1.a1', 'projective_image': '1296.2922', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.e1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 71006939
    {'ambient': '1296.2922', 'aut_centralizer_order': 432, 'aut_label': '648.a1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '1.1', 'aut_weyl_index': 1296, 'centralizer': '3.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.b1.a1', '216.c1.a1', '216.d1.a1', '216.e1.a1', '216.f1.a1', '216.g1.a1', '216.h1.a1', '324.a1.a1', '324.b1.a1', '324.c1.a1', '324.d1.a1', '324.e1.a1', '324.f1.a1', '324.g1.a1'], 'contains': ['1296.a1.a1'], 'core': '1296.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6097, -1, 6078, -1, 6951, -1, 6916, -1], 'generators': [108], 'label': '1296.2922.648.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '324.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1.a1', 'old_label': '648.a1.a1', 'projective_image': '1296.2922', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 71006940
    {'ambient': '1296.2922', 'aut_centralizer_order': 432, 'aut_label': '648.b1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '1.1', 'aut_weyl_index': 1296, 'centralizer': '3.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.a1.a1', '216.i1.a1', '216.j1.a1', '324.b1.a1', '324.h1.a1'], 'contains': ['1296.a1.a1'], 'core': '1296.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5580, -1, 4351, -1, 3831, -1, 5389, -1], 'generators': [54], 'label': '1296.2922.648.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '216.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '648.b1.a1', 'projective_image': '1296.2922', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.b1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 71006941
    {'ambient': '1296.2922', 'aut_centralizer_order': 144, 'aut_label': '648.c1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '1.1', 'aut_weyl_index': 1296, 'centralizer': '9.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.k1.a1', '216.l1.a1', '216.m1.a1', '216.n1.a1', '324.b1.a1', '324.c1.a1', '324.i1.a1'], 'contains': ['1296.a1.a1'], 'core': '1296.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [6976, -1, 7064, -1, 5841, -1, 7021, -1], 'generators': [162], 'label': '1296.2922.648.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '54.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '648.c1.a1', 'projective_image': '1296.2922', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.c1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 71006942
    {'ambient': '1296.2922', 'aut_centralizer_order': 72, 'aut_label': '648.d1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '1.1', 'aut_weyl_index': 1296, 'centralizer': '18.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.o1.a1', '216.p1.a1', '216.q1.a1', '216.r1.a1', '324.d1.a1', '324.h1.a1', '324.i1.a1'], 'contains': ['1296.a1.a1'], 'core': '1296.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [5518, -1, 4150, -1, 3654, -1, 5318, -1], 'generators': [3], 'label': '1296.2922.648.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.e1.a1', 'old_label': '648.d1.a1', 'projective_image': '1296.2922', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.d1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 71006943
    {'ambient': '1296.2922', 'aut_centralizer_order': 24, 'aut_label': '648.e1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '1.1', 'aut_weyl_index': 1296, 'centralizer': '54.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.s1.a1', '216.t1.a1', '216.u1.a1', '216.v1.a1', '324.e1.a1', '324.h1.a1', '324.i1.a1'], 'contains': ['1296.a1.a1'], 'core': '1296.a1.a1', 'coset_action_label': None, 'count': 54, 'diagramx': [5453, -1, 4469, -1, 3743, -1, 5072, -1], 'generators': [81], 'label': '1296.2922.648.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.b1.a1', 'old_label': '648.e1.a1', 'projective_image': '1296.2922', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.e1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 71006944
    {'ambient': '1296.2922', 'aut_centralizer_order': None, 'aut_label': '1296.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1.a1.a1', 'complements': ['1.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['432.a1.a1', '432.b1.a1', '432.c1.a1', '432.d1.a1', '432.e1.a1', '648.a1.a1', '648.b1.a1', '648.c1.a1', '648.d1.a1', '648.e1.a1'], 'contains': [], 'core': '1296.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5549, 4967, 4438, 5062, 3865, 4935, 5352, 4686], 'generators': [], 'label': '1296.2922.1296.a1.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '1296.a1.a1', 'normal_contained_in': ['324.a1.a1', '432.a1.a1', '432.b1.a1'], 'normal_contains': [], 'normalizer': '1.a1.a1', 'old_label': '1296.a1.a1', 'projective_image': '1296.2922', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1296.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 71006945
    {'ambient': '1296.2922', 'aut_centralizer_order': 12, 'aut_label': '9.a1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '12.4', 'aut_weyl_index': 108, 'centralizer': '108.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.b1.a1', '3.c1.a1'], 'contains': ['18.c1.a1', '18.d1.a1', '18.i1.a1', '18.j1.a1', '18.o1.a1', '18.u1.a1', '18.w1.a1', '27.a1.a1', '27.b1.a1'], 'core': '36.b1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [5193, -1, 4337, -1, 4915, -1, 5333, -1], 'generators': [3, 36, 648, 54, 108, 2], 'label': '1296.2922.9.a1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '9.a1.a1', 'projective_image': '1296.2922', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '9.a1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 71006946
    {'ambient': '1296.2922', 'aut_centralizer_order': 3, 'aut_label': '2.b1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '432.533', 'aut_weyl_index': 3, 'centralizer': '432.b1.a1', 'complements': ['648.b1.a1', '648.c1.a1', '648.e1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1', '6.c1.a1', '6.d1.a1', '6.l1.a1', '6.m1.a1', '8.b1.a1'], 'core': '2.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1707, 2190, 819, 2213, 2124, 1765, 2104, 8235], 'generators': [3, 108, 36, 2, 648, 432, 48], 'label': '1296.2922.2.b1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.b1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.a1.a1', '6.c1.a1', '6.d1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.b1.a1', 'projective_image': '1296.2922', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.b1.a1', 'subgroup_fusion': None, 'weyl_group': '432.533'}
  • id: 71006947
    {'ambient': '1296.2922', 'aut_centralizer_order': 2, 'aut_label': '9.b1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '216.90', 'aut_weyl_index': 6, 'centralizer': '648.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1.a1', '3.b1.a1'], 'contains': ['18.b1.a1', '18.p1.a1', '18.ba1.a1', '27.b1.a1', '36.bi1.a1'], 'core': '18.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [1716, -1, 995, -1, 2582, -1, 2775, -1], 'generators': [3, 648, 108, 54, 48, 36], 'label': '1296.2922.9.b1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '9.b1.a1', 'projective_image': '1296.2922', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '9.b1.a1', 'subgroup_fusion': None, 'weyl_group': '216.90'}
  • id: 71006948
    {'ambient': '1296.2922', 'aut_centralizer_order': 6, 'aut_label': '9.c1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '24.14', 'aut_weyl_index': 54, 'centralizer': '216.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.c1.a1'], 'contains': ['18.e1.a1', '18.h1.a1', '18.k1.a1', '18.m1.a1', '18.r1.a1', '18.s1.a1', '18.x1.a1', '27.a1.a1', '27.c1.a1'], 'core': '54.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [8391, -1, 8472, -1, 8233, -1, 8156, -1], 'generators': [3, 432, 648, 54, 108, 2], 'label': '1296.2922.9.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1.a1', 'old_label': '9.c1.a1', 'projective_image': '1296.2922', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '9.c1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 71006949
