Abstract group data - 1296.3190

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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': '24.15', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 2, 'aut_exponent': 6, 'aut_gen_orders': [2, 6, 6, 2, 6, 6, 2, 2], 'aut_gens': [[1, 6, 36, 432], [245, 30, 396, 864], [25, 174, 828, 432], [245, 390, 900, 864], [217, 318, 396, 432], [29, 366, 828, 864], [29, 318, 612, 432], [245, 30, 612, 864], [29, 246, 612, 864]], 'aut_group': None, 'aut_hash': 2534858294950307745, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 3456, 'aut_permdeg': 20, 'aut_perms': [931344540392483747, 2077734402360875094, 225551693987379231, 66671147330647873, 1385590196689946136, 65483249918947392, 929144670902013347, 121702698091841952], 'aut_phi_ratio': 8.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 3, 2, 1], [2, 6, 1, 1], [2, 18, 1, 2], [2, 54, 1, 1], [3, 1, 2, 1], [3, 2, 1, 3], [3, 2, 2, 3], [3, 4, 1, 3], [3, 4, 2, 3], [3, 8, 1, 1], [3, 8, 2, 1], [4, 6, 1, 1], [4, 18, 1, 1], [6, 1, 2, 1], [6, 2, 1, 3], [6, 2, 2, 3], [6, 3, 4, 1], [6, 4, 1, 3], [6, 4, 2, 3], [6, 6, 2, 4], [6, 6, 4, 3], [6, 8, 1, 1], [6, 8, 2, 1], [6, 12, 1, 1], [6, 12, 2, 3], [6, 12, 4, 2], [6, 18, 2, 3], [6, 18, 4, 1], [6, 36, 1, 1], [6, 36, 2, 1], [6, 54, 2, 1], [12, 6, 2, 2], [12, 6, 4, 1], [12, 12, 1, 1], [12, 12, 2, 2], [12, 12, 4, 1], [12, 18, 2, 2], [12, 18, 4, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_3^3.C_2^6.C_2', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 2, 'autcent_group': '16.14', 'autcent_hash': 14, 'autcent_nilpotent': True, 'autcent_order': 16, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^4', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 6, 'autcentquo_group': '216.162', 'autcentquo_hash': 162, 'autcentquo_nilpotent': False, 'autcentquo_order': 216, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'S_3^3', 'cc_stats': [[1, 1, 1], [2, 1, 1], [2, 3, 2], [2, 6, 1], [2, 18, 2], [2, 54, 1], [3, 1, 2], [3, 2, 9], [3, 4, 9], [3, 8, 3], [4, 6, 1], [4, 18, 1], [6, 1, 2], [6, 2, 9], [6, 3, 4], [6, 4, 9], [6, 6, 20], [6, 8, 3], [6, 12, 15], [6, 18, 10], [6, 36, 3], [6, 54, 2], [12, 6, 8], [12, 12, 9], [12, 18, 8]], 'center_label': '6.2', 'center_order': 6, 'central_product': True, 'central_quotient': '216.162', 'commutator_count': 1, 'commutator_label': '54.15', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '3.1', '3.1', '3.1', '3.1'], 'composition_length': 8, 'conjugacy_classes_known': True, 'counter': 3190, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [['3.1', 1], ['6.1', 1], ['72.23', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 3, 1, 2], [2, 6, 1, 1], [2, 18, 1, 2], [2, 54, 1, 1], [3, 1, 2, 1], [3, 2, 1, 3], [3, 2, 2, 3], [3, 4, 1, 3], [3, 4, 2, 3], [3, 8, 1, 1], [3, 8, 2, 1], [4, 6, 1, 1], [4, 18, 1, 1], [6, 1, 2, 1], [6, 2, 1, 3], [6, 2, 2, 3], [6, 3, 2, 2], [6, 4, 1, 3], [6, 4, 2, 3], [6, 6, 1, 4], [6, 6, 2, 8], [6, 8, 1, 1], [6, 8, 2, 1], [6, 12, 1, 3], [6, 12, 2, 6], [6, 18, 2, 5], [6, 36, 1, 1], [6, 36, 2, 1], [6, 54, 2, 1], [12, 6, 2, 2], [12, 6, 4, 1], [12, 12, 1, 1], [12, 12, 2, 2], [12, 12, 4, 1], [12, 18, 2, 2], [12, 18, 4, 1]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 139776, 'exponent': 12, 'exponents_of_order': [4, 4], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [[8, 0, 2]], 'familial': False, 'frattini_label': '2.1', 'frattini_quotient': '648.731', 'hash': 3190, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 6, 'inner_gen_orders': [2, 6, 6, 3], 'inner_gens': [[1, 30, 36, 432], [13, 6, 396, 432], [1, 78, 36, 864], [1, 6, 900, 432]], 'inner_hash': 162, 'inner_nilpotent': False, 'inner_order': 216, 'inner_split': True, 'inner_tex': 'S_3^3', 'inner_used': [1, 2, 3, 4], 'irrC_degree': 8, 'irrQ_degree': 16, 'irrQ_dim': 16, 'irrR_degree': 16, 'irrep_stats': [[1, 24], [2, 66], [4, 39], [8, 6]], 'label': '1296.3190', 'linC_count': 5440, 'linC_degree': 6, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 8, 'linQ_degree_count': 144, 'linQ_dim': 8, 'linQ_dim_count': 144, 'linR_count': 1064, 'linR_degree': 8, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': False, 'monomial': True, 'name': 'C6.S3^3', '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': 70, 'number_characteristic_subgroups': 92, 'number_conjugacy_classes': 135, 'number_divisions': 81, 'number_normal_subgroups': 108, 'number_subgroup_autclasses': 677, 'number_subgroup_classes': 791, 'number_subgroups': 5396, 'old_label': None, 'order': 1296, 'order_factorization_type': 33, 'order_stats': [[1, 1], [2, 103], [3, 80], [4, 24], [6, 788], [12, 300]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 2, 'outer_gen_orders': [2, 2, 2, 2], 'outer_gen_pows': [0, 0, 0, 0], 'outer_gens': [[217, 6, 180, 864], [1, 222, 180, 432], [5, 30, 36, 864], [1, 6, 180, 432]], 'outer_group': '16.14', 'outer_hash': 14, 'outer_nilpotent': True, 'outer_order': 16, 'outer_permdeg': 8, 'outer_perms': [5040, 120, 6, 1], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^4', 'pc_rank': 4, 'perfect': False, 'permutation_degree': 16, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 2, 3], 'quasisimple': False, 'rank': 3, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 8], [2, 22], [4, 31], [8, 17], [16, 3]], 'representations': {'PC': {'code': 90936980092599672835762631952120684950867, 'gens': [1, 3, 5, 8], 'pres': [8, -2, -3, -2, -3, -2, -2, -3, -3, 16, 722, 66, 771, 2660, 116, 2901, 141, 2710, 1575]}, 'GLZN': {'d': 2, 'p': 18, 'gens': [68839, 40831, 5941, 96397, 5995, 42997, 99161, 6137]}, 'Perm': {'d': 16, 'gens': [368056, 1321086417840, 811583, 2889377568000, 367920, 4185076896000, 325, 435]}}, 'schur_multiplier': [2, 2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 6], 'solvability_type': 7, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_6.S_3^3', 'transitive_degree': 48, '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: 114753326
    {'aut_label': '1A', 'centralizer': '1.a1.a1', 'counter': 1, 'group_counter': 3190, 'group_order': 1296, 'label': '1A', 'order': 1, 'powers': [1, 1], 'representative': 0, 'size': 1}
  • id: 114753373
    {'aut_label': '2A', 'centralizer': '1.a1.a1', 'counter': 2, 'group_counter': 3190, 'group_order': 1296, 'label': '2A', 'order': 2, 'powers': [1, 2], 'representative': 216, 'size': 1}
  • id: 114753384
    {'aut_label': '2B', 'centralizer': '3.b1.a1', 'counter': 3, 'group_counter': 3190, 'group_order': 1296, 'label': '2B', 'order': 2, 'powers': [1, 3], 'representative': 3, 'size': 3}
  • id: 114753395
    {'aut_label': '2B', 'centralizer': '3.b1.a1', 'counter': 4, 'group_counter': 3190, 'group_order': 1296, 'label': '2C', 'order': 2, 'powers': [1, 4], 'representative': 219, 'size': 3}
  • id: 114753406
    {'aut_label': '2D', 'centralizer': '6.n1.a1', 'counter': 5, 'group_counter': 3190, 'group_order': 1296, 'label': '2D', 'order': 2, 'powers': [1, 5], 'representative': 18, 'size': 6}
  • id: 114753417
    {'aut_label': '2E', 'centralizer': '18.d1.a1', 'counter': 6, 'group_counter': 3190, 'group_order': 1296, 'label': '2E', 'order': 2, 'powers': [1, 6], 'representative': 9, 'size': 18}
  • id: 114753428
    {'aut_label': '2F', 'centralizer': '18.s1.a1', 'counter': 7, 'group_counter': 3190, 'group_order': 1296, 'label': '2F', 'order': 2, 'powers': [1, 7], 'representative': 54, 'size': 18}
  • id: 114753439
    {'aut_label': '2G', 'centralizer': '54.e1.a1', 'counter': 8, 'group_counter': 3190, 'group_order': 1296, 'label': '2G', 'order': 2, 'powers': [1, 8], 'representative': 45, 'size': 54}
  • id: 114753450
    {'aut_label': '3A1', 'centralizer': '1.a1.a1', 'counter': 9, 'group_counter': 3190, 'group_order': 1296, 'label': '3A1', 'order': 3, 'powers': [10, 1], 'representative': 2, 'size': 1}
  • id: 114753327
    {'aut_label': '3A1', 'centralizer': '1.a1.a1', 'counter': 10, 'group_counter': 3190, 'group_order': 1296, 'label': '3A-1', 'order': 3, 'powers': [9, 1], 'representative': 4, 'size': 1}
  • id: 114753338
    {'aut_label': '3B', 'centralizer': '2.a1.a1', 'counter': 11, 'group_counter': 3190, 'group_order': 1296, 'label': '3B', 'order': 3, 'powers': [11, 1], 'representative': 864, 'size': 2}
  • id: 114753349
    {'aut_label': '3C', 'centralizer': '2.c1.a1', 'counter': 12, 'group_counter': 3190, 'group_order': 1296, 'label': '3C', 'order': 3, 'powers': [12, 1], 'representative': 288, 'size': 2}
  • id: 114753360
    {'aut_label': '3D', 'centralizer': '2.d1.a1', 'counter': 13, 'group_counter': 3190, 'group_order': 1296, 'label': '3D', 'order': 3, 'powers': [13, 1], 'representative': 12, 'size': 2}
  • id: 114753367
    {'aut_label': '3E1', 'centralizer': '2.a1.a1', 'counter': 14, 'group_counter': 3190, 'group_order': 1296, 'label': '3E1', 'order': 3, 'powers': [15, 1], 'representative': 868, 'size': 2}
  • id: 114753368