    {'ambient': '1296.2922', 'aut_centralizer_order': 6, 'aut_label': '9.d1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '72.46', 'aut_weyl_index': 18, 'centralizer': '216.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1.a1', '3.c1.a1'], 'contains': ['18.a1.a1', '18.f1.a1', '18.g1.a1', '18.l1.a1', '18.n1.a1', '18.t1.a1', '18.z1.a1', '27.b1.a1', '27.c1.a1'], 'core': '18.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3621, -1, 3861, -1, 4605, -1, 4762, -1], 'generators': [3, 432, 36, 54, 108, 648], 'label': '1296.2922.9.d1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1.a1', 'old_label': '9.d1.a1', 'projective_image': '1296.2922', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '9.d1.a1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 71006950
    {'ambient': '1296.2922', 'aut_centralizer_order': 108, 'aut_label': '12.a1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '12.4', 'aut_weyl_index': 108, 'centralizer': '12.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '6.a1.a1', '6.l1.a1', '6.n1.a1'], 'contains': ['24.b1.a1', '36.a1.a1', '36.b1.a1', '36.bb1.a1', '36.bf1.a1', '36.bg1.a1'], 'core': '12.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4278, 6238, 5969, 6559, 4297, 5653, 4607, 4347], 'generators': [108, 432, 648, 2, 36], 'label': '1296.2922.12.a1.a1', 'mobius_quo': 0, 'mobius_sub': -6, 'normal_closure': '12.a1.a1', 'normal_contained_in': ['4.a1.a1', '6.a1.a1'], 'normal_contains': ['36.a1.a1', '36.b1.a1', '48.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '12.a1.a1', 'projective_image': '1296.2922', 'quotient_action_image': '12.4', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '12.a1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 71006951
    {'ambient': '1296.2922', 'aut_centralizer_order': 9, 'aut_label': '12.b1', 'aut_quo_index': 12, 'aut_stab_index': 1, 'aut_weyl_group': '144.188', 'aut_weyl_index': 9, 'centralizer': '144.a1.a1', 'complements': ['108.bd1.a1', '108.bg1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '6.b1.a1', '6.c1.a1', '6.e1.a1'], 'contains': ['36.a1.a1', '36.c1.a1', '36.bd1.a1', '48.b1.a1'], 'core': '12.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [939, 4325, 1815, 4626, 2258, 3928, 2091, 6072], 'generators': [84, 648, 432, 36, 756], 'label': '1296.2922.12.b1.a1', 'mobius_quo': 0, 'mobius_sub': -2, 'normal_closure': '12.b1.a1', 'normal_contained_in': ['4.a1.a1', '6.b1.a1', '6.c1.a1', '6.e1.a1'], 'normal_contains': ['36.a1.a1', '36.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '12.b1.a1', 'projective_image': '1296.2922', 'quotient_action_image': '12.5', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '12.b1.a1', 'subgroup_fusion': None, 'weyl_group': '144.188'}
  • id: 71006952
    {'ambient': '1296.2922', 'aut_centralizer_order': 18, 'aut_label': '12.c1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '72.42', 'aut_weyl_index': 18, 'centralizer': '72.a1.a1', 'complements': ['108.bf1.a1', '108.bi1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '6.d1.a1', '6.j1.a1', '6.o1.a1'], 'contains': ['36.b1.a1', '36.c1.a1', '36.bc1.a1', '48.d1.a1'], 'core': '12.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2460, 2666, 1687, 2950, 2008, 2433, 2632, 7567], 'generators': [2, 648, 84, 36, 108], 'label': '1296.2922.12.c1.a1', 'mobius_quo': 0, 'mobius_sub': -6, 'normal_closure': '12.c1.a1', 'normal_contained_in': ['4.a1.a1', '6.d1.a1'], 'normal_contains': ['36.b1.a1', '36.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '12.c1.a1', 'projective_image': '1296.2922', 'quotient_action_image': '2.1', 'quotient_action_kernel': '6.1', 'quotient_action_kernel_order': 6, 'quotient_fusion': None, 'short_label': '12.c1.a1', 'subgroup_fusion': None, 'weyl_group': '72.42'}
  • id: 71006953
    {'ambient': '1296.2922', 'aut_centralizer_order': 36, 'aut_label': '12.d1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '12.4', 'aut_weyl_index': 108, 'centralizer': '36.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.a1.a1', '6.f1.a1', '6.g1.a1'], 'contains': ['24.a1.a1', '24.b1.a1', '24.f1.a1', '36.d1.a1', '36.e1.a1', '36.f1.a1', '36.g1.a1'], 'core': '24.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7120, -1, 6994, -1, 5369, -1, 5261, -1], 'generators': [54, 432, 108, 2, 36], 'label': '1296.2922.12.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1.a1', 'old_label': '12.d1.a1', 'projective_image': '1296.2922', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.d1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 71006954
    {'ambient': '1296.2922', 'aut_centralizer_order': 36, 'aut_label': '12.e1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '12.4', 'aut_weyl_index': 108, 'centralizer': '36.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.a1.a1', '6.h1.a1', '6.i1.a1'], 'contains': ['24.b1.a1', '24.f1.a1', '36.h1.a1', '36.i1.a1', '36.j1.a1', '36.k1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7392, -1, 7391, -1, 6464, -1, 6468, -1], 'generators': [702, 432, 108, 2, 36], 'label': '1296.2922.12.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1.a1', 'old_label': '12.e1.a1', 'projective_image': '1296.2922', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.e1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 71006955
    {'ambient': '1296.2922', 'aut_centralizer_order': 18, 'aut_label': '12.f1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '24.14', 'aut_weyl_index': 54, 'centralizer': '72.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.f1.a1', '6.h1.a1', '6.l1.a1'], 'contains': ['24.b1.a1', '24.g1.a1', '36.l1.a1', '36.m1.a1', '36.n1.a1', '36.o1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5558, -1, 6159, -1, 3600, -1, 3803, -1], 'generators': [3, 36, 648, 2, 432], 'label': '1296.2922.12.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1.a1', 'old_label': '12.f1.a1', 'projective_image': '1296.2922', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.f1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 71006956
    {'ambient': '1296.2922', 'aut_centralizer_order': 6, 'aut_label': '12.g1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '72.46', 'aut_weyl_index': 18, 'centralizer': '216.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.f1.a1', '6.i1.a1', '6.n1.a1'], 'contains': ['24.b1.a1', '24.k1.a1', '36.p1.a1', '36.q1.a1', '36.r1.a1', '36.s1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5749, -1, 6416, -1, 5080, -1, 3623, -1], 'generators': [81, 432, 756, 2, 36], 'label': '1296.2922.12.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1.a1', 'old_label': '12.g1.a1', 'projective_image': '1296.2922', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.g1.a1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 71006957
    {'ambient': '1296.2922', 'aut_centralizer_order': 1, 'aut_label': '2.c1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '1296.2922', 'aut_weyl_index': 1, 'centralizer': '1296.a1.a1', 'complements': ['648.b1.a1', '648.c1.a1', '648.d1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1', '6.e1.a1', '6.n1.a1', '6.o1.a1', '6.p1.a1', '8.c1.a1'], 'core': '2.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1511, 4900, 1540, 4950, 2725, 3838, 1905, 6161], 'generators': [81, 756, 36, 2, 648, 48, 432], 'label': '1296.2922.2.c1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.c1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.a1.a1', '6.e1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.c1.a1', 'projective_image': '1296.2922', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.c1.a1', 'subgroup_fusion': None, 'weyl_group': '1296.2922'}
  • id: 71006958
    {'ambient': '1296.2922', 'aut_centralizer_order': 18, 'aut_label': '12.h1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '24.14', 'aut_weyl_index': 54, 'centralizer': '72.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.g1.a1', '6.i1.a1', '6.l1.a1'], 'contains': ['24.b1.a1', '36.t1.a1', '36.v1.a1', '36.x1.a1', '36.y1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6715, -1, 6791, -1, 5915, -1, 5959, -1], 'generators': [111, 36, 2, 432, 648], 'label': '1296.2922.12.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1.a1', 'old_label': '12.h1.a1', 'projective_image': '1296.2922', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.h1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 71006959
    {'ambient': '1296.2922', 'aut_centralizer_order': 6, 'aut_label': '12.i1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '72.46', 'aut_weyl_index': 18, 'centralizer': '216.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.g1.a1', '6.h1.a1', '6.n1.a1'], 'contains': ['24.b1.a1', '36.u1.a1', '36.w1.a1', '36.z1.a1', '36.ba1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5975, -1, 6600, -1, 7134, -1, 6978, -1], 'generators': [729, 432, 2, 756, 36], 'label': '1296.2922.12.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1.a1', 'old_label': '12.i1.a1', 'projective_image': '1296.2922', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.i1.a1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 71006960
    {'ambient': '1296.2922', 'aut_centralizer_order': 9, 'aut_label': '12.j1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '72.47', 'aut_weyl_index': 18, 'centralizer': '144.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '6.k1.a1'], 'contains': ['36.a1.a1', '36.bc1.a1', '36.be1.a1', '48.c1.a1'], 'core': '36.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2637, -1, 2914, -1, 1362, -1, 2380, -1], 'generators': [86, 648, 432, 36, 756], 'label': '1296.2922.12.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '12.j1.a1', 'projective_image': '1296.2922', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.j1.a1', 'subgroup_fusion': None, 'weyl_group': '72.47'}
  • id: 71006961
    {'ambient': '1296.2922', 'aut_centralizer_order': 9, 'aut_label': '12.k1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '72.42', 'aut_weyl_index': 18, 'centralizer': '144.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '6.p1.a1'], 'contains': ['36.b1.a1', '36.bd1.a1', '36.be1.a1', '48.e1.a1'], 'core': '36.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1333, -1, 2462, -1, 2115, -1, 1734, -1], 'generators': [2, 648, 516, 36, 108], 'label': '1296.2922.12.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '12.k1.a1', 'projective_image': '1296.2922', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.k1.a1', 'subgroup_fusion': None, 'weyl_group': '72.42'}
  • id: 71006962
    {'ambient': '1296.2922', 'aut_centralizer_order': 9, 'aut_label': '12.l1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '72.42', 'aut_weyl_index': 18, 'centralizer': '144.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '6.m1.a1'], 'contains': ['36.c1.a1', '36.bb1.a1', '36.be1.a1', '48.f1.a1'], 'core': '36.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1998, -1, 1487, -1, 1901, -1, 1948, -1], 'generators': [434, 648, 84, 36, 108], 'label': '1296.2922.12.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '12.l1.a1', 'projective_image': '1296.2922', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.l1.a1', 'subgroup_fusion': None, 'weyl_group': '72.42'}
  • id: 71006963
    {'ambient': '1296.2922', 'aut_centralizer_order': 9, 'aut_label': '12.m1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '36.11', 'aut_weyl_index': 36, 'centralizer': '144.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1'], 'contains': ['36.bb1.a1', '36.bc1.a1', '36.bd1.a1', '36.be1.a1', '48.g1.a1'], 'core': '108.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [2131, -1, 2340, -1, 1794, -1, 1841, -1], 'generators': [434, 648, 516, 36, 108], 'label': '1296.2922.12.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '12.m1.a1', 'projective_image': '1296.2922', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.m1.a1', 'subgroup_fusion': None, 'weyl_group': '36.11'}
  • id: 71006964
    {'ambient': '1296.2922', 'aut_centralizer_order': 2, 'aut_label': '12.n1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '54.6', 'aut_weyl_index': 24, 'centralizer': '648.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.b1.a1', '4.b1.a1'], 'contains': ['24.c1.a1', '24.i1.a1', '24.l1.a1', '36.bh1.a1', '36.bi1.a1'], 'core': '144.b1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [1215, -1, 344, -1, 822, -1, 1003, -1], 'generators': [3, 36, 54, 2, 48], 'label': '1296.2922.12.n1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.n1.a1', 'old_label': '12.n1.a1', 'projective_image': '1296.2922', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.n1.a1', 'subgroup_fusion': None, 'weyl_group': '54.6'}
  • id: 71006965
    {'ambient': '1296.2922', 'aut_centralizer_order': 6, 'aut_label': '12.o1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '36.10', 'aut_weyl_index': 36, 'centralizer': '216.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '6.f1.a1'], 'contains': ['24.a1.a1', '24.g1.a1', '24.k1.a1', '36.bh1.a1', '36.bj1.a1', '36.bk1.a1'], 'core': '24.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2820, -1, 3133, -1, 2927, -1, 1497, -1], 'generators': [3, 432, 54, 2, 36], 'label': '1296.2922.12.o1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1.a1', 'old_label': '12.o1.a1', 'projective_image': '1296.2922', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.o1.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 71006966
    {'ambient': '1296.2922', 'aut_centralizer_order': 1, 'aut_label': '12.p1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '324.118', 'aut_weyl_index': 4, 'centralizer': '1296.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1.a1', '4.b1.a1'], 'contains': ['24.d1.a1', '24.h1.a1', '24.n1.a1', '36.bi1.a1', '36.bk1.a1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [193, -1, 505, -1, 1003, -1, 858, -1], 'generators': [3, 36, 54, 48, 432], 'label': '1296.2922.12.p1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.a1', 'old_label': '12.p1.a1', 'projective_image': '1296.2922', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.p1.a1', 'subgroup_fusion': None, 'weyl_group': '324.118'}
  • id: 71006967
    {'ambient': '1296.2922', 'aut_centralizer_order': 6, 'aut_label': '12.q1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '36.10', 'aut_weyl_index': 36, 'centralizer': '216.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.f1.a1'], 'contains': ['24.f1.a1', '24.g1.a1', '24.k1.a1', '36.bl1.a1', '36.bm1.a1', '36.bn1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [4930, -1, 4672, -1, 3076, -1, 3119, -1], 'generators': [3, 432, 702, 2, 36], 'label': '1296.2922.12.q1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1.a1', 'old_label': '12.q1.a1', 'projective_image': '1296.2922', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.q1.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 71006968
    {'ambient': '1296.2922', 'aut_centralizer_order': 1, 'aut_label': '3.a1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '1296.2922', 'aut_weyl_index': 1, 'centralizer': '1296.a1.a1', 'complements': ['432.c1.a1', '432.e1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['6.b1.a1', '6.c1.a1', '6.e1.a1', '9.b1.a1', '9.d1.a1', '12.p1.a1'], 'core': '3.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1399, 3429, 1258, 3464, 2482, 5912, 2283, 4088], 'generators': [3, 108, 36, 54, 648, 48, 432], 'label': '1296.2922.3.a1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '3.a1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['6.b1.a1', '6.c1.a1', '6.e1.a1'], 'normalizer': '1.a1.a1', 'old_label': '3.a1.a1', 'projective_image': '1296.2922', 'quotient_action_image': '3.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '3.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1296.2922'}
  • id: 71006969
    {'ambient': '1296.2922', 'aut_centralizer_order': 9, 'aut_label': '16.a1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '36.12', 'aut_weyl_index': 36, 'centralizer': '144.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '8.a1.a1', '8.b1.a1', '8.c1.a1'], 'contains': ['48.a1.a1', '48.b1.a1', '48.c1.a1', '48.d1.a1', '48.e1.a1', '48.f1.a1', '48.g1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [821, -1, 989, -1, 273, -1, 319, -1], 'generators': [2, 84, 432], 'label': '1296.2922.16.a1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.a1', 'old_label': '16.a1.a1', 'projective_image': '1296.2922', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.a1.a1', 'subgroup_fusion': None, 'weyl_group': '36.12'}
  • id: 71006970