    {'aut_label': '3E1', 'centralizer': '2.a1.a1', 'counter': 15, 'group_counter': 3190, 'group_order': 1296, 'label': '3E-1', 'order': 3, 'powers': [14, 1], 'representative': 434, 'size': 2}
  • id: 114753369
    {'aut_label': '3F1', 'centralizer': '2.c1.a1', 'counter': 16, 'group_counter': 3190, 'group_order': 1296, 'label': '3F1', 'order': 3, 'powers': [17, 1], 'representative': 290, 'size': 2}
  • id: 114753370
    {'aut_label': '3F1', 'centralizer': '2.c1.a1', 'counter': 17, 'group_counter': 3190, 'group_order': 1296, 'label': '3F-1', 'order': 3, 'powers': [16, 1], 'representative': 148, 'size': 2}
  • id: 114753371
    {'aut_label': '3G1', 'centralizer': '2.d1.a1', 'counter': 18, 'group_counter': 3190, 'group_order': 1296, 'label': '3G1', 'order': 3, 'powers': [19, 1], 'representative': 16, 'size': 2}
  • id: 114753372
    {'aut_label': '3G1', 'centralizer': '2.d1.a1', 'counter': 19, 'group_counter': 3190, 'group_order': 1296, 'label': '3G-1', 'order': 3, 'powers': [18, 1], 'representative': 26, 'size': 2}
  • id: 114753374
    {'aut_label': '3H', 'centralizer': '4.a1.a1', 'counter': 20, 'group_counter': 3190, 'group_order': 1296, 'label': '3H', 'order': 3, 'powers': [20, 1], 'representative': 1008, 'size': 4}
  • id: 114753375
    {'aut_label': '3I', 'centralizer': '4.b1.a1', 'counter': 21, 'group_counter': 3190, 'group_order': 1296, 'label': '3I', 'order': 3, 'powers': [21, 1], 'representative': 888, 'size': 4}
  • id: 114753376
    {'aut_label': '3J', 'centralizer': '4.f1.a1', 'counter': 22, 'group_counter': 3190, 'group_order': 1296, 'label': '3J', 'order': 3, 'powers': [22, 1], 'representative': 156, 'size': 4}
  • id: 114753377
    {'aut_label': '3K1', 'centralizer': '4.a1.a1', 'counter': 23, 'group_counter': 3190, 'group_order': 1296, 'label': '3K1', 'order': 3, 'powers': [24, 1], 'representative': 1012, 'size': 4}
  • id: 114753378
    {'aut_label': '3K1', 'centralizer': '4.a1.a1', 'counter': 24, 'group_counter': 3190, 'group_order': 1296, 'label': '3K-1', 'order': 3, 'powers': [23, 1], 'representative': 722, 'size': 4}
  • id: 114753379
    {'aut_label': '3L1', 'centralizer': '4.b1.a1', 'counter': 25, 'group_counter': 3190, 'group_order': 1296, 'label': '3L1', 'order': 3, 'powers': [26, 1], 'representative': 892, 'size': 4}
  • id: 114753380
    {'aut_label': '3L1', 'centralizer': '4.b1.a1', 'counter': 26, 'group_counter': 3190, 'group_order': 1296, 'label': '3L-1', 'order': 3, 'powers': [25, 1], 'representative': 446, 'size': 4}
  • id: 114753381
    {'aut_label': '3M1', 'centralizer': '4.f1.a1', 'counter': 27, 'group_counter': 3190, 'group_order': 1296, 'label': '3M1', 'order': 3, 'powers': [28, 1], 'representative': 158, 'size': 4}
  • id: 114753382
    {'aut_label': '3M1', 'centralizer': '4.f1.a1', 'counter': 28, 'group_counter': 3190, 'group_order': 1296, 'label': '3M-1', 'order': 3, 'powers': [27, 1], 'representative': 316, 'size': 4}
  • id: 114753383
    {'aut_label': '3N', 'centralizer': '8.a1.a1', 'counter': 29, 'group_counter': 3190, 'group_order': 1296, 'label': '3N', 'order': 3, 'powers': [29, 1], 'representative': 1032, 'size': 8}
  • id: 114753385
    {'aut_label': '3O1', 'centralizer': '8.a1.a1', 'counter': 30, 'group_counter': 3190, 'group_order': 1296, 'label': '3O1', 'order': 3, 'powers': [31, 1], 'representative': 1036, 'size': 8}
  • id: 114753386
    {'aut_label': '3O1', 'centralizer': '8.a1.a1', 'counter': 31, 'group_counter': 3190, 'group_order': 1296, 'label': '3O-1', 'order': 3, 'powers': [30, 1], 'representative': 734, 'size': 8}
  • id: 114753387
    {'aut_label': '4A', 'centralizer': '6.s1.a1', 'counter': 32, 'group_counter': 3190, 'group_order': 1296, 'label': '4A', 'order': 4, 'powers': [2, 32], 'representative': 108, 'size': 6}
  • id: 114753388
    {'aut_label': '4B', 'centralizer': '18.m1.a1', 'counter': 33, 'group_counter': 3190, 'group_order': 1296, 'label': '4B', 'order': 4, 'powers': [2, 33], 'representative': 327, 'size': 18}
  • id: 114753389
    {'aut_label': '6A1', 'centralizer': '1.a1.a1', 'counter': 34, 'group_counter': 3190, 'group_order': 1296, 'label': '6A1', 'order': 6, 'powers': [9, 2], 'representative': 220, 'size': 1}
  • id: 114753390
    {'aut_label': '6A1', 'centralizer': '1.a1.a1', 'counter': 35, 'group_counter': 3190, 'group_order': 1296, 'label': '6A-1', 'order': 6, 'powers': [10, 2], 'representative': 218, 'size': 1}
  • id: 114753391
    {'aut_label': '6B', 'centralizer': '2.a1.a1', 'counter': 36, 'group_counter': 3190, 'group_order': 1296, 'label': '6B', 'order': 6, 'powers': [11, 2], 'representative': 648, 'size': 2}
  • id: 114753392
    {'aut_label': '6C', 'centralizer': '2.c1.a1', 'counter': 37, 'group_counter': 3190, 'group_order': 1296, 'label': '6C', 'order': 6, 'powers': [12, 2], 'representative': 72, 'size': 2}
  • id: 114753393
    {'aut_label': '6D', 'centralizer': '2.d1.a1', 'counter': 38, 'group_counter': 3190, 'group_order': 1296, 'label': '6D', 'order': 6, 'powers': [13, 2], 'representative': 240, 'size': 2}
  • id: 114753394
    {'aut_label': '6E1', 'centralizer': '2.a1.a1', 'counter': 39, 'group_counter': 3190, 'group_order': 1296, 'label': '6E1', 'order': 6, 'powers': [14, 2], 'representative': 650, 'size': 2}
  • id: 114753396
    {'aut_label': '6E1', 'centralizer': '2.a1.a1', 'counter': 40, 'group_counter': 3190, 'group_order': 1296, 'label': '6E-1', 'order': 6, 'powers': [15, 2], 'representative': 652, 'size': 2}
  • id: 114753397
    {'aut_label': '6F1', 'centralizer': '2.c1.a1', 'counter': 41, 'group_counter': 3190, 'group_order': 1296, 'label': '6F1', 'order': 6, 'powers': [16, 2], 'representative': 76, 'size': 2}
  • id: 114753398
    {'aut_label': '6F1', 'centralizer': '2.c1.a1', 'counter': 42, 'group_counter': 3190, 'group_order': 1296, 'label': '6F-1', 'order': 6, 'powers': [17, 2], 'representative': 362, 'size': 2}
  • id: 114753399
    {'aut_label': '6G1', 'centralizer': '2.d1.a1', 'counter': 43, 'group_counter': 3190, 'group_order': 1296, 'label': '6G1', 'order': 6, 'powers': [19, 2], 'representative': 244, 'size': 2}
  • id: 114753400
    {'aut_label': '6G1', 'centralizer': '2.d1.a1', 'counter': 44, 'group_counter': 3190, 'group_order': 1296, 'label': '6G-1', 'order': 6, 'powers': [18, 2], 'representative': 230, 'size': 2}
  • id: 114753401
    {'aut_label': '6H1', 'centralizer': '3.b1.a1', 'counter': 45, 'group_counter': 3190, 'group_order': 1296, 'label': '6H1', 'order': 6, 'powers': [9, 3], 'representative': 1, 'size': 3}
  • id: 114753402
    {'aut_label': '6H1', 'centralizer': '3.b1.a1', 'counter': 46, 'group_counter': 3190, 'group_order': 1296, 'label': '6H-1', 'order': 6, 'powers': [10, 3], 'representative': 5, 'size': 3}
  • id: 114753403
    {'aut_label': '6H1', 'centralizer': '3.b1.a1', 'counter': 47, 'group_counter': 3190, 'group_order': 1296, 'label': '6I1', 'order': 6, 'powers': [9, 4], 'representative': 217, 'size': 3}
  • id: 114753404
    {'aut_label': '6H1', 'centralizer': '3.b1.a1', 'counter': 48, 'group_counter': 3190, 'group_order': 1296, 'label': '6I-1', 'order': 6, 'powers': [10, 4], 'representative': 221, 'size': 3}
  • id: 114753405
    {'aut_label': '6J', 'centralizer': '4.a1.a1', 'counter': 49, 'group_counter': 3190, 'group_order': 1296, 'label': '6J', 'order': 6, 'powers': [20, 2], 'representative': 504, 'size': 4}
  • id: 114753407
    {'aut_label': '6K', 'centralizer': '4.b1.a1', 'counter': 50, 'group_counter': 3190, 'group_order': 1296, 'label': '6K', 'order': 6, 'powers': [21, 2], 'representative': 660, 'size': 4}
  • id: 114753408
    {'aut_label': '6L', 'centralizer': '4.f1.a1', 'counter': 51, 'group_counter': 3190, 'group_order': 1296, 'label': '6L', 'order': 6, 'powers': [22, 2], 'representative': 96, 'size': 4}
  • id: 114753409
    {'aut_label': '6M1', 'centralizer': '4.a1.a1', 'counter': 52, 'group_counter': 3190, 'group_order': 1296, 'label': '6M1', 'order': 6, 'powers': [23, 2], 'representative': 506, 'size': 4}
  • id: 114753410
    {'aut_label': '6M1', 'centralizer': '4.a1.a1', 'counter': 53, 'group_counter': 3190, 'group_order': 1296, 'label': '6M-1', 'order': 6, 'powers': [24, 2], 'representative': 508, 'size': 4}
  • id: 114753411
    {'aut_label': '6N1', 'centralizer': '4.b1.a1', 'counter': 54, 'group_counter': 3190, 'group_order': 1296, 'label': '6N1', 'order': 6, 'powers': [25, 2], 'representative': 662, 'size': 4}
  • id: 114753412
    {'aut_label': '6N1', 'centralizer': '4.b1.a1', 'counter': 55, 'group_counter': 3190, 'group_order': 1296, 'label': '6N-1', 'order': 6, 'powers': [26, 2], 'representative': 664, 'size': 4}
  • id: 114753413
    {'aut_label': '6O1', 'centralizer': '4.f1.a1', 'counter': 56, 'group_counter': 3190, 'group_order': 1296, 'label': '6O1', 'order': 6, 'powers': [27, 2], 'representative': 100, 'size': 4}
  • id: 114753414