    {'ambient': '1296.2922', 'aut_centralizer_order': 36, 'aut_label': '18.a1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '36.10', 'aut_weyl_index': 36, 'centralizer': '36.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['6.a1.a1', '6.b1.a1', '6.k1.a1', '9.d1.a1'], 'contains': ['36.a1.a1', '36.e1.a1', '36.i1.a1', '54.a1.a1', '54.n1.a1'], 'core': '18.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3868, 7611, 3465, 8011, 4121, 7488, 4431, 2512], 'generators': [54, 432, 108, 648, 36], 'label': '1296.2922.18.a1.a1', 'mobius_quo': 0, 'mobius_sub': -3, 'normal_closure': '18.a1.a1', 'normal_contained_in': ['6.a1.a1', '6.b1.a1'], 'normal_contains': ['36.a1.a1', '54.a1.a1', '72.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '18.a1.a1', 'projective_image': '1296.2922', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.a1.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 71006971
    {'ambient': '1296.2922', 'aut_centralizer_order': 6, 'aut_label': '18.b1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '216.90', 'aut_weyl_index': 6, 'centralizer': '216.a1.a1', 'complements': ['72.l1.a1', '72.p1.a1', '72.o1.a1', '72.w1.a1', '72.x1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['6.c1.a1', '6.d1.a1', '6.m1.a1', '9.b1.a1'], 'contains': ['36.c1.a1', '54.s1.a1', '72.u1.a1'], 'core': '18.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1526, 1825, 703, 2100, 2582, 1306, 2524, 8694], 'generators': [3, 648, 48, 36, 108], 'label': '1296.2922.18.b1.a1', 'mobius_quo': 0, 'mobius_sub': -3, 'normal_closure': '18.b1.a1', 'normal_contained_in': ['6.c1.a1', '6.d1.a1'], 'normal_contains': ['36.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '18.b1.a1', 'projective_image': '1296.2922', 'quotient_action_image': '3.1', 'quotient_action_kernel': '6.1', 'quotient_action_kernel_order': 6, 'quotient_fusion': None, 'short_label': '18.b1.a1', 'subgroup_fusion': None, 'weyl_group': '216.90'}
  • id: 71006972
    {'ambient': '1296.2922', 'aut_centralizer_order': 12, 'aut_label': '18.c1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '12.4', 'aut_weyl_index': 108, 'centralizer': '108.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.f1.a1', '9.a1.a1'], 'contains': ['36.d1.a1', '36.n1.a1', '36.p1.a1', '36.bh1.a1', '36.bl1.a1', '54.b1.a1', '54.c1.a1'], 'core': '144.b1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [5437, -1, 4258, -1, 3400, -1, 3443, -1], 'generators': [3, 36, 54, 648, 2], 'label': '1296.2922.18.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '18.c1.a1', 'projective_image': '1296.2922', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.c1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 71006973
    {'ambient': '1296.2922', 'aut_centralizer_order': 12, 'aut_label': '18.d1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '12.4', 'aut_weyl_index': 108, 'centralizer': '108.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.g1.a1', '9.a1.a1'], 'contains': ['36.d1.a1', '36.v1.a1', '36.w1.a1', '54.d1.a1', '54.e1.a1'], 'core': '144.b1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [6419, -1, 6070, -1, 6964, -1, 6808, -1], 'generators': [111, 36, 54, 2, 648], 'label': '1296.2922.18.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '18.d1.a1', 'projective_image': '1296.2922', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.d1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 71006974
    {'ambient': '1296.2922', 'aut_centralizer_order': 12, 'aut_label': '18.e1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '12.4', 'aut_weyl_index': 108, 'centralizer': '108.l1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.f1.a1', '9.c1.a1'], 'contains': ['36.f1.a1', '36.l1.a1', '36.q1.a1', '36.bj1.a1', '36.bm1.a1', '54.b1.a1', '54.f1.a1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [7621, -1, 7437, -1, 6264, -1, 7169, -1], 'generators': [3, 432, 54, 648, 2], 'label': '1296.2922.18.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1.a1', 'old_label': '18.e1.a1', 'projective_image': '1296.2922', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.e1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 71006975
    {'ambient': '1296.2922', 'aut_centralizer_order': 6, 'aut_label': '18.f1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '72.46', 'aut_weyl_index': 18, 'centralizer': '216.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.f1.a1', '9.d1.a1'], 'contains': ['36.e1.a1', '36.m1.a1', '36.s1.a1', '36.bk1.a1', '36.bn1.a1', '54.c1.a1', '54.f1.a1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4533, -1, 4023, -1, 3225, -1, 3268, -1], 'generators': [3, 432, 54, 648, 36], 'label': '1296.2922.18.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1.a1', 'old_label': '18.f1.a1', 'projective_image': '1296.2922', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.f1.a1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 71006976
    {'ambient': '1296.2922', 'aut_centralizer_order': 6, 'aut_label': '18.g1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '72.46', 'aut_weyl_index': 18, 'centralizer': '216.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.g1.a1', '9.d1.a1'], 'contains': ['36.e1.a1', '36.t1.a1', '36.u1.a1', '54.d1.a1', '54.g1.a1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4883, -1, 5184, -1, 6084, -1, 6289, -1], 'generators': [111, 432, 54, 648, 36], 'label': '1296.2922.18.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1.a1', 'old_label': '18.g1.a1', 'projective_image': '1296.2922', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.g1.a1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 71006977
    {'ambient': '1296.2922', 'aut_centralizer_order': 12, 'aut_label': '18.h1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '12.4', 'aut_weyl_index': 108, 'centralizer': '108.w1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.g1.a1', '9.c1.a1'], 'contains': ['36.f1.a1', '36.y1.a1', '36.z1.a1', '54.e1.a1', '54.g1.a1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [8651, -1, 8537, -1, 9486, -1, 8744, -1], 'generators': [111, 432, 54, 2, 648], 'label': '1296.2922.18.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1.a1', 'old_label': '18.h1.a1', 'projective_image': '1296.2922', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.h1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 71006978
    {'ambient': '1296.2922', 'aut_centralizer_order': 12, 'aut_label': '18.i1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '12.4', 'aut_weyl_index': 108, 'centralizer': '108.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.h1.a1', '9.a1.a1'], 'contains': ['36.h1.a1', '36.n1.a1', '36.w1.a1', '54.h1.a1', '54.i1.a1'], 'core': '144.b1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [6218, -1, 5928, -1, 6645, -1, 6649, -1], 'generators': [3, 36, 162, 2, 648], 'label': '1296.2922.18.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '18.i1.a1', 'projective_image': '1296.2922', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.i1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 71006979
    {'ambient': '1296.2922', 'aut_centralizer_order': 2, 'aut_label': '3.b1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '216.90', 'aut_weyl_index': 6, 'centralizer': '648.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['6.d1.a1', '6.j1.a1', '6.o1.a1', '9.a1.a1', '9.b1.a1', '12.n1.a1'], 'core': '6.d1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [2057, -1, 1091, -1, 2303, -1, 2463, -1], 'generators': [3, 108, 36, 54, 648, 2, 48], 'label': '1296.2922.3.b1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '3.b1.a1', 'projective_image': '1296.2922', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3.b1.a1', 'subgroup_fusion': None, 'weyl_group': '216.90'}
  • id: 71006980
    {'ambient': '1296.2922', 'aut_centralizer_order': 12, 'aut_label': '18.j1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '12.4', 'aut_weyl_index': 108, 'centralizer': '108.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.i1.a1', '9.a1.a1'], 'contains': ['36.h1.a1', '36.p1.a1', '36.v1.a1', '54.j1.a1', '54.k1.a1'], 'core': '144.b1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [7203, -1, 6495, -1, 6805, -1, 6129, -1], 'generators': [111, 36, 162, 2, 648], 'label': '1296.2922.18.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '18.j1.a1', 'projective_image': '1296.2922', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.j1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 71006981