    {'aut_label': '6O1', 'centralizer': '4.f1.a1', 'counter': 57, 'group_counter': 3190, 'group_order': 1296, 'label': '6O-1', 'order': 6, 'powers': [28, 2], 'representative': 374, 'size': 4}
  • id: 114753415
    {'aut_label': '6P', 'centralizer': '6.k1.a1', 'counter': 58, 'group_counter': 3190, 'group_order': 1296, 'label': '6P', 'order': 6, 'powers': [11, 3], 'representative': 435, 'size': 6}
  • id: 114753416
    {'aut_label': '6Q', 'centralizer': '6.m1.a1', 'counter': 59, 'group_counter': 3190, 'group_order': 1296, 'label': '6Q', 'order': 6, 'powers': [12, 3], 'representative': 147, 'size': 6}
  • id: 114753418
    {'aut_label': '6Q', 'centralizer': '6.m1.a1', 'counter': 60, 'group_counter': 3190, 'group_order': 1296, 'label': '6R', 'order': 6, 'powers': [12, 4], 'representative': 75, 'size': 6}
  • id: 114753419
    {'aut_label': '6P', 'centralizer': '6.k1.a1', 'counter': 61, 'group_counter': 3190, 'group_order': 1296, 'label': '6S', 'order': 6, 'powers': [11, 4], 'representative': 651, 'size': 6}
  • id: 114753420
    {'aut_label': '6T1', 'centralizer': '6.k1.a1', 'counter': 62, 'group_counter': 3190, 'group_order': 1296, 'label': '6T1', 'order': 6, 'powers': [15, 3], 'representative': 433, 'size': 6}
  • id: 114753421
    {'aut_label': '6T1', 'centralizer': '6.k1.a1', 'counter': 63, 'group_counter': 3190, 'group_order': 1296, 'label': '6T-1', 'order': 6, 'powers': [14, 3], 'representative': 437, 'size': 6}
  • id: 114753422
    {'aut_label': '6U1', 'centralizer': '6.m1.a1', 'counter': 64, 'group_counter': 3190, 'group_order': 1296, 'label': '6U1', 'order': 6, 'powers': [16, 3], 'representative': 145, 'size': 6}
  • id: 114753423
    {'aut_label': '6U1', 'centralizer': '6.m1.a1', 'counter': 65, 'group_counter': 3190, 'group_order': 1296, 'label': '6U-1', 'order': 6, 'powers': [17, 3], 'representative': 149, 'size': 6}
  • id: 114753424
    {'aut_label': '6U1', 'centralizer': '6.m1.a1', 'counter': 66, 'group_counter': 3190, 'group_order': 1296, 'label': '6V1', 'order': 6, 'powers': [16, 4], 'representative': 73, 'size': 6}
  • id: 114753425
    {'aut_label': '6U1', 'centralizer': '6.m1.a1', 'counter': 67, 'group_counter': 3190, 'group_order': 1296, 'label': '6V-1', 'order': 6, 'powers': [17, 4], 'representative': 77, 'size': 6}
  • id: 114753426
    {'aut_label': '6W1', 'centralizer': '6.n1.a1', 'counter': 68, 'group_counter': 3190, 'group_order': 1296, 'label': '6W1', 'order': 6, 'powers': [11, 5], 'representative': 450, 'size': 6}
  • id: 114753427
    {'aut_label': '6W1', 'centralizer': '6.n1.a1', 'counter': 69, 'group_counter': 3190, 'group_order': 1296, 'label': '6W-1', 'order': 6, 'powers': [11, 5], 'representative': 882, 'size': 6}
  • id: 114753429
    {'aut_label': '6X1', 'centralizer': '6.n1.a1', 'counter': 70, 'group_counter': 3190, 'group_order': 1296, 'label': '6X1', 'order': 6, 'powers': [10, 5], 'representative': 20, 'size': 6}
  • id: 114753430
    {'aut_label': '6X1', 'centralizer': '6.n1.a1', 'counter': 71, 'group_counter': 3190, 'group_order': 1296, 'label': '6X-1', 'order': 6, 'powers': [9, 5], 'representative': 22, 'size': 6}
  • id: 114753431
    {'aut_label': '6Y1', 'centralizer': '6.n1.a1', 'counter': 72, 'group_counter': 3190, 'group_order': 1296, 'label': '6Y1', 'order': 6, 'powers': [14, 5], 'representative': 452, 'size': 6}
  • id: 114753432
    {'aut_label': '6Y1', 'centralizer': '6.n1.a1', 'counter': 73, 'group_counter': 3190, 'group_order': 1296, 'label': '6Y-1', 'order': 6, 'powers': [15, 5], 'representative': 886, 'size': 6}
  • id: 114753433
    {'aut_label': '6T1', 'centralizer': '6.k1.a1', 'counter': 74, 'group_counter': 3190, 'group_order': 1296, 'label': '6Z1', 'order': 6, 'powers': [15, 4], 'representative': 649, 'size': 6}
  • id: 114753434
    {'aut_label': '6T1', 'centralizer': '6.k1.a1', 'counter': 75, 'group_counter': 3190, 'group_order': 1296, 'label': '6Z-1', 'order': 6, 'powers': [14, 4], 'representative': 653, 'size': 6}
  • id: 114753435
    {'aut_label': '6Y1', 'centralizer': '6.n1.a1', 'counter': 76, 'group_counter': 3190, 'group_order': 1296, 'label': '6AA1', 'order': 6, 'powers': [14, 5], 'representative': 884, 'size': 6}
  • id: 114753436
    {'aut_label': '6Y1', 'centralizer': '6.n1.a1', 'counter': 77, 'group_counter': 3190, 'group_order': 1296, 'label': '6AA-1', 'order': 6, 'powers': [15, 5], 'representative': 454, 'size': 6}
  • id: 114753437
    {'aut_label': '6AB', 'centralizer': '8.a1.a1', 'counter': 78, 'group_counter': 3190, 'group_order': 1296, 'label': '6AB', 'order': 6, 'powers': [29, 2], 'representative': 516, 'size': 8}
  • id: 114753438
    {'aut_label': '6AC1', 'centralizer': '8.a1.a1', 'counter': 79, 'group_counter': 3190, 'group_order': 1296, 'label': '6AC1', 'order': 6, 'powers': [30, 2], 'representative': 518, 'size': 8}
  • id: 114753440
    {'aut_label': '6AC1', 'centralizer': '8.a1.a1', 'counter': 80, 'group_counter': 3190, 'group_order': 1296, 'label': '6AC-1', 'order': 6, 'powers': [31, 2], 'representative': 520, 'size': 8}
  • id: 114753441
    {'aut_label': '6AD', 'centralizer': '12.v1.a1', 'counter': 81, 'group_counter': 3190, 'group_order': 1296, 'label': '6AD', 'order': 6, 'powers': [13, 5], 'representative': 6, 'size': 12}
  • id: 114753442
    {'aut_label': '6AE', 'centralizer': '12.q1.a1', 'counter': 82, 'group_counter': 3190, 'group_order': 1296, 'label': '6AE', 'order': 6, 'powers': [20, 3], 'representative': 579, 'size': 12}
  • id: 114753443
    {'aut_label': '6AE', 'centralizer': '12.q1.a1', 'counter': 83, 'group_counter': 3190, 'group_order': 1296, 'label': '6AF', 'order': 6, 'powers': [20, 4], 'representative': 507, 'size': 12}
  • id: 114753444
    {'aut_label': '6AG1', 'centralizer': '12.v1.a1', 'counter': 84, 'group_counter': 3190, 'group_order': 1296, 'label': '6AG1', 'order': 6, 'powers': [21, 5], 'representative': 438, 'size': 12}
  • id: 114753445
    {'aut_label': '6AG1', 'centralizer': '12.v1.a1', 'counter': 85, 'group_counter': 3190, 'group_order': 1296, 'label': '6AG-1', 'order': 6, 'powers': [21, 5], 'representative': 870, 'size': 12}
  • id: 114753446
    {'aut_label': '6AH1', 'centralizer': '12.v1.a1', 'counter': 86, 'group_counter': 3190, 'group_order': 1296, 'label': '6AH1', 'order': 6, 'powers': [18, 5], 'representative': 8, 'size': 12}
  • id: 114753447
    {'aut_label': '6AH1', 'centralizer': '12.v1.a1', 'counter': 87, 'group_counter': 3190, 'group_order': 1296, 'label': '6AH-1', 'order': 6, 'powers': [19, 5], 'representative': 10, 'size': 12}
  • id: 114753448
    {'aut_label': '6AI1', 'centralizer': '12.v1.a1', 'counter': 88, 'group_counter': 3190, 'group_order': 1296, 'label': '6AI1', 'order': 6, 'powers': [25, 5], 'representative': 440, 'size': 12}
  • id: 114753449
    {'aut_label': '6AI1', 'centralizer': '12.v1.a1', 'counter': 89, 'group_counter': 3190, 'group_order': 1296, 'label': '6AI-1', 'order': 6, 'powers': [26, 5], 'representative': 874, 'size': 12}
  • id: 114753451
    {'aut_label': '6AJ1', 'centralizer': '12.q1.a1', 'counter': 90, 'group_counter': 3190, 'group_order': 1296, 'label': '6AJ1', 'order': 6, 'powers': [24, 3], 'representative': 577, 'size': 12}
  • id: 114753452
    {'aut_label': '6AJ1', 'centralizer': '12.q1.a1', 'counter': 91, 'group_counter': 3190, 'group_order': 1296, 'label': '6AJ-1', 'order': 6, 'powers': [23, 3], 'representative': 581, 'size': 12}
  • id: 114753453
    {'aut_label': '6AJ1', 'centralizer': '12.q1.a1', 'counter': 92, 'group_counter': 3190, 'group_order': 1296, 'label': '6AK1', 'order': 6, 'powers': [24, 4], 'representative': 505, 'size': 12}
  • id: 114753454
    {'aut_label': '6AJ1', 'centralizer': '12.q1.a1', 'counter': 93, 'group_counter': 3190, 'group_order': 1296, 'label': '6AK-1', 'order': 6, 'powers': [23, 4], 'representative': 509, 'size': 12}
  • id: 114753455
    {'aut_label': '6AI1', 'centralizer': '12.v1.a1', 'counter': 94, 'group_counter': 3190, 'group_order': 1296, 'label': '6AL1', 'order': 6, 'powers': [25, 5], 'representative': 872, 'size': 12}
  • id: 114753456
    {'aut_label': '6AI1', 'centralizer': '12.v1.a1', 'counter': 95, 'group_counter': 3190, 'group_order': 1296, 'label': '6AL-1', 'order': 6, 'powers': [26, 5], 'representative': 442, 'size': 12}
  • id: 114753457
    {'aut_label': '6AM1', 'centralizer': '18.d1.a1', 'counter': 96, 'group_counter': 3190, 'group_order': 1296, 'label': '6AM1', 'order': 6, 'powers': [9, 6], 'representative': 7, 'size': 18}
  • id: 114753458
    {'aut_label': '6AM1', 'centralizer': '18.d1.a1', 'counter': 97, 'group_counter': 3190, 'group_order': 1296, 'label': '6AM-1', 'order': 6, 'powers': [10, 6], 'representative': 11, 'size': 18}
  • id: 114753459
    {'aut_label': '6AN1', 'centralizer': '18.d1.a1', 'counter': 98, 'group_counter': 3190, 'group_order': 1296, 'label': '6AN1', 'order': 6, 'powers': [15, 6], 'representative': 439, 'size': 18}
  • id: 114753460
    {'aut_label': '6AN1', 'centralizer': '18.d1.a1', 'counter': 99, 'group_counter': 3190, 'group_order': 1296, 'label': '6AN-1', 'order': 6, 'powers': [14, 6], 'representative': 875, 'size': 18}
  • id: 114753328
    {'aut_label': '6AN1', 'centralizer': '18.d1.a1', 'counter': 100, 'group_counter': 3190, 'group_order': 1296, 'label': '6AO1', 'order': 6, 'powers': [15, 6], 'representative': 871, 'size': 18}
  • id: 114753329
    {'aut_label': '6AN1', 'centralizer': '18.d1.a1', 'counter': 101, 'group_counter': 3190, 'group_order': 1296, 'label': '6AO-1', 'order': 6, 'powers': [14, 6], 'representative': 443, 'size': 18}
  • id: 114753330
    {'aut_label': '6AP1', 'centralizer': '18.s1.a1', 'counter': 102, 'group_counter': 3190, 'group_order': 1296, 'label': '6AP1', 'order': 6, 'powers': [10, 7], 'representative': 56, 'size': 18}
  • id: 114753331
    {'aut_label': '6AP1', 'centralizer': '18.s1.a1', 'counter': 103, 'group_counter': 3190, 'group_order': 1296, 'label': '6AP-1', 'order': 6, 'powers': [9, 7], 'representative': 58, 'size': 18}
  • id: 114753332
    {'aut_label': '6AQ1', 'centralizer': '18.d1.a1', 'counter': 104, 'group_counter': 3190, 'group_order': 1296, 'label': '6AQ1', 'order': 6, 'powers': [11, 6], 'representative': 441, 'size': 18}
  • id: 114753333
    {'aut_label': '6AQ1', 'centralizer': '18.d1.a1', 'counter': 105, 'group_counter': 3190, 'group_order': 1296, 'label': '6AQ-1', 'order': 6, 'powers': [11, 6], 'representative': 873, 'size': 18}
  • id: 114753334
    {'aut_label': '6AR', 'centralizer': '36.bs1.a1', 'counter': 106, 'group_counter': 3190, 'group_order': 1296, 'label': '6AR', 'order': 6, 'powers': [13, 7], 'representative': 42, 'size': 36}
  • id: 114753335
    {'aut_label': '6AS1', 'centralizer': '36.bs1.a1', 'counter': 107, 'group_counter': 3190, 'group_order': 1296, 'label': '6AS1', 'order': 6, 'powers': [18, 7], 'representative': 44, 'size': 36}
  • id: 114753336
    {'aut_label': '6AS1', 'centralizer': '36.bs1.a1', 'counter': 108, 'group_counter': 3190, 'group_order': 1296, 'label': '6AS-1', 'order': 6, 'powers': [19, 7], 'representative': 46, 'size': 36}
  • id: 114753337
    {'aut_label': '6AT1', 'centralizer': '54.e1.a1', 'counter': 109, 'group_counter': 3190, 'group_order': 1296, 'label': '6AT1', 'order': 6, 'powers': [9, 8], 'representative': 43, 'size': 54}
  • id: 114753339
    {'aut_label': '6AT1', 'centralizer': '54.e1.a1', 'counter': 110, 'group_counter': 3190, 'group_order': 1296, 'label': '6AT-1', 'order': 6, 'powers': [10, 8], 'representative': 47, 'size': 54}
  • id: 114753340
    {'aut_label': '12A1', 'centralizer': '6.s1.a1', 'counter': 111, 'group_counter': 3190, 'group_order': 1296, 'label': '12A1', 'order': 12, 'powers': [37, 32], 'representative': 36, 'size': 6}
  • id: 114753341
    {'aut_label': '12A1', 'centralizer': '6.s1.a1', 'counter': 112, 'group_counter': 3190, 'group_order': 1296, 'label': '12A5', 'order': 12, 'powers': [37, 32], 'representative': 180, 'size': 6}
  • id: 114753342
    {'aut_label': '12B1', 'centralizer': '6.s1.a1', 'counter': 113, 'group_counter': 3190, 'group_order': 1296, 'label': '12B1', 'order': 12, 'powers': [34, 32], 'representative': 110, 'size': 6}
  • id: 114753343
    {'aut_label': '12B1', 'centralizer': '6.s1.a1', 'counter': 114, 'group_counter': 3190, 'group_order': 1296, 'label': '12B-1', 'order': 12, 'powers': [35, 32], 'representative': 112, 'size': 6}
  • id: 114753344
    {'aut_label': '12C1', 'centralizer': '6.s1.a1', 'counter': 115, 'group_counter': 3190, 'group_order': 1296, 'label': '12C1', 'order': 12, 'powers': [41, 32], 'representative': 38, 'size': 6}
  • id: 114753345
    {'aut_label': '12C1', 'centralizer': '6.s1.a1', 'counter': 116, 'group_counter': 3190, 'group_order': 1296, 'label': '12C-1', 'order': 12, 'powers': [42, 32], 'representative': 40, 'size': 6}
  • id: 114753346
    {'aut_label': '12C1', 'centralizer': '6.s1.a1', 'counter': 117, 'group_counter': 3190, 'group_order': 1296, 'label': '12C5', 'order': 12, 'powers': [42, 32], 'representative': 184, 'size': 6}
  • id: 114753347
    {'aut_label': '12C1', 'centralizer': '6.s1.a1', 'counter': 118, 'group_counter': 3190, 'group_order': 1296, 'label': '12C-5', 'order': 12, 'powers': [41, 32], 'representative': 182, 'size': 6}
  • id: 114753348
    {'aut_label': '12D', 'centralizer': '12.br1.a1', 'counter': 119, 'group_counter': 3190, 'group_order': 1296, 'label': '12D', 'order': 12, 'powers': [38, 32], 'representative': 120, 'size': 12}
  • id: 114753350
    {'aut_label': '12E1', 'centralizer': '12.br1.a1', 'counter': 120, 'group_counter': 3190, 'group_order': 1296, 'label': '12E1', 'order': 12, 'powers': [51, 32], 'representative': 48, 'size': 12}
  • id: 114753351
    {'aut_label': '12E1', 'centralizer': '12.br1.a1', 'counter': 121, 'group_counter': 3190, 'group_order': 1296, 'label': '12E5', 'order': 12, 'powers': [51, 32], 'representative': 192, 'size': 12}
  • id: 114753352
    {'aut_label': '12F1', 'centralizer': '12.br1.a1', 'counter': 122, 'group_counter': 3190, 'group_order': 1296, 'label': '12F1', 'order': 12, 'powers': [43, 32], 'representative': 122, 'size': 12}
  • id: 114753353
    {'aut_label': '12F1', 'centralizer': '12.br1.a1', 'counter': 123, 'group_counter': 3190, 'group_order': 1296, 'label': '12F-1', 'order': 12, 'powers': [44, 32], 'representative': 124, 'size': 12}
  • id: 114753354
    {'aut_label': '12G1', 'centralizer': '12.br1.a1', 'counter': 124, 'group_counter': 3190, 'group_order': 1296, 'label': '12G1', 'order': 12, 'powers': [56, 32], 'representative': 50, 'size': 12}
  • id: 114753355
    {'aut_label': '12G1', 'centralizer': '12.br1.a1', 'counter': 125, 'group_counter': 3190, 'group_order': 1296, 'label': '12G-1', 'order': 12, 'powers': [57, 32], 'representative': 52, 'size': 12}
  • id: 114753356
    {'aut_label': '12G1', 'centralizer': '12.br1.a1', 'counter': 126, 'group_counter': 3190, 'group_order': 1296, 'label': '12G5', 'order': 12, 'powers': [57, 32], 'representative': 196, 'size': 12}
  • id: 114753357
    {'aut_label': '12G1', 'centralizer': '12.br1.a1', 'counter': 127, 'group_counter': 3190, 'group_order': 1296, 'label': '12G-5', 'order': 12, 'powers': [56, 32], 'representative': 194, 'size': 12}
  • id: 114753358
    {'aut_label': '12H1', 'centralizer': '18.m1.a1', 'counter': 128, 'group_counter': 3190, 'group_order': 1296, 'label': '12H1', 'order': 12, 'powers': [35, 33], 'representative': 109, 'size': 18}
  • id: 114753359
    {'aut_label': '12H1', 'centralizer': '18.m1.a1', 'counter': 129, 'group_counter': 3190, 'group_order': 1296, 'label': '12H-1', 'order': 12, 'powers': [34, 33], 'representative': 113, 'size': 18}
  • id: 114753361
    {'aut_label': '12I1', 'centralizer': '18.m1.a1', 'counter': 130, 'group_counter': 3190, 'group_order': 1296, 'label': '12I1', 'order': 12, 'powers': [37, 33], 'representative': 39, 'size': 18}
  • id: 114753362
    {'aut_label': '12I1', 'centralizer': '18.m1.a1', 'counter': 131, 'group_counter': 3190, 'group_order': 1296, 'label': '12I5', 'order': 12, 'powers': [37, 33], 'representative': 183, 'size': 18}
  • id: 114753363
    {'aut_label': '12J1', 'centralizer': '18.m1.a1', 'counter': 132, 'group_counter': 3190, 'group_order': 1296, 'label': '12J1', 'order': 12, 'powers': [42, 33], 'representative': 37, 'size': 18}
  • id: 114753364
    {'aut_label': '12J1', 'centralizer': '18.m1.a1', 'counter': 133, 'group_counter': 3190, 'group_order': 1296, 'label': '12J-1', 'order': 12, 'powers': [41, 33], 'representative': 41, 'size': 18}
  • id: 114753365
    {'aut_label': '12J1', 'centralizer': '18.m1.a1', 'counter': 134, 'group_counter': 3190, 'group_order': 1296, 'label': '12J5', 'order': 12, 'powers': [41, 33], 'representative': 185, 'size': 18}
  • id: 114753366
    {'aut_label': '12J1', 'centralizer': '18.m1.a1', 'counter': 135, 'group_counter': 3190, 'group_order': 1296, 'label': '12J-5', 'order': 12, 'powers': [42, 33], 'representative': 181, 'size': 18}
• 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: 5461526
    {'cdim': 1, 'counter': 1, 'faithful': False, 'group': '1296.3190', 'group_order': 1296, 'image': None, 'label': '1296.3190.1a', 'multiplicity': 1, 'nt': [1, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 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: 5461537
    {'cdim': 1, 'counter': 2, 'faithful': False, 'group': '1296.3190', 'group_order': 1296, 'image': None, 'label': '1296.3190.1b', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, -1, -1, -1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, -1, 1, -1, 1, -1, -1, -1, 1, 1, 1, 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: 5461548
    {'cdim': 1, 'counter': 3, 'faithful': False, 'group': '1296.3190', 'group_order': 1296, 'image': None, 'label': '1296.3190.1c', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, -1, -1, -1, 1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -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: 5461559