    {'ambient': '1296.2922', 'aut_centralizer_order': 6, 'aut_label': '18.k1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '24.14', 'aut_weyl_index': 54, 'centralizer': '216.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.h1.a1', '9.c1.a1'], 'contains': ['36.j1.a1', '36.l1.a1', '36.z1.a1', '54.h1.a1', '54.l1.a1'], 'core': '432.b1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [8407, -1, 8235, -1, 8721, -1, 8997, -1], 'generators': [3, 432, 162, 2, 648], 'label': '1296.2922.18.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1.a1', 'old_label': '18.k1.a1', 'projective_image': '1296.2922', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.k1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 71006982
    {'ambient': '1296.2922', 'aut_centralizer_order': 6, 'aut_label': '18.l1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '72.46', 'aut_weyl_index': 18, 'centralizer': '216.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.h1.a1', '9.d1.a1'], 'contains': ['36.i1.a1', '36.m1.a1', '36.u1.a1', '54.i1.a1', '54.l1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4725, -1, 4129, -1, 5513, -1, 5515, -1], 'generators': [3, 432, 162, 648, 36], 'label': '1296.2922.18.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1.a1', 'old_label': '18.l1.a1', 'projective_image': '1296.2922', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.l1.a1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 71006983
    {'ambient': '1296.2922', 'aut_centralizer_order': 6, 'aut_label': '18.m1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '24.14', 'aut_weyl_index': 54, 'centralizer': '216.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.i1.a1', '9.c1.a1'], 'contains': ['36.j1.a1', '36.q1.a1', '36.y1.a1', '54.j1.a1', '54.m1.a1'], 'core': '432.b1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [9195, -1, 8920, -1, 8879, -1, 8588, -1], 'generators': [111, 432, 162, 2, 648], 'label': '1296.2922.18.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1.a1', 'old_label': '18.m1.a1', 'projective_image': '1296.2922', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.m1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 71006984
    {'ambient': '1296.2922', 'aut_centralizer_order': 6, 'aut_label': '18.n1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '72.46', 'aut_weyl_index': 18, 'centralizer': '216.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.i1.a1', '9.d1.a1'], 'contains': ['36.i1.a1', '36.s1.a1', '36.t1.a1', '54.k1.a1', '54.m1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5033, -1, 5670, -1, 5611, -1, 5416, -1], 'generators': [111, 432, 162, 648, 36], 'label': '1296.2922.18.n1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1.a1', 'old_label': '18.n1.a1', 'projective_image': '1296.2922', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.n1.a1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 71006985
    {'ambient': '1296.2922', 'aut_centralizer_order': 72, 'aut_label': '18.o1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '6.1', 'aut_weyl_index': 216, 'centralizer': '18.o1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.a1.a1', '6.j1.a1', '9.a1.a1'], 'contains': ['36.b1.a1', '36.d1.a1', '36.h1.a1', '54.n1.a1', '54.o1.a1'], 'core': '36.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5623, -1, 4414, -1, 4606, -1, 5794, -1], 'generators': [54, 36, 108, 648, 2], 'label': '1296.2922.18.o1.a1', 'mobius_quo': None, 'mobius_sub': -3, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '18.o1.a1', 'projective_image': '1296.2922', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.o1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 71006986
    {'ambient': '1296.2922', 'aut_centralizer_order': 6, 'aut_label': '18.p1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '72.42', 'aut_weyl_index': 18, 'centralizer': '216.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1.a1', '6.j1.a1', '9.b1.a1'], 'contains': ['36.c1.a1', '54.n1.a1', '72.j1.a1'], 'core': '36.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [1844, -1, 1848, -1, 2438, -1, 2775, -1], 'generators': [54, 648, 84, 36, 108], 'label': '1296.2922.18.p1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '6.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '18.p1.a1', 'projective_image': '1296.2922', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.p1.a1', 'subgroup_fusion': None, 'weyl_group': '72.42'}
  • id: 71006987
    {'ambient': '1296.2922', 'aut_centralizer_order': 6, 'aut_label': '18.q1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '36.11', 'aut_weyl_index': 36, 'centralizer': '216.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.j1.a1', '6.k1.a1'], 'contains': ['36.bc1.a1', '54.n1.a1', '72.k1.a1'], 'core': '108.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [3056, -1, 2461, -1, 1541, -1, 2955, -1], 'generators': [54, 648, 86, 36, 108], 'label': '1296.2922.18.q1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.j1.a1', 'old_label': '18.q1.a1', 'projective_image': '1296.2922', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.q1.a1', 'subgroup_fusion': None, 'weyl_group': '36.11'}
  • id: 71006988
    {'ambient': '1296.2922', 'aut_centralizer_order': 36, 'aut_label': '18.r1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '12.4', 'aut_weyl_index': 108, 'centralizer': '36.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.a1.a1', '9.c1.a1'], 'contains': ['36.f1.a1', '36.g1.a1', '36.j1.a1', '36.k1.a1', '36.bf1.a1', '54.a1.a1', '54.o1.a1'], 'core': '54.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8872, -1, 8761, -1, 7980, -1, 8075, -1], 'generators': [54, 432, 108, 648, 2], 'label': '1296.2922.18.r1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1.a1', 'old_label': '18.r1.a1', 'projective_image': '1296.2922', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.r1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 71006989
    {'ambient': '1296.2922', 'aut_centralizer_order': 18, 'aut_label': '18.s1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '8.5', 'aut_weyl_index': 162, 'centralizer': '72.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.l1.a1', '9.c1.a1'], 'contains': ['36.l1.a1', '36.y1.a1', '36.bf1.a1', '54.p1.a1', '54.q1.a1', '54.r1.a1'], 'core': '108.b1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [7435, -1, 6794, -1, 7804, -1, 7616, -1], 'generators': [3, 648, 108, 2, 432], 'label': '1296.2922.18.s1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1.a1', 'old_label': '18.s1.a1', 'projective_image': '1296.2922', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.s1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 71006990
    {'ambient': '1296.2922', 'aut_centralizer_order': 6, 'aut_label': '3.c1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '72.46', 'aut_weyl_index': 18, 'centralizer': '216.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['6.a1.a1', '6.f1.a1', '6.g1.a1', '6.h1.a1', '6.i1.a1', '6.l1.a1', '6.n1.a1', '9.a1.a1', '9.c1.a1', '9.d1.a1'], 'core': '6.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5392, -1, 5347, -1, 4915, -1, 5178, -1], 'generators': [3, 36, 648, 54, 432, 108, 2], 'label': '1296.2922.3.c1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1.a1', 'old_label': '3.c1.a1', 'projective_image': '1296.2922', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3.c1.a1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 71006991
    {'ambient': '1296.2922', 'aut_centralizer_order': 18, 'aut_label': '18.t1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '24.14', 'aut_weyl_index': 54, 'centralizer': '72.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.c1.a1', '6.l1.a1', '9.d1.a1'], 'contains': ['36.a1.a1', '36.m1.a1', '36.t1.a1', '54.p1.a1', '54.s1.a1'], 'core': '36.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3677, -1, 3130, -1, 3940, -1, 4143, -1], 'generators': [3, 36, 108, 432, 648], 'label': '1296.2922.18.t1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '6.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1.a1', 'old_label': '18.t1.a1', 'projective_image': '1296.2922', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.t1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 71006992