    {'cdim': 1, 'counter': 4, 'faithful': False, 'group': '1296.3190', 'group_order': 1296, 'image': None, 'label': '1296.3190.1d', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, -1, -1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, 1, -1, 1, -1, -1, -1, -1, 1, 1, 1, -1, -1, 1, -1, 1, -1, 1, 1, 1, -1, -1, 1, 1, 1, 1, -1, 1, 1, -1, 1, -1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, -1, -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: 5461570
    {'cdim': 1, 'counter': 5, 'faithful': False, 'group': '1296.3190', 'group_order': 1296, 'image': None, 'label': '1296.3190.1e', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, -1, -1, 1, -1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, 1, -1, 1, -1, -1, -1, -1, 1, 1, 1, -1, -1, 1, -1, 1, -1, 1, 1, 1, -1, -1, 1, 1, 1, 1, -1, 1, 1, -1, 1, -1, 1, 1, -1, -1, -1, -1, -1, -1, -1, 1, -1, 1, -1, 1, 1, 1, -1, -1, 1, 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: 5461581
    {'cdim': 1, 'counter': 6, 'faithful': False, 'group': '1296.3190', 'group_order': 1296, 'image': None, 'label': '1296.3190.1f', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 1, 1, 1, -1, 1, -1, 1, 1, 1, 1, -1, -1, -1, 1, 1, -1, 1, -1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, -1, -1, 1, -1, 1, -1, -1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 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: 5461592
    {'cdim': 1, 'counter': 7, 'faithful': False, 'group': '1296.3190', 'group_order': 1296, 'image': None, 'label': '1296.3190.1g', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 1, 1, 1, -1, 1, -1, 1, 1, 1, 1, -1, -1, -1, 1, 1, -1, 1, -1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, -1, -1, 1, -1, 1, -1, -1, 1, -1, -1, -1, -1, -1, -1, 1, -1, 1, -1, 1, 1, 1, 1, 1, -1, -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: 5461603
    {'cdim': 1, 'counter': 8, 'faithful': False, 'group': '1296.3190', 'group_order': 1296, 'image': None, 'label': '1296.3190.1h', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 1, -1, 1, -1, -1, -1, -1, -1, -1, -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: 5461606
    {'cdim': 1, 'counter': 9, 'faithful': False, 'group': '1296.3190', 'group_order': 1296, 'image': None, 'label': '1296.3190.1i', 'multiplicity': 2, 'nt': [3, 1], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 2, 2, 2, 2, -1, -1, -1, 2, -1, -1, -1, -1, -1, 2, 2, -1, -1, -1, 2, -1, -1, 2, 2, -1, 2, -1, -1, 2, 2, -1, -1, -1, -1, -1, -1, 2, -1, 2, -1, 2, -1, -1, -1, -1, 2, -1, -1, -1, 2, -1, -1, 2, -1, 2, 2, 2, -1, 2, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 2, 2, -1, -1, -1, 2, -1, -1, 2, -1, 2, -1, 2, -1, -1, -1, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, 2, -1, 2, 2, -1, -1, -1, -1, -1, 2, -1, -1, -1, -1, 2, -1, 2, -1, 2, 2, -1, -1, -1, -1, -1, -1, 2, 2, -1, -1, -1, -1, -1], 'schur_index': 1}
  • id: 5461527
    {'cdim': 1, 'counter': 10, 'faithful': False, 'group': '1296.3190', 'group_order': 1296, 'image': None, 'label': '1296.3190.1j', 'multiplicity': 2, 'nt': [6, 1], 'qdim': 2, 'qvalues': [2, 2, -2, -2, -2, 2, -2, 2, -1, -1, -1, 2, -1, -1, -1, -1, -1, 2, 2, -1, -1, -1, 2, -1, -1, 2, 2, -1, 2, -1, -1, 2, -2, -1, -1, -1, -1, -1, -1, 2, -1, 2, -1, 2, 1, 1, 1, 1, 2, -1, -1, -1, 2, -1, -1, 2, -1, -2, -2, -2, 1, -2, -2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -2, 2, -1, -1, 1, -2, 1, 1, -2, 1, -2, 1, -2, 1, 1, 1, -2, 1, 1, -1, -1, -1, -1, -1, -1, 1, 2, 1, 2, -2, 1, 1, -1, -1, -1, 2, -1, -1, -1, -1, 2, -1, 2, -1, 2, 2, -1, -1, -1, -1, -1, 1, -2, -2, 1, 1, 1, 1, 1], 'schur_index': 1}
  • id: 5461528
    {'cdim': 1, 'counter': 11, 'faithful': False, 'group': '1296.3190', 'group_order': 1296, 'image': None, 'label': '1296.3190.1k', 'multiplicity': 2, 'nt': [6, 1], 'qdim': 2, 'qvalues': [2, 2, -2, -2, -2, 2, 2, -2, -1, -1, -1, 2, -1, -1, -1, -1, -1, 2, 2, -1, -1, -1, 2, -1, -1, 2, 2, -1, 2, -1, -1, -2, 2, -1, -1, -1, -1, -1, -1, 2, -1, 2, -1, 2, 1, 1, 1, 1, 2, -1, -1, -1, 2, -1, -1, 2, -1, -2, -2, -2, 1, -2, -2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -2, 2, -1, -1, 1, -2, 1, 1, -2, 1, -2, 1, -2, 1, 1, 1, -2, 1, 1, -1, -1, -1, -1, -1, -1, -1, 2, -1, 2, 2, -1, -1, 1, 1, 1, -2, 1, 1, 1, 1, -2, 1, -2, 1, -2, -2, 1, 1, 1, 1, 1, -1, 2, 2, -1, -1, -1, -1, -1], 'schur_index': 1}
  • id: 5461529
    {'cdim': 1, 'counter': 12, 'faithful': False, 'group': '1296.3190', 'group_order': 1296, 'image': None, 'label': '1296.3190.1l', 'multiplicity': 2, 'nt': [6, 1], 'qdim': 2, 'qvalues': [2, 2, -2, -2, 2, -2, -2, 2, -1, -1, -1, 2, -1, -1, -1, -1, -1, 2, 2, -1, -1, -1, 2, -1, -1, 2, 2, -1, 2, -1, -1, -2, 2, -1, -1, -1, -1, -1, -1, 2, -1, 2, -1, 2, 1, 1, 1, 1, 2, -1, -1, -1, 2, -1, -1, 2, -1, 2, -2, -2, 1, 2, -2, -1, 1, 1, 1, 1, -1, -1, -1, 1, 1, -1, 1, -1, -2, 2, -1, -1, 1, -2, -1, -1, 2, -1, -2, -1, 2, 1, -1, 1, 2, -1, 1, 1, 1, 1, 1, 1, 1, 1, -2, 1, -2, -2, 1, 1, -1, -1, 1, -2, 1, 1, 1, 1, -2, 1, -2, 1, -2, -2, 1, 1, 1, 1, 1, -1, 2, 2, -1, -1, -1, -1, -1], 'schur_index': 1}
  • id: 5461530
    {'cdim': 1, 'counter': 13, 'faithful': False, 'group': '1296.3190', 'group_order': 1296, 'image': None, 'label': '1296.3190.1m', 'multiplicity': 2, 'nt': [6, 1], 'qdim': 2, 'qvalues': [2, 2, -2, -2, 2, -2, 2, -2, -1, -1, -1, 2, -1, -1, -1, -1, -1, 2, 2, -1, -1, -1, 2, -1, -1, 2, 2, -1, 2, -1, -1, 2, -2, -1, -1, -1, -1, -1, -1, 2, -1, 2, -1, 2, 1, 1, 1, 1, 2, -1, -1, -1, 2, -1, -1, 2, -1, 2, -2, -2, 1, 2, -2, -1, 1, 1, 1, 1, -1, -1, -1, 1, 1, -1, 1, -1, -2, 2, -1, -1, 1, -2, -1, -1, 2, -1, -2, -1, 2, 1, -1, 1, 2, -1, 1, 1, 1, 1, 1, 1, 1, -1, -2, -1, -2, 2, -1, -1, 1, 1, -1, 2, -1, -1, -1, -1, 2, -1, 2, -1, 2, 2, -1, -1, -1, -1, -1, 1, -2, -2, 1, 1, 1, 1, 1], 'schur_index': 1}
  • id: 5461531
    {'cdim': 1, 'counter': 14, 'faithful': False, 'group': '1296.3190', 'group_order': 1296, 'image': None, 'label': '1296.3190.1n', 'multiplicity': 2, 'nt': [6, 1], 'qdim': 2, 'qvalues': [2, 2, 2, 2, -2, -2, -2, -2, -1, -1, -1, 2, -1, -1, -1, -1, -1, 2, 2, -1, -1, -1, 2, -1, -1, 2, 2, -1, 2, -1, -1, 2, 2, -1, -1, -1, -1, -1, -1, 2, -1, 2, -1, 2, -1, -1, -1, -1, 2, -1, -1, -1, 2, -1, -1, 2, -1, -2, 2, 2, -1, -2, 2, 1, -1, -1, -1, -1, 1, 1, 1, -1, -1, 1, -1, 1, 2, 2, -1, -1, -1, 2, 1, 1, -2, 1, 2, 1, -2, -1, 1, -1, -2, 1, -1, 1, 1, 1, 1, 1, 1, 1, -2, 1, -2, -2, 1, 1, 1, 1, -1, 2, -1, -1, -1, -1, 2, -1, 2, -1, 2, 2, -1, -1, -1, -1, -1, -1, 2, 2, -1, -1, -1, -1, -1], 'schur_index': 1}
  • id: 5461532
    {'cdim': 1, 'counter': 15, 'faithful': False, 'group': '1296.3190', 'group_order': 1296, 'image': None, 'label': '1296.3190.1o', 'multiplicity': 2, 'nt': [6, 1], 'qdim': 2, 'qvalues': [2, 2, 2, 2, -2, -2, 2, 2, -1, -1, -1, 2, -1, -1, -1, -1, -1, 2, 2, -1, -1, -1, 2, -1, -1, 2, 2, -1, 2, -1, -1, -2, -2, -1, -1, -1, -1, -1, -1, 2, -1, 2, -1, 2, -1, -1, -1, -1, 2, -1, -1, -1, 2, -1, -1, 2, -1, -2, 2, 2, -1, -2, 2, 1, -1, -1, -1, -1, 1, 1, 1, -1, -1, 1, -1, 1, 2, 2, -1, -1, -1, 2, 1, 1, -2, 1, 2, 1, -2, -1, 1, -1, -2, 1, -1, 1, 1, 1, 1, 1, 1, -1, -2, -1, -2, 2, -1, -1, -1, -1, 1, -2, 1, 1, 1, 1, -2, 1, -2, 1, -2, -2, 1, 1, 1, 1, 1, 1, -2, -2, 1, 1, 1, 1, 1], 'schur_index': 1}
  • id: 5461533
    {'cdim': 1, 'counter': 16, 'faithful': False, 'group': '1296.3190', 'group_order': 1296, 'image': None, 'label': '1296.3190.1p', 'multiplicity': 2, 'nt': [6, 1], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 2, 2, -2, -2, -1, -1, -1, 2, -1, -1, -1, -1, -1, 2, 2, -1, -1, -1, 2, -1, -1, 2, 2, -1, 2, -1, -1, -2, -2, -1, -1, -1, -1, -1, -1, 2, -1, 2, -1, 2, -1, -1, -1, -1, 2, -1, -1, -1, 2, -1, -1, 2, -1, 2, 2, 2, -1, 2, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 2, 2, -1, -1, -1, 2, -1, -1, 2, -1, 2, -1, 2, -1, -1, -1, 2, -1, -1, -1, -1, -1, -1, -1, -1, 1, 2, 1, 2, -2, 1, 1, 1, 1, 1, -2, 1, 1, 1, 1, -2, 1, -2, 1, -2, -2, 1, 1, 1, 1, 1, 1, -2, -2, 1, 1, 1, 1, 1], 'schur_index': 1}
  • id: 5461534
    {'cdim': 2, 'counter': 17, 'faithful': False, 'group': '1296.3190', 'group_order': 1296, 'image': None, 'label': '1296.3190.2a', 'multiplicity': 1, 'nt': [3, 2], 'qdim': 2, 'qvalues': [2, 2, 0, 0, 2, 0, 2, 0, 2, 2, 2, 2, 2, -1, 2, -1, 2, -1, 2, 2, -1, -1, 2, 2, -1, -1, -1, -1, -1, -1, -1, 2, 0, 2, 2, 2, 2, -1, 2, 2, 2, 2, -1, -1, 0, 0, 0, 0, -1, -1, 2, 2, 2, -1, -1, -1, -1, 2, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 2, 2, 2, 0, 0, 2, 0, 2, 0, -1, -1, -1, 0, 0, -1, -1, -1, -1, 0, -1, -1, 0, -1, 0, -1, -1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, -1, -1, -1, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 5461535
    {'cdim': 2, 'counter': 18, 'faithful': False, 'group': '1296.3190', 'group_order': 1296, 'image': None, 'label': '1296.3190.2b', 'multiplicity': 1, 'nt': [3, 2], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 0, 0, 0, 0, 2, 2, -1, -1, 2, 2, 2, 2, -1, 2, 2, -1, -1, -1, -1, -1, 2, 2, -1, 2, -1, -1, -1, 2, 2, 2, 2, -1, -1, 2, 2, 2, 2, -1, 2, 2, 2, 2, 2, 2, 2, -1, -1, -1, -1, -1, 2, -1, 2, 0, -1, -1, -1, 0, 2, 0, 2, -1, -1, 2, 0, 0, 0, 2, 2, 0, -1, 0, 2, -1, -1, -1, -1, -1, 0, 0, 0, 0, -1, 0, 0, -1, 0, -1, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, 2, 2, -1, -1, -1, 2, -1, -1, -1, -1, -1, 2, -1, 2, -1, -1, -1, -1, -1, -1, 2, 2], 'schur_index': 1}
  • id: 5461536
    {'cdim': 2, 'counter': 19, 'faithful': False, 'group': '1296.3190', 'group_order': 1296, 'image': None, 'label': '1296.3190.2c', 'multiplicity': 1, 'nt': [3, 2], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 2, 2, 0, 0, 2, 2, 2, 2, -1, 2, -1, 2, 2, 2, -1, -1, 2, 2, -1, -1, -1, -1, 2, -1, -1, -1, -1, 0, 0, 2, 2, 2, 2, 2, -1, -1, -1, 2, 2, 2, 2, 2, 2, 2, -1, 2, -1, -1, -1, 2, -1, 2, -1, -1, 2, 2, 2, -1, -1, -1, -1, 2, 2, -1, -1, 2, 2, -1, -1, -1, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, 2, -1, -1, 2, -1, -1, -1, -1, -1, 2, -1, 2, -1, -1, -1, 2, -1, 0, -1, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 5461538
    {'cdim': 2, 'counter': 20, 'faithful': False, 'group': '1296.3190', 'group_order': 1296, 'image': None, 'label': '1296.3190.2d', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, -2, -2, 2, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 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, -2, -2, -2, -2, -2, -2, -2, 0, -2, 2, -2, 0, 2, 0, -2, 2, 2, -2, 0, 0, 0, 2, 2, 0, -2, 0, -2, -2, -2, -2, 2, -2, 0, 0, 0, 0, 2, 0, 0, 2, 0, -2, 0, 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], 'schur_index': 1}
  • id: 5461539
    {'cdim': 2, 'counter': 21, 'faithful': False, 'group': '1296.3190', 'group_order': 1296, 'image': None, 'label': '1296.3190.2e', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, -2, 2, -2, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 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, -2, -2, -2, -2, -2, -2, -2, 0, 2, -2, 2, 0, -2, 0, 2, -2, -2, 2, 0, 0, 0, -2, -2, 0, 2, 0, 2, -2, -2, -2, -2, 2, 0, 0, 0, 0, -2, 0, 0, -2, 0, 2, 0, 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], 'schur_index': 1}
  • id: 5461540
    {'cdim': 2, 'counter': 22, 'faithful': False, 'group': '1296.3190', 'group_order': 1296, 'image': None, 'label': '1296.3190.2f', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, 2, -2, -2, -2, 2, 0, 0, 2, 2, 2, 2, -1, 2, -1, 2, 2, 2, -1, -1, 2, 2, -1, -1, -1, -1, 2, -1, -1, -1, -1, 0, 0, 2, 2, 2, 2, 2, -1, -1, -1, 2, 2, 2, -2, -2, -2, -2, -1, 2, -1, -1, -1, 2, -1, 2, -1, 1, -2, -2, -2, 1, 1, 1, 1, -2, -2, 1, 1, -2, -2, 1, 1, 1, -2, 1, 1, -1, -1, -1, 1, 1, 1, 1, -2, 1, 1, -2, 1, 1, 1, 1, 1, -2, 1, 2, -1, -1, -1, 2, -1, 0, -1, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 5461541
    {'cdim': 2, 'counter': 23, 'faithful': False, 'group': '1296.3190', 'group_order': 1296, 'image': None, 'label': '1296.3190.2g', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, 2, -2, -2, 0, 0, 0, 0, 2, 2, -1, -1, 2, 2, 2, 2, -1, 2, 2, -1, -1, -1, -1, -1, 2, 2, -1, 2, -1, -1, -1, -2, 2, 2, 2, -1, -1, 2, 2, 2, 2, -1, 2, 2, -2, -2, -2, -2, 2, -1, -1, -1, -1, -1, 2, -1, 2, 0, 1, 1, 1, 0, -2, 0, -2, 1, 1, -2, 0, 0, 0, -2, -2, 0, 1, 0, -2, -1, -1, -1, 1, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, -2, -2, 1, 1, 1, -2, 1, 1, 1, 1, 1, -2, 1, -2, -1, -1, -1, -1, -1, -1, 2, 2], 'schur_index': 1}
  • id: 5461542
    {'cdim': 2, 'counter': 24, 'faithful': False, 'group': '1296.3190', 'group_order': 1296, 'image': None, 'label': '1296.3190.2h', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, 2, -2, -2, 0, 0, 0, 0, 2, 2, -1, -1, 2, 2, 2, 2, -1, 2, 2, -1, -1, -1, -1, -1, 2, 2, -1, 2, -1, -1, -1, 2, -2, 2, 2, -1, -1, 2, 2, 2, 2, -1, 2, 2, -2, -2, -2, -2, 2, -1, -1, -1, -1, -1, 2, -1, 2, 0, 1, 1, 1, 0, -2, 0, -2, 1, 1, -2, 0, 0, 0, -2, -2, 0, 1, 0, -2, -1, -1, -1, 1, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, 2, 2, -1, -1, -1, 2, -1, -1, -1, -1, -1, 2, -1, 2, 1, 1, 1, 1, 1, 1, -2, -2], 'schur_index': 1}
  • id: 5461543
    {'cdim': 2, 'counter': 25, 'faithful': False, 'group': '1296.3190', 'group_order': 1296, 'image': None, 'label': '1296.3190.2i', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, 2, -2, -2, 2, -2, 0, 0, 2, 2, 2, 2, -1, 2, -1, 2, 2, 2, -1, -1, 2, 2, -1, -1, -1, -1, 2, -1, -1, -1, -1, 0, 0, 2, 2, 2, 2, 2, -1, -1, -1, 2, 2, 2, -2, -2, -2, -2, -1, 2, -1, -1, -1, 2, -1, 2, -1, -1, -2, -2, -2, -1, 1, -1, 1, -2, -2, 1, -1, 2, 2, 1, 1, -1, -2, -1, 1, -1, -1, -1, 1, 1, -1, -1, 2, -1, 1, 2, -1, 1, -1, 1, -1, 2, 1, -2, 1, 1, 1, -2, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 5461544
    {'cdim': 2, 'counter': 26, 'faithful': False, 'group': '1296.3190', 'group_order': 1296, 'image': None, 'label': '1296.3190.2j', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, 2, 0, 0, -2, 0, -2, 0, 2, 2, 2, 2, 2, -1, 2, -1, 2, -1, 2, 2, -1, -1, 2, 2, -1, -1, -1, -1, -1, -1, -1, 2, 0, 2, 2, 2, 2, -1, 2, 2, 2, 2, -1, -1, 0, 0, 0, 0, -1, -1, 2, 2, 2, -1, -1, -1, -1, -2, 0, 0, 0, -2, 0, -2, 0, 0, 0, 0, -2, -2, -2, 0, 0, -2, 0, -2, 0, -1, -1, -1, 0, 0, 1, 1, 1, 1, 0, 1, 1, 0, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, -2, 0, -2, 0, 1, 1, 1, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 5461545
    {'cdim': 2, 'counter': 27, 'faithful': False, 'group': '1296.3190', 'group_order': 1296, 'image': None, 'label': '1296.3190.2k', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, 2, 0, 0, -2, 0, 2, 0, 2, 2, 2, 2, 2, -1, 2, -1, 2, -1, 2, 2, -1, -1, 2, 2, -1, -1, -1, -1, -1, -1, -1, -2, 0, 2, 2, 2, 2, -1, 2, 2, 2, 2, -1, -1, 0, 0, 0, 0, -1, -1, 2, 2, 2, -1, -1, -1, -1, -2, 0, 0, 0, -2, 0, -2, 0, 0, 0, 0, -2, -2, -2, 0, 0, -2, 0, -2, 0, -1, -1, -1, 0, 0, 1, 1, 1, 1, 0, 1, 1, 0, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, -1, -1, -1, 0, 0, -2, -2, -2, -2, -2, -2, -2, -2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 5461546
    {'cdim': 2, 'counter': 28, 'faithful': False, 'group': '1296.3190', 'group_order': 1296, 'image': None, 'label': '1296.3190.2l', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, 2, 0, 0, 2, 0, -2, 0, 2, 2, 2, 2, 2, -1, 2, -1, 2, -1, 2, 2, -1, -1, 2, 2, -1, -1, -1, -1, -1, -1, -1, -2, 0, 2, 2, 2, 2, -1, 2, 2, 2, 2, -1, -1, 0, 0, 0, 0, -1, -1, 2, 2, 2, -1, -1, -1, -1, 2, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 2, 2, 2, 0, 0, 2, 0, 2, 0, -1, -1, -1, 0, 0, -1, -1, -1, -1, 0, -1, -1, 0, -1, 0, -1, -1, 0, 0, 0, 0, 0, 0, 0, -2, 0, -2, 0, 1, 1, 1, 0, 0, -2, -2, -2, -2, -2, -2, -2, -2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 5461547
    {'cdim': 2, 'counter': 29, 'faithful': False, 'group': '1296.3190', 'group_order': 1296, 'image': None, 'label': '1296.3190.2m', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, 2, 2, 2, -2, -2, 0, 0, 2, 2, 2, 2, -1, 2, -1, 2, 2, 2, -1, -1, 2, 2, -1, -1, -1, -1, 2, -1, -1, -1, -1, 0, 0, 2, 2, 2, 2, 2, -1, -1, -1, 2, 2, 2, 2, 2, 2, 2, -1, 2, -1, -1, -1, 2, -1, 2, -1, 1, 2, 2, 2, 1, -1, 1, -1, 2, 2, -1, 1, -2, -2, -1, -1, 1, 2, 1, -1, -1, -1, -1, -1, -1, 1, 1, -2, 1, -1, -2, 1, -1, 1, -1, 1, -2, -1, -2, 1, 1, 1, -2, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 5461549
    {'cdim': 2, 'counter': 30, 'faithful': False, 'group': '1296.3190', 'group_order': 1296, 'image': None, 'label': '1296.3190.2n', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 0, 0, 0, 0, 2, 2, -1, -1, 2, 2, 2, 2, -1, 2, 2, -1, -1, -1, -1, -1, 2, 2, -1, 2, -1, -1, -1, -2, -2, 2, 2, -1, -1, 2, 2, 2, 2, -1, 2, 2, 2, 2, 2, 2, 2, -1, -1, -1, -1, -1, 2, -1, 2, 0, -1, -1, -1, 0, 2, 0, 2, -1, -1, 2, 0, 0, 0, 2, 2, 0, -1, 0, 2, -1, -1, -1, -1, -1, 0, 0, 0, 0, -1, 0, 0, -1, 0, -1, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, -2, -2, 1, 1, 1, -2, 1, 1, 1, 1, 1, -2, 1, -2, 1, 1, 1, 1, 1, 1, -2, -2], 'schur_index': 1}
  • id: 5461550
    {'cdim': 2, 'counter': 31, 'faithful': False, 'group': '1296.3190', 'group_order': 1296, 'image': None, 'label': '1296.3190.2o', 'multiplicity': 2, 'nt': [6, 5], 'qdim': 4, 'qvalues': [4, 4, 0, 0, 4, 0, 4, 0, -2, -2, -2, 4, -2, 1, -2, 1, -2, -2, 4, -2, 1, 1, 4, -2, 1, -2, -2, 1, -2, 1, 1, 4, 0, -2, -2, -2, -2, 1, -2, 4, -2, 4, 1, -2, 0, 0, 0, 0, -2, 1, -2, -2, 4, 1, 1, -2, 1, 4, 0, 0, 0, 4, 0, -2, 0, 0, 0, 0, -2, -2, -2, 0, 0, -2, 0, -2, 0, -2, 1, 1, 0, 0, 1, 1, -2, 1, 0, 1, -2, 0, 1, 0, -2, 1, 0, 0, 0, 0, 0, 0, 0, -2, 0, -2, 0, -2, 1, 1, 0, 0, -2, 4, -2, -2, -2, -2, 4, -2, -2, 1, -2, -2, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 5461551
    {'cdim': 2, 'counter': 32, 'faithful': False, 'group': '1296.3190', 'group_order': 1296, 'image': None, 'label': '1296.3190.2p', 'multiplicity': 2, 'nt': [6, 5], 'qdim': 4, 'qvalues': [4, 4, 4, 4, 0, 0, 0, 0, -2, -2, 1, -2, -2, -2, -2, -2, 1, 4, 4, 1, 1, 1, -2, 1, -2, 4, -2, -2, -2, 1, 1, 4, 4, -2, -2, 1, 1, -2, -2, 4, -2, -2, -2, 4, -2, -2, -2, -2, 4, 1, 1, 1, -2, 1, -2, -2, -2, 0, -2, -2, 1, 0, 4, 0, -2, 1, 1, -2, 0, 0, 0, -2, -2, 0, 1, 0, 4, -2, 1, 1, 1, -2, 0, 0, 0, 0, -2, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -2, 1, -2, -2, 1, -2, 1, 4, 1, -2, -2, 1, 1, -2, 1, -2, 1, -2, -2, 1, 1, 1, -2, -2], 'schur_index': 1}