    {'ambient': '1296.2922', 'aut_centralizer_order': 36, 'aut_label': '18.u1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '12.4', 'aut_weyl_index': 108, 'centralizer': '36.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.d1.a1', '6.l1.a1', '9.a1.a1'], 'contains': ['36.b1.a1', '36.n1.a1', '36.v1.a1', '54.q1.a1', '54.s1.a1'], 'core': '36.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5183, -1, 3789, -1, 4761, -1, 5081, -1], 'generators': [3, 36, 108, 2, 648], 'label': '1296.2922.18.u1.a1', 'mobius_quo': None, 'mobius_sub': -3, 'normal_closure': '6.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1.a1', 'old_label': '18.u1.a1', 'projective_image': '1296.2922', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.u1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 71006993
    {'ambient': '1296.2922', 'aut_centralizer_order': 18, 'aut_label': '18.v1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '12.4', 'aut_weyl_index': 108, 'centralizer': '72.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.l1.a1', '6.m1.a1'], 'contains': ['36.o1.a1', '36.x1.a1', '36.bb1.a1', '54.r1.a1', '54.s1.a1'], 'core': '108.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2812, -1, 1664, -1, 3781, -1, 3983, -1], 'generators': [3, 36, 108, 434, 648], 'label': '1296.2922.18.v1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.l1.a1', 'old_label': '18.v1.a1', 'projective_image': '1296.2922', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.v1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 71006994
    {'ambient': '1296.2922', 'aut_centralizer_order': 12, 'aut_label': '18.w1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '12.4', 'aut_weyl_index': 108, 'centralizer': '108.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.n1.a1', '6.o1.a1', '6.p1.a1', '9.a1.a1'], 'contains': ['36.b1.a1', '36.p1.a1', '36.w1.a1', '54.t1.a1', '54.u1.a1'], 'core': '36.b1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [3366, -1, 4553, -1, 4921, -1, 4921, -1], 'generators': [81, 36, 648, 2, 756], 'label': '1296.2922.18.w1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '18.w1.a1', 'projective_image': '1296.2922', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.w1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 71006995
    {'ambient': '1296.2922', 'aut_centralizer_order': 6, 'aut_label': '18.x1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '24.14', 'aut_weyl_index': 54, 'centralizer': '216.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.n1.a1', '9.c1.a1'], 'contains': ['36.q1.a1', '36.z1.a1', '36.bf1.a1', '54.t1.a1', '54.v1.a1'], 'core': '108.b1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [6656, -1, 7662, -1, 8160, -1, 7894, -1], 'generators': [81, 432, 648, 38, 756], 'label': '1296.2922.18.x1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1.a1', 'old_label': '18.x1.a1', 'projective_image': '1296.2922', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.x1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 71006996
    {'ambient': '1296.2922', 'aut_centralizer_order': 6, 'aut_label': '18.y1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '12.4', 'aut_weyl_index': 108, 'centralizer': '216.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.n1.a1'], 'contains': ['36.r1.a1', '36.ba1.a1', '36.bg1.a1', '54.t1.a1', '54.w1.a1'], 'core': '324.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [3537, -1, 6933, -1, 5745, -1, 5639, -1], 'generators': [81, 900, 648, 434, 756], 'label': '1296.2922.18.y1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.y1.a1', 'old_label': '18.y1.a1', 'projective_image': '1296.2922', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.y1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 71006997
    {'ambient': '1296.2922', 'aut_centralizer_order': 6, 'aut_label': '18.z1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '72.46', 'aut_weyl_index': 18, 'centralizer': '216.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.e1.a1', '6.n1.a1', '9.d1.a1'], 'contains': ['36.a1.a1', '36.s1.a1', '36.u1.a1', '54.u1.a1', '54.v1.a1', '54.w1.a1'], 'core': '36.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3248, -1, 3670, -1, 5214, -1, 4276, -1], 'generators': [81, 432, 648, 756, 36], 'label': '1296.2922.18.z1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '6.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1.a1', 'old_label': '18.z1.a1', 'projective_image': '1296.2922', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.z1.a1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 71006998
    {'ambient': '1296.2922', 'aut_centralizer_order': 2, 'aut_label': '18.ba1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '216.90', 'aut_weyl_index': 6, 'centralizer': '648.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.e1.a1', '6.o1.a1', '9.b1.a1'], 'contains': ['36.c1.a1', '54.u1.a1', '72.z1.a1'], 'core': '36.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [1718, -1, 1189, -1, 2690, -1, 2236, -1], 'generators': [81, 648, 48, 36, 756], 'label': '1296.2922.18.ba1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '6.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '18.ba1.a1', 'projective_image': '1296.2922', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.ba1.a1', 'subgroup_fusion': None, 'weyl_group': '216.90'}
  • id: 71006999
    {'ambient': '1296.2922', 'aut_centralizer_order': 1, 'aut_label': '18.bb1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '216.90', 'aut_weyl_index': 6, 'centralizer': '1296.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.e1.a1', '6.p1.a1'], 'contains': ['36.bd1.a1', '54.u1.a1', '72.ba1.a1'], 'core': '108.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [376, -1, 2073, -1, 2798, -1, 1626, -1], 'generators': [81, 648, 480, 36, 756], 'label': '1296.2922.18.bb1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.p1.a1', 'old_label': '18.bb1.a1', 'projective_image': '1296.2922', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.bb1.a1', 'subgroup_fusion': None, 'weyl_group': '216.90'}
  • id: 71007000
    {'ambient': '1296.2922', 'aut_centralizer_order': 36, 'aut_label': '24.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '36.10', 'aut_weyl_index': 36, 'centralizer': '36.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '12.d1.a1', '12.o1.a1'], 'contains': ['48.a1.a1', '72.a1.a1', '72.i1.a1', '72.l1.a1'], 'core': '24.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2357, 9480, 2164, 9475, 2341, 9312, 2214, 688], 'generators': [54, 2, 36, 432], 'label': '1296.2922.24.a1.a1', 'mobius_quo': 0, 'mobius_sub': -12, 'normal_closure': '24.a1.a1', 'normal_contained_in': ['6.a1.a1'], 'normal_contains': ['48.a1.a1', '72.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '24.a1.a1', 'projective_image': '1296.2922', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.a1.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 71007001
    {'ambient': '1296.2922', 'aut_centralizer_order': 9, 'aut_label': '4.a1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '144.188', 'aut_weyl_index': 9, 'centralizer': '144.a1.a1', 'complements': ['324.h1.a1', '324.i1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '2.b1.a1', '2.c1.a1'], 'contains': ['12.a1.a1', '12.b1.a1', '12.c1.a1', '12.j1.a1', '12.k1.a1', '12.l1.a1', '12.m1.a1', '16.a1.a1'], 'core': '4.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1757, 5918, 2045, 5978, 1650, 3838, 1916, 6161], 'generators': [2, 648, 756, 84, 432, 36], 'label': '1296.2922.4.a1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.a1.a1', 'normal_contained_in': ['2.a1.a1', '2.b1.a1', '2.c1.a1'], 'normal_contains': ['12.a1.a1', '12.b1.a1', '12.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.a1.a1', 'projective_image': '1296.2922', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.a1.a1', 'subgroup_fusion': None, 'weyl_group': '144.188'}
  • id: 71007002