  • id: 5461552
    {'cdim': 2, 'counter': 33, 'faithful': False, 'group': '1296.3190', 'group_order': 1296, 'image': None, 'label': '1296.3190.2q', 'multiplicity': 2, 'nt': [6, 5], 'qdim': 4, 'qvalues': [4, 4, 4, 4, 4, 4, 0, 0, -2, -2, -2, 4, 1, -2, 1, -2, -2, 4, -2, 1, -2, -2, -2, 1, 1, -2, 4, 1, -2, 1, 1, 0, 0, -2, -2, -2, -2, -2, 1, -2, 1, 4, -2, 4, -2, -2, -2, -2, -2, -2, 1, 1, -2, -2, 1, 4, 1, -2, 4, 4, -2, -2, -2, 1, 1, -2, -2, 1, 1, -2, -2, 1, 1, 1, -2, 1, -2, -2, 1, 1, 1, -2, 1, 1, 4, 1, -2, -2, -2, 1, 1, 1, -2, -2, 1, -2, 1, 1, 1, -2, 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], 'schur_index': 1}
  • id: 5461553
    {'cdim': 2, 'counter': 34, 'faithful': False, 'group': '1296.3190', 'group_order': 1296, 'image': None, 'label': '1296.3190.2r', 'multiplicity': 2, 'nt': [12, 12], 'qdim': 4, 'qvalues': [4, -4, -4, 4, 0, 0, 0, 0, 4, 4, -2, -2, 4, 4, 4, 4, -2, 4, 4, -2, -2, -2, -2, -2, 4, 4, -2, 4, -2, -2, -2, 0, 0, -4, -4, 2, 2, -4, -4, -4, -4, 2, -4, -4, -4, 4, 4, -4, -4, 2, 2, 2, 2, 2, -4, 2, -4, 0, 2, -2, 2, 0, 4, 0, -4, -2, -2, -4, 0, 0, 0, 4, 4, 0, 2, 0, -4, 2, 2, 2, -2, 2, 0, 0, 0, 0, -2, 0, 0, -2, 0, 2, 0, 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], 'schur_index': 1}
  • id: 5461554
    {'cdim': 2, 'counter': 35, 'faithful': False, 'group': '1296.3190', 'group_order': 1296, 'image': None, 'label': '1296.3190.2s', 'multiplicity': 2, 'nt': [12, 12], 'qdim': 4, 'qvalues': [4, -4, 4, -4, 0, 0, 0, 0, 4, 4, -2, -2, 4, 4, 4, 4, -2, 4, 4, -2, -2, -2, -2, -2, 4, 4, -2, 4, -2, -2, -2, 0, 0, -4, -4, 2, 2, -4, -4, -4, -4, 2, -4, -4, 4, -4, -4, 4, -4, 2, 2, 2, 2, 2, -4, 2, -4, 0, -2, 2, -2, 0, -4, 0, 4, 2, 2, 4, 0, 0, 0, -4, -4, 0, -2, 0, 4, 2, 2, 2, 2, -2, 0, 0, 0, 0, 2, 0, 0, 2, 0, -2, 0, 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], 'schur_index': 1}
  • id: 5461555
    {'cdim': 2, 'counter': 36, 'faithful': False, 'group': '1296.3190', 'group_order': 1296, 'image': None, 'label': '1296.3190.2t', 'multiplicity': 2, 'nt': [12, 13], 'qdim': 4, 'qvalues': [4, -4, -4, 4, 0, 0, 0, 0, 4, 4, 4, 4, -2, 4, -2, 4, 4, 4, -2, -2, 4, 4, -2, -2, -2, -2, 4, -2, -2, -2, -2, 0, 0, -4, -4, -4, -4, -4, 2, 2, 2, -4, -4, -4, -4, 4, 4, -4, 2, -4, 2, 2, 2, -4, 2, -4, 2, 0, -4, 4, -4, 0, -2, 0, 2, 4, 4, 2, 0, 0, 0, -2, -2, 0, -4, 0, 2, 2, 2, 2, -2, 2, 0, 0, 0, 0, -2, 0, 0, -2, 0, 2, 0, 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], 'schur_index': 1}
  • id: 5461556
    {'cdim': 2, 'counter': 37, 'faithful': False, 'group': '1296.3190', 'group_order': 1296, 'image': None, 'label': '1296.3190.2u', 'multiplicity': 2, 'nt': [12, 13], 'qdim': 4, 'qvalues': [4, -4, 4, -4, 0, 0, 0, 0, 4, 4, 4, 4, -2, 4, -2, 4, 4, 4, -2, -2, 4, 4, -2, -2, -2, -2, 4, -2, -2, -2, -2, 0, 0, -4, -4, -4, -4, -4, 2, 2, 2, -4, -4, -4, 4, -4, -4, 4, 2, -4, 2, 2, 2, -4, 2, -4, 2, 0, 4, -4, 4, 0, 2, 0, -2, -4, -4, -2, 0, 0, 0, 2, 2, 0, 4, 0, -2, 2, 2, 2, 2, -2, 0, 0, 0, 0, 2, 0, 0, 2, 0, -2, 0, 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], 'schur_index': 1}
  • id: 5461557
    {'cdim': 2, 'counter': 38, 'faithful': False, 'group': '1296.3190', 'group_order': 1296, 'image': None, 'label': '1296.3190.2v', 'multiplicity': 2, 'nt': [12, 14], 'qdim': 4, 'qvalues': [4, -4, -4, 4, 0, 0, 0, 0, -2, -2, -2, 4, -2, -2, -2, -2, -2, 4, 4, -2, -2, -2, 4, -2, -2, 4, 4, -2, 4, -2, -2, 0, 0, 2, 2, 2, 2, 2, 2, -4, 2, -4, 2, -4, 2, -2, -2, 2, -4, 2, 2, 2, -4, 2, 2, -4, 2, 0, -4, 4, 2, 0, 4, 0, 2, -2, -2, 2, 0, 0, 0, -2, -2, 0, 2, 0, -4, -4, 2, 2, -2, -4, 0, 0, 0, 0, 4, 0, 0, -2, 0, 2, 0, 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], 'schur_index': 1}
  • id: 5461558
    {'cdim': 2, 'counter': 39, 'faithful': False, 'group': '1296.3190', 'group_order': 1296, 'image': None, 'label': '1296.3190.2w', 'multiplicity': 2, 'nt': [12, 14], 'qdim': 4, 'qvalues': [4, -4, 4, -4, 0, 0, 0, 0, -2, -2, -2, 4, -2, -2, -2, -2, -2, 4, 4, -2, -2, -2, 4, -2, -2, 4, 4, -2, 4, -2, -2, 0, 0, 2, 2, 2, 2, 2, 2, -4, 2, -4, 2, -4, -2, 2, 2, -2, -4, 2, 2, 2, -4, 2, 2, -4, 2, 0, 4, -4, -2, 0, -4, 0, -2, 2, 2, -2, 0, 0, 0, 2, 2, 0, -2, 0, 4, -4, 2, 2, 2, 4, 0, 0, 0, 0, -4, 0, 0, 2, 0, -2, 0, 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], 'schur_index': 1}
  • id: 5461560
    {'cdim': 2, 'counter': 40, 'faithful': False, 'group': '1296.3190', 'group_order': 1296, 'image': None, 'label': '1296.3190.2x', 'multiplicity': 2, 'nt': [12, 18], 'qdim': 4, 'qvalues': [4, 4, -4, -4, -4, 4, 0, 0, -2, -2, -2, 4, 1, -2, 1, -2, -2, 4, -2, 1, -2, -2, -2, 1, 1, -2, 4, 1, -2, 1, 1, 0, 0, -2, -2, -2, -2, -2, 1, -2, 1, 4, -2, 4, 2, 2, 2, 2, -2, -2, 1, 1, -2, -2, 1, 4, 1, 2, -4, -4, 2, 2, 2, -1, -1, 2, 2, -1, -1, 2, 2, -1, -1, -1, 2, -1, 2, -2, 1, 1, -1, 2, -1, -1, -4, -1, 2, 2, 2, -1, -1, -1, 2, 2, -1, -2, 1, 1, 1, -2, 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], 'schur_index': 1}
  • id: 5461561
    {'cdim': 2, 'counter': 41, 'faithful': False, 'group': '1296.3190', 'group_order': 1296, 'image': None, 'label': '1296.3190.2y', 'multiplicity': 2, 'nt': [12, 18], 'qdim': 4, 'qvalues': [4, 4, -4, -4, 0, 0, 0, 0, -2, -2, 1, -2, -2, -2, -2, -2, 1, 4, 4, 1, 1, 1, -2, 1, -2, 4, -2, -2, -2, 1, 1, -4, 4, -2, -2, 1, 1, -2, -2, 4, -2, -2, -2, 4, 2, 2, 2, 2, 4, 1, 1, 1, -2, 1, -2, -2, -2, 0, 2, 2, -1, 0, -4, 0, 2, -1, -1, 2, 0, 0, 0, 2, 2, 0, -1, 0, -4, -2, 1, 1, -1, 2, 0, 0, 0, 0, 2, 0, 0, -1, 0, -1, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 2, -1, 2, 2, -1, 2, -1, -4, -1, 2, 2, -1, -1, 2, -1, 2, 1, -2, -2, 1, 1, 1, -2, -2], 'schur_index': 1}
  • id: 5461562
    {'cdim': 2, 'counter': 42, 'faithful': False, 'group': '1296.3190', 'group_order': 1296, 'image': None, 'label': '1296.3190.2z', 'multiplicity': 2, 'nt': [12, 18], 'qdim': 4, 'qvalues': [4, 4, -4, -4, 0, 0, 0, 0, -2, -2, 1, -2, -2, -2, -2, -2, 1, 4, 4, 1, 1, 1, -2, 1, -2, 4, -2, -2, -2, 1, 1, 4, -4, -2, -2, 1, 1, -2, -2, 4, -2, -2, -2, 4, 2, 2, 2, 2, 4, 1, 1, 1, -2, 1, -2, -2, -2, 0, 2, 2, -1, 0, -4, 0, 2, -1, -1, 2, 0, 0, 0, 2, 2, 0, -1, 0, -4, -2, 1, 1, -1, 2, 0, 0, 0, 0, 2, 0, 0, -1, 0, -1, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -2, 1, -2, -2, 1, -2, 1, 4, 1, -2, -2, 1, 1, -2, 1, -2, -1, 2, 2, -1, -1, -1, 2, 2], 'schur_index': 1}
  • id: 5461563
    {'cdim': 2, 'counter': 43, 'faithful': False, 'group': '1296.3190', 'group_order': 1296, 'image': None, 'label': '1296.3190.2aa', 'multiplicity': 2, 'nt': [12, 18], 'qdim': 4, 'qvalues': [4, 4, -4, -4, 4, -4, 0, 0, -2, -2, -2, 4, 1, -2, 1, -2, -2, 4, -2, 1, -2, -2, -2, 1, 1, -2, 4, 1, -2, 1, 1, 0, 0, -2, -2, -2, -2, -2, 1, -2, 1, 4, -2, 4, 2, 2, 2, 2, -2, -2, 1, 1, -2, -2, 1, 4, 1, -2, -4, -4, 2, -2, 2, 1, -1, 2, 2, -1, 1, -2, -2, -1, -1, 1, 2, 1, 2, -2, 1, 1, -1, 2, 1, 1, 4, 1, 2, -2, -2, -1, 1, -1, -2, -2, -1, 2, -1, -1, -1, 2, -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], 'schur_index': 1}
  • id: 5461564
    {'cdim': 2, 'counter': 44, 'faithful': False, 'group': '1296.3190', 'group_order': 1296, 'image': None, 'label': '1296.3190.2ab', 'multiplicity': 2, 'nt': [12, 18], 'qdim': 4, 'qvalues': [4, 4, 0, 0, -4, 0, -4, 0, -2, -2, -2, 4, -2, 1, -2, 1, -2, -2, 4, -2, 1, 1, 4, -2, 1, -2, -2, 1, -2, 1, 1, 4, 0, -2, -2, -2, -2, 1, -2, 4, -2, 4, 1, -2, 0, 0, 0, 0, -2, 1, -2, -2, 4, 1, 1, -2, 1, -4, 0, 0, 0, -4, 0, 2, 0, 0, 0, 0, 2, 2, 2, 0, 0, 2, 0, 2, 0, -2, 1, 1, 0, 0, -1, -1, 2, -1, 0, -1, 2, 0, -1, 0, 2, -1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 2, -1, -1, 0, 0, -2, 4, -2, -2, -2, -2, 4, -2, -2, 1, -2, -2, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 5461565
    {'cdim': 2, 'counter': 45, 'faithful': False, 'group': '1296.3190', 'group_order': 1296, 'image': None, 'label': '1296.3190.2ac', 'multiplicity': 2, 'nt': [12, 18], 'qdim': 4, 'qvalues': [4, 4, 0, 0, -4, 0, 4, 0, -2, -2, -2, 4, -2, 1, -2, 1, -2, -2, 4, -2, 1, 1, 4, -2, 1, -2, -2, 1, -2, 1, 1, -4, 0, -2, -2, -2, -2, 1, -2, 4, -2, 4, 1, -2, 0, 0, 0, 0, -2, 1, -2, -2, 4, 1, 1, -2, 1, -4, 0, 0, 0, -4, 0, 2, 0, 0, 0, 0, 2, 2, 2, 0, 0, 2, 0, 2, 0, -2, 1, 1, 0, 0, -1, -1, 2, -1, 0, -1, 2, 0, -1, 0, 2, -1, 0, 0, 0, 0, 0, 0, 0, -2, 0, -2, 0, -2, 1, 1, 0, 0, 2, -4, 2, 2, 2, 2, -4, 2, 2, -1, 2, 2, -1, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 5461566
    {'cdim': 2, 'counter': 46, 'faithful': False, 'group': '1296.3190', 'group_order': 1296, 'image': None, 'label': '1296.3190.2ad', 'multiplicity': 2, 'nt': [12, 18], 'qdim': 4, 'qvalues': [4, 4, 0, 0, 4, 0, -4, 0, -2, -2, -2, 4, -2, 1, -2, 1, -2, -2, 4, -2, 1, 1, 4, -2, 1, -2, -2, 1, -2, 1, 1, -4, 0, -2, -2, -2, -2, 1, -2, 4, -2, 4, 1, -2, 0, 0, 0, 0, -2, 1, -2, -2, 4, 1, 1, -2, 1, 4, 0, 0, 0, 4, 0, -2, 0, 0, 0, 0, -2, -2, -2, 0, 0, -2, 0, -2, 0, -2, 1, 1, 0, 0, 1, 1, -2, 1, 0, 1, -2, 0, 1, 0, -2, 1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 2, -1, -1, 0, 0, 2, -4, 2, 2, 2, 2, -4, 2, 2, -1, 2, 2, -1, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 5461567