    {'ambient': '1296.2922', 'aut_centralizer_order': 108, 'aut_label': '24.b1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '4.2', 'aut_weyl_index': 324, 'centralizer': '12.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.a1.a1', '12.d1.a1', '12.e1.a1', '12.f1.a1', '12.g1.a1', '12.h1.a1', '12.i1.a1'], 'contains': ['48.a1.a1', '72.b1.a1', '72.c1.a1', '72.d1.a1', '72.e1.a1', '72.f1.a1', '72.g1.a1', '72.h1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6907, -1, 7247, -1, 5267, -1, 4570, -1], 'generators': [108, 2, 36, 432], 'label': '1296.2922.24.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1.a1', 'old_label': '24.b1.a1', 'projective_image': '1296.2922', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.b1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 71007003
    {'ambient': '1296.2922', 'aut_centralizer_order': 6, 'aut_label': '24.c1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '18.3', 'aut_weyl_index': 72, 'centralizer': '216.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.j1.a1', '8.a1.a1', '12.n1.a1'], 'contains': ['48.d1.a1', '72.i1.a1', '72.j1.a1', '72.k1.a1'], 'core': '144.b1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [1319, -1, 972, -1, 432, -1, 1270, -1], 'generators': [54, 2, 84, 36], 'label': '1296.2922.24.c1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.n1.a1', 'old_label': '24.c1.a1', 'projective_image': '1296.2922', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.c1.a1', 'subgroup_fusion': None, 'weyl_group': '18.3'}
  • id: 71007004
    {'ambient': '1296.2922', 'aut_centralizer_order': 9, 'aut_label': '24.d1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '36.12', 'aut_weyl_index': 36, 'centralizer': '144.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1.a1', '8.a1.a1', '12.p1.a1'], 'contains': ['48.b1.a1', '72.a1.a1', '72.j1.a1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [513, -1, 714, -1, 577, -1, 1053, -1], 'generators': [54, 84, 36, 432], 'label': '1296.2922.24.d1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '6.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.a1', 'old_label': '24.d1.a1', 'projective_image': '1296.2922', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.d1.a1', 'subgroup_fusion': None, 'weyl_group': '36.12'}
  • id: 71007005
    {'ambient': '1296.2922', 'aut_centralizer_order': 9, 'aut_label': '24.e1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '18.3', 'aut_weyl_index': 72, 'centralizer': '144.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.k1.a1', '8.a1.a1'], 'contains': ['48.c1.a1', '72.a1.a1', '72.k1.a1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [1957, -1, 1716, -1, 56, -1, 1414, -1], 'generators': [54, 86, 36, 432], 'label': '1296.2922.24.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.a1.a1', 'old_label': '24.e1.a1', 'projective_image': '1296.2922', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.e1.a1', 'subgroup_fusion': None, 'weyl_group': '18.3'}
  • id: 71007006
    {'ambient': '1296.2922', 'aut_centralizer_order': 36, 'aut_label': '24.f1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '12.4', 'aut_weyl_index': 108, 'centralizer': '36.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.d1.a1', '12.e1.a1', '12.q1.a1'], 'contains': ['48.a1.a1', '72.m1.a1', '72.n1.a1', '72.o1.a1', '72.p1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8176, -1, 7990, -1, 4780, -1, 5145, -1], 'generators': [162, 2, 36, 432], 'label': '1296.2922.24.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1.a1', 'old_label': '24.f1.a1', 'projective_image': '1296.2922', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.f1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 71007007
    {'ambient': '1296.2922', 'aut_centralizer_order': 18, 'aut_label': '24.g1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '12.4', 'aut_weyl_index': 108, 'centralizer': '72.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.b1.a1', '12.f1.a1', '12.o1.a1', '12.q1.a1'], 'contains': ['48.a1.a1', '72.q1.a1', '72.r1.a1', '72.s1.a1', '72.t1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [3820, -1, 3953, -1, 2490, -1, 2065, -1], 'generators': [3, 2, 432, 36], 'label': '1296.2922.24.g1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1.a1', 'old_label': '24.g1.a1', 'projective_image': '1296.2922', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.g1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 71007008
    {'ambient': '1296.2922', 'aut_centralizer_order': 3, 'aut_label': '24.h1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '108.26', 'aut_weyl_index': 12, 'centralizer': '432.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.c1.a1', '8.b1.a1', '12.p1.a1'], 'contains': ['48.b1.a1', '72.r1.a1', '72.u1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [191, -1, 246, -1, 956, -1, 713, -1], 'generators': [3, 432, 48, 36], 'label': '1296.2922.24.h1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '6.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.a1', 'old_label': '24.h1.a1', 'projective_image': '1296.2922', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.h1.a1', 'subgroup_fusion': None, 'weyl_group': '108.26'}
  • id: 71007009
    {'ambient': '1296.2922', 'aut_centralizer_order': 6, 'aut_label': '24.i1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '54.6', 'aut_weyl_index': 24, 'centralizer': '216.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.d1.a1', '8.b1.a1', '12.n1.a1'], 'contains': ['48.d1.a1', '72.s1.a1', '72.u1.a1'], 'core': '144.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [1006, -1, 116, -1, 846, -1, 859, -1], 'generators': [3, 2, 48, 36], 'label': '1296.2922.24.i1.a1', 'mobius_quo': None, 'mobius_sub': -3, 'normal_closure': '6.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.a1', 'old_label': '24.i1.a1', 'projective_image': '1296.2922', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.i1.a1', 'subgroup_fusion': None, 'weyl_group': '54.6'}
  • id: 71007010
    {'ambient': '1296.2922', 'aut_centralizer_order': 3, 'aut_label': '24.j1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '54.6', 'aut_weyl_index': 24, 'centralizer': '432.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.m1.a1', '8.b1.a1'], 'contains': ['48.f1.a1', '72.t1.a1', '72.u1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [704, -1, 38, -1, 722, -1, 567, -1], 'generators': [3, 434, 48, 36], 'label': '1296.2922.24.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.b1.a1', 'old_label': '24.j1.a1', 'projective_image': '1296.2922', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.j1.a1', 'subgroup_fusion': None, 'weyl_group': '54.6'}
  • id: 71007011
    {'ambient': '1296.2922', 'aut_centralizer_order': 6, 'aut_label': '24.k1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '36.10', 'aut_weyl_index': 36, 'centralizer': '216.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.c1.a1', '12.g1.a1', '12.o1.a1', '12.q1.a1'], 'contains': ['48.a1.a1', '72.v1.a1', '72.w1.a1', '72.x1.a1', '72.y1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [3684, -1, 3607, -1, 2644, -1, 1911, -1], 'generators': [81, 2, 36, 432], 'label': '1296.2922.24.k1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.f1.a1', 'old_label': '24.k1.a1', 'projective_image': '1296.2922', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.k1.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 71007012
    {'ambient': '1296.2922', 'aut_centralizer_order': 1, 'aut_label': '4.b1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '324.118', 'aut_weyl_index': 4, 'centralizer': '1296.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['8.a1.a1', '8.b1.a1', '8.c1.a1', '12.n1.a1', '12.o1.a1', '12.p1.a1'], 'core': '24.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [945, -1, 478, -1, 1003, -1, 1003, -1], 'generators': [3, 36, 432, 54, 2, 48], 'label': '1296.2922.4.b1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.a1', 'old_label': '4.b1.a1', 'projective_image': '1296.2922', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.b1.a1', 'subgroup_fusion': None, 'weyl_group': '324.118'}
  • id: 71007013
    {'ambient': '1296.2922', 'aut_centralizer_order': 2, 'aut_label': '24.l1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '54.6', 'aut_weyl_index': 24, 'centralizer': '648.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.o1.a1', '8.c1.a1', '12.n1.a1'], 'contains': ['48.d1.a1', '72.v1.a1', '72.z1.a1'], 'core': '144.b1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [1115, -1, 442, -1, 1261, -1, 479, -1], 'generators': [81, 2, 48, 36], 'label': '1296.2922.24.l1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.n1.a1', 'old_label': '24.l1.a1', 'projective_image': '1296.2922', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.l1.a1', 'subgroup_fusion': None, 'weyl_group': '54.6'}
  • id: 71007014
    {'ambient': '1296.2922', 'aut_centralizer_order': 1, 'aut_label': '24.m1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '54.6', 'aut_weyl_index': 24, 'centralizer': '1296.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.p1.a1', '8.c1.a1'], 'contains': ['48.e1.a1', '72.v1.a1', '72.ba1.a1'], 'core': '144.b1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [288, -1, 1522, -1, 1436, -1, 35, -1], 'generators': [81, 2, 480, 36], 'label': '1296.2922.24.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.m1.a1', 'old_label': '24.m1.a1', 'projective_image': '1296.2922', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.m1.a1', 'subgroup_fusion': None, 'weyl_group': '54.6'}
  • id: 71007015
    {'ambient': '1296.2922', 'aut_centralizer_order': 1, 'aut_label': '24.n1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '324.118', 'aut_weyl_index': 4, 'centralizer': '1296.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.e1.a1', '8.c1.a1', '12.p1.a1'], 'contains': ['48.b1.a1', '72.y1.a1', '72.z1.a1', '72.ba1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [32, -1, 520, -1, 1348, -1, 160, -1], 'generators': [81, 48, 432, 36], 'label': '1296.2922.24.n1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '6.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.a1', 'old_label': '24.n1.a1', 'projective_image': '1296.2922', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.n1.a1', 'subgroup_fusion': None, 'weyl_group': '324.118'}
  • id: 71007016
    {'ambient': '1296.2922', 'aut_centralizer_order': 12, 'aut_label': '27.a1', 'aut_quo_index': None, 'aut_stab_index': 27, 'aut_weyl_group': '4.2', 'aut_weyl_index': 324, 'centralizer': '108.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['9.a1.a1', '9.c1.a1'], 'contains': ['54.b1.a1', '54.e1.a1', '54.h1.a1', '54.j1.a1', '54.o1.a1', '54.q1.a1', '54.t1.a1', '81.a1.a1'], 'core': '324.a1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [8322, -1, 7609, -1, 8305, -1, 9259, -1], 'generators': [3, 648, 54, 108, 2], 'label': '1296.2922.27.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1.a1', 'old_label': '27.a1.a1', 'projective_image': '1296.2922', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '27.a1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 71007017
    {'ambient': '1296.2922', 'aut_centralizer_order': 12, 'aut_label': '27.b1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '12.4', 'aut_weyl_index': 108, 'centralizer': '108.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['9.a1.a1', '9.b1.a1', '9.d1.a1'], 'contains': ['54.c1.a1', '54.d1.a1', '54.i1.a1', '54.k1.a1', '54.n1.a1', '54.s1.a1', '54.u1.a1', '81.a1.a1'], 'core': '108.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [2960, -1, 3089, -1, 4451, -1, 4762, -1], 'generators': [3, 36, 54, 108, 648], 'label': '1296.2922.27.b1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '27.b1.a1', 'projective_image': '1296.2922', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '27.b1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 71007018
    {'ambient': '1296.2922', 'aut_centralizer_order': 6, 'aut_label': '27.c1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '24.14', 'aut_weyl_index': 54, 'centralizer': '216.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['9.c1.a1', '9.d1.a1'], 'contains': ['54.a1.a1', '54.f1.a1', '54.g1.a1', '54.l1.a1', '54.m1.a1', '54.p1.a1', '54.v1.a1', '81.a1.a1'], 'core': '54.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [6131, -1, 6118, -1, 8547, -1, 8240, -1], 'generators': [3, 432, 54, 108, 648], 'label': '1296.2922.27.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1.a1', 'old_label': '27.c1.a1', 'projective_image': '1296.2922', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '27.c1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 71007019
    {'ambient': '1296.2922', 'aut_centralizer_order': 108, 'aut_label': '36.a1', 'aut_quo_index': 4, 'aut_stab_index': 1, 'aut_weyl_group': '12.4', 'aut_weyl_index': 108, 'centralizer': '12.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['12.a1.a1', '12.b1.a1', '12.j1.a1', '18.a1.a1', '18.t1.a1', '18.z1.a1'], 'contains': ['72.b1.a1', '108.a1.a1', '108.b1.a1', '108.bb1.a1'], 'core': '36.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3193, 5254, 3381, 5285, 3715, 5483, 3612, 4516], 'generators': [108, 648, 36, 432], 'label': '1296.2922.36.a1.a1', 'mobius_quo': -1, 'mobius_sub': 6, 'normal_closure': '36.a1.a1', 'normal_contained_in': ['12.a1.a1', '12.b1.a1', '18.a1.a1'], 'normal_contains': ['108.a1.a1', '108.b1.a1', '144.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '36.a1.a1', 'projective_image': '1296.2922', 'quotient_action_image': '12.4', 'quotient_action_kernel': '3.1', 'quotient_action_kernel_order': 3, 'quotient_fusion': None, 'short_label': '36.a1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 71007020
    {'ambient': '1296.2922', 'aut_centralizer_order': 216, 'aut_label': '36.b1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '6.1', 'aut_weyl_index': 216, 'centralizer': '6.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['12.a1.a1', '12.c1.a1', '12.k1.a1', '18.o1.a1', '18.u1.a1', '18.w1.a1'], 'contains': ['72.c1.a1', '108.a1.a1', '108.ba1.a1'], 'core': '36.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3358, 3673, 3580, 4011, 4032, 4456, 5031, 5932], 'generators': [108, 648, 2, 36], 'label': '1296.2922.36.b1.a1', 'mobius_quo': 0, 'mobius_sub': 18, 'normal_closure': '36.b1.a1', 'normal_contained_in': ['12.a1.a1', '12.c1.a1'], 'normal_contains': ['108.a1.a1', '144.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '36.b1.a1', 'projective_image': '1296.2922', 'quotient_action_image': '6.1', 'quotient_action_kernel': '6.1', 'quotient_action_kernel_order': 6, 'quotient_fusion': None, 'short_label': '36.b1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 71007021
    {'ambient': '1296.2922', 'aut_centralizer_order': 18, 'aut_label': '36.c1', 'aut_quo_index': 4, 'aut_stab_index': 1, 'aut_weyl_group': '72.42', 'aut_weyl_index': 18, 'centralizer': '72.a1.a1', 'complements': ['36.bj1.a1', '36.bm1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['12.b1.a1', '12.c1.a1', '12.l1.a1', '18.b1.a1', '18.p1.a1', '18.ba1.a1'], 'contains': ['108.a1.a1', '144.d1.a1'], 'core': '36.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1597, 2588, 1319, 2917, 1896, 3180, 2559, 7238], 'generators': [84, 36, 108, 648], 'label': '1296.2922.36.c1.a1', 'mobius_quo': 0, 'mobius_sub': 6, 'normal_closure': '36.c1.a1', 'normal_contained_in': ['12.b1.a1', '12.c1.a1', '18.b1.a1'], 'normal_contains': ['108.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '36.c1.a1', 'projective_image': '1296.2922', 'quotient_action_image': '6.2', 'quotient_action_kernel': '6.1', 'quotient_action_kernel_order': 6, 'quotient_fusion': None, 'short_label': '36.c1.a1', 'subgroup_fusion': None, 'weyl_group': '72.42'}
  • id: 71007022
    {'ambient': '1296.2922', 'aut_centralizer_order': 72, 'aut_label': '36.d1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '2.1', 'aut_weyl_index': 648, 'centralizer': '18.o1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.d1.a1', '18.c1.a1', '18.d1.a1', '18.o1.a1'], 'contains': ['72.c1.a1', '72.i1.a1', '72.m1.a1', '108.c1.a1', '108.d1.a1', '108.e1.a1'], 'core': '144.b1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [6488, -1, 5649, -1, 5024, -1, 5714, -1], 'generators': [54, 108, 2, 36], 'label': '1296.2922.36.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '36.d1.a1', 'projective_image': '1296.2922', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.d1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}