    {'cdim': 2, 'counter': 47, 'faithful': False, 'group': '1296.3190', 'group_order': 1296, 'image': None, 'label': '1296.3190.2ae', 'multiplicity': 2, 'nt': [12, 18], 'qdim': 4, 'qvalues': [4, 4, 4, 4, -4, -4, 0, 0, -2, -2, -2, 4, 1, -2, 1, -2, -2, 4, -2, 1, -2, -2, -2, 1, 1, -2, 4, 1, -2, 1, 1, 0, 0, -2, -2, -2, -2, -2, 1, -2, 1, 4, -2, 4, -2, -2, -2, -2, -2, -2, 1, 1, -2, -2, 1, 4, 1, 2, 4, 4, -2, 2, -2, -1, 1, -2, -2, 1, -1, 2, 2, 1, 1, -1, -2, -1, -2, -2, 1, 1, 1, -2, -1, -1, -4, -1, -2, 2, 2, 1, -1, 1, 2, 2, 1, 2, -1, -1, -1, 2, -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], 'schur_index': 1}
  • id: 5461568
    {'cdim': 2, 'counter': 48, 'faithful': False, 'group': '1296.3190', 'group_order': 1296, 'image': None, 'label': '1296.3190.2af', 'multiplicity': 2, 'nt': [12, 18], 'qdim': 4, 'qvalues': [4, 4, 4, 4, 0, 0, 0, 0, -2, -2, 1, -2, -2, -2, -2, -2, 1, 4, 4, 1, 1, 1, -2, 1, -2, 4, -2, -2, -2, 1, 1, -4, -4, -2, -2, 1, 1, -2, -2, 4, -2, -2, -2, 4, -2, -2, -2, -2, 4, 1, 1, 1, -2, 1, -2, -2, -2, 0, -2, -2, 1, 0, 4, 0, -2, 1, 1, -2, 0, 0, 0, -2, -2, 0, 1, 0, 4, -2, 1, 1, 1, -2, 0, 0, 0, 0, -2, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 2, -1, 2, 2, -1, 2, -1, -4, -1, 2, 2, -1, -1, 2, -1, 2, -1, 2, 2, -1, -1, -1, 2, 2], 'schur_index': 1}
  • id: 5461569
    {'cdim': 2, 'counter': 49, 'faithful': False, 'group': '1296.3190', 'group_order': 1296, 'image': None, 'label': '1296.3190.2ag', 'multiplicity': 2, 'nt': [12, 42], 'qdim': 4, 'qvalues': [4, -4, -4, 4, 0, 0, 0, 0, -2, -2, -2, 4, 1, -2, 1, -2, -2, 4, -2, 1, -2, -2, -2, 1, 1, -2, 4, 1, -2, 1, 1, 0, 0, 2, 2, 2, 2, 2, -1, 2, -1, -4, 2, -4, 2, -2, -2, 2, 2, 2, -1, -1, 2, 2, -1, -4, -1, 0, -4, 4, 2, 0, -2, -3, -1, -2, -2, -1, 3, 0, 0, 1, 1, -3, 2, 3, 2, 2, -1, -1, 1, 2, -3, -3, 0, 3, -2, 0, 0, 1, 3, -1, 0, 0, -1, 0, -3, 3, -3, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 5461571
    {'cdim': 2, 'counter': 50, 'faithful': False, 'group': '1296.3190', 'group_order': 1296, 'image': None, 'label': '1296.3190.2ah', 'multiplicity': 2, 'nt': [12, 42], 'qdim': 4, 'qvalues': [4, -4, -4, 4, 0, 0, 0, 0, -2, -2, -2, 4, 1, -2, 1, -2, -2, 4, -2, 1, -2, -2, -2, 1, 1, -2, 4, 1, -2, 1, 1, 0, 0, 2, 2, 2, 2, 2, -1, 2, -1, -4, 2, -4, 2, -2, -2, 2, 2, 2, -1, -1, 2, 2, -1, -4, -1, 0, -4, 4, 2, 0, -2, 3, -1, -2, -2, -1, -3, 0, 0, 1, 1, 3, 2, -3, 2, 2, -1, -1, 1, 2, 3, 3, 0, -3, -2, 0, 0, 1, -3, -1, 0, 0, -1, 0, 3, -3, 3, 0, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 5461572
    {'cdim': 2, 'counter': 51, 'faithful': False, 'group': '1296.3190', 'group_order': 1296, 'image': None, 'label': '1296.3190.2ai', 'multiplicity': 2, 'nt': [12, 42], 'qdim': 4, 'qvalues': [4, -4, 4, -4, 0, 0, 0, 0, -2, -2, -2, 4, 1, -2, 1, -2, -2, 4, -2, 1, -2, -2, -2, 1, 1, -2, 4, 1, -2, 1, 1, 0, 0, 2, 2, 2, 2, 2, -1, 2, -1, -4, 2, -4, -2, 2, 2, -2, 2, 2, -1, -1, 2, 2, -1, -4, -1, 0, 4, -4, -2, 0, 2, -3, 1, 2, 2, 1, 3, 0, 0, -1, -1, -3, -2, 3, -2, 2, -1, -1, -1, -2, -3, -3, 0, 3, 2, 0, 0, -1, 3, 1, 0, 0, 1, 0, 3, -3, 3, 0, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 5461573
    {'cdim': 2, 'counter': 52, 'faithful': False, 'group': '1296.3190', 'group_order': 1296, 'image': None, 'label': '1296.3190.2aj', 'multiplicity': 2, 'nt': [12, 42], 'qdim': 4, 'qvalues': [4, -4, 4, -4, 0, 0, 0, 0, -2, -2, -2, 4, 1, -2, 1, -2, -2, 4, -2, 1, -2, -2, -2, 1, 1, -2, 4, 1, -2, 1, 1, 0, 0, 2, 2, 2, 2, 2, -1, 2, -1, -4, 2, -4, -2, 2, 2, -2, 2, 2, -1, -1, 2, 2, -1, -4, -1, 0, 4, -4, -2, 0, 2, 3, 1, 2, 2, 1, -3, 0, 0, -1, -1, 3, -2, -3, -2, 2, -1, -1, -1, -2, 3, 3, 0, -3, 2, 0, 0, -1, -3, 1, 0, 0, 1, 0, -3, 3, -3, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 5461576
    {'cdim': 4, 'counter': 55, 'faithful': False, 'group': '1296.3190', 'group_order': 1296, 'image': None, 'label': '1296.3190.4a', 'multiplicity': 1, 'nt': [6, 9], 'qdim': 4, 'qvalues': [4, 4, 0, 0, 0, 0, 0, 0, 4, 4, -2, -2, 4, -2, 4, -2, -2, -2, 4, -2, 1, 1, -2, -2, -2, -2, 1, -2, 1, 1, 1, 4, 0, 4, 4, -2, -2, -2, 4, 4, 4, -2, -2, -2, 0, 0, 0, 0, -2, 1, -2, -2, -2, 1, -2, 1, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, 4, 4, -2, -2, -2, -2, 1, 1, 1, 1, 1, -2, 1, -2, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 5461577
    {'cdim': 4, 'counter': 56, 'faithful': False, 'group': '1296.3190', 'group_order': 1296, 'image': None, 'label': '1296.3190.4b', 'multiplicity': 1, 'nt': [6, 9], 'qdim': 4, 'qvalues': [4, 4, 0, 0, 4, 0, 0, 0, 4, 4, 4, 4, -2, -2, -2, -2, 4, -2, -2, -2, -2, -2, -2, -2, 1, 1, -2, 1, 1, 1, 1, 0, 0, 4, 4, 4, 4, -2, -2, -2, -2, 4, -2, -2, 0, 0, 0, 0, 1, -2, -2, -2, -2, -2, 1, -2, 1, -2, 0, 0, 0, -2, 0, -2, 0, 0, 0, 0, -2, 4, 4, 0, 0, -2, 0, -2, 0, 1, 1, 1, 0, 0, 1, 1, -2, 1, 0, -2, 1, 0, 1, 0, 1, -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], 'schur_index': 1}
  • id: 5461578
    {'cdim': 4, 'counter': 57, 'faithful': False, 'group': '1296.3190', 'group_order': 1296, 'image': None, 'label': '1296.3190.4c', 'multiplicity': 1, 'nt': [6, 9], 'qdim': 4, 'qvalues': [4, 4, 4, 4, 0, 0, 0, 0, 4, 4, -2, -2, -2, 4, -2, 4, -2, 4, -2, 1, -2, -2, 1, 1, -2, -2, -2, -2, 1, 1, 1, 0, 0, 4, 4, -2, -2, 4, -2, -2, -2, -2, 4, 4, 4, 4, 4, 4, -2, -2, 1, 1, 1, -2, -2, -2, -2, 0, -2, -2, -2, 0, -2, 0, -2, -2, -2, -2, 0, 0, 0, -2, -2, 0, -2, 0, -2, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 5461579
    {'cdim': 4, 'counter': 58, 'faithful': False, 'group': '1296.3190', 'group_order': 1296, 'image': None, 'label': '1296.3190.4d', 'multiplicity': 1, 'nt': [12, 28], 'qdim': 4, 'qvalues': [4, -4, 0, 0, 0, 0, 0, 0, 4, 4, 4, 4, 4, -2, 4, -2, 4, -2, 4, 4, -2, -2, 4, 4, -2, -2, -2, -2, -2, -2, -2, 0, 0, -4, -4, -4, -4, 2, -4, -4, -4, -4, 2, 2, 0, 0, 0, 0, 2, 2, -4, -4, -4, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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: 5461580
    {'cdim': 4, 'counter': 59, 'faithful': False, 'group': '1296.3190', 'group_order': 1296, 'image': None, 'label': '1296.3190.4e', 'multiplicity': 1, 'nt': [12, 37], 'qdim': 4, 'qvalues': [4, 4, -4, -4, 0, 0, 0, 0, 4, 4, -2, -2, -2, 4, -2, 4, -2, 4, -2, 1, -2, -2, 1, 1, -2, -2, -2, -2, 1, 1, 1, 0, 0, 4, 4, -2, -2, 4, -2, -2, -2, -2, 4, 4, -4, -4, -4, -4, -2, -2, 1, 1, 1, -2, -2, -2, -2, 0, 2, 2, 2, 0, 2, 0, 2, 2, 2, 2, 0, 0, 0, 2, 2, 0, 2, 0, 2, 1, 1, 1, -1, -1, 0, 0, 0, 0, -1, 0, 0, -1, 0, -1, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 5461582
    {'cdim': 4, 'counter': 60, 'faithful': False, 'group': '1296.3190', 'group_order': 1296, 'image': None, 'label': '1296.3190.4f', 'multiplicity': 1, 'nt': [12, 37], 'qdim': 4, 'qvalues': [4, 4, 0, 0, -4, 0, 0, 0, 4, 4, 4, 4, -2, -2, -2, -2, 4, -2, -2, -2, -2, -2, -2, -2, 1, 1, -2, 1, 1, 1, 1, 0, 0, 4, 4, 4, 4, -2, -2, -2, -2, 4, -2, -2, 0, 0, 0, 0, 1, -2, -2, -2, -2, -2, 1, -2, 1, 2, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 2, -4, -4, 0, 0, 2, 0, 2, 0, 1, 1, 1, 0, 0, -1, -1, 2, -1, 0, 2, -1, 0, -1, 0, -1, 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], 'schur_index': 1}
  • id: 5461583
    {'cdim': 4, 'counter': 61, 'faithful': False, 'group': '1296.3190', 'group_order': 1296, 'image': None, 'label': '1296.3190.4g', 'multiplicity': 1, 'nt': [12, 37], 'qdim': 4, 'qvalues': [4, 4, 0, 0, 0, 0, 0, 0, 4, 4, -2, -2, 4, -2, 4, -2, -2, -2, 4, -2, 1, 1, -2, -2, -2, -2, 1, -2, 1, 1, 1, -4, 0, 4, 4, -2, -2, -2, 4, 4, 4, -2, -2, -2, 0, 0, 0, 0, -2, 1, -2, -2, -2, 1, -2, 1, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, -4, -4, 2, 2, 2, 2, -1, -1, -1, -1, -1, 2, -1, 2, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 5461584
    {'cdim': 4, 'counter': 62, 'faithful': False, 'group': '1296.3190', 'group_order': 1296, 'image': None, 'label': '1296.3190.4h', 'multiplicity': 1, 'nt': [12, 38], 'qdim': 4, 'qvalues': [4, -4, -4, 4, 0, 0, 0, 0, 4, 4, -2, -2, -2, 4, -2, 4, -2, 4, -2, 1, -2, -2, 1, 1, -2, -2, -2, -2, 1, 1, 1, 0, 0, -4, -4, 2, 2, -4, 2, 2, 2, 2, -4, -4, -4, 4, 4, -4, 2, 2, -1, -1, -1, 2, 2, 2, 2, 0, 2, -2, 2, 0, -2, 0, 2, -2, -2, 2, 0, 0, 0, -2, -2, 0, 2, 0, 2, -1, -1, -1, 1, -1, 0, 0, 0, 0, 1, 0, 0, 1, 0, -1, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 5461585
    {'cdim': 4, 'counter': 63, 'faithful': False, 'group': '1296.3190', 'group_order': 1296, 'image': None, 'label': '1296.3190.4i', 'multiplicity': 1, 'nt': [12, 38], 'qdim': 4, 'qvalues': [4, -4, 4, -4, 0, 0, 0, 0, 4, 4, -2, -2, -2, 4, -2, 4, -2, 4, -2, 1, -2, -2, 1, 1, -2, -2, -2, -2, 1, 1, 1, 0, 0, -4, -4, 2, 2, -4, 2, 2, 2, 2, -4, -4, 4, -4, -4, 4, 2, 2, -1, -1, -1, 2, 2, 2, 2, 0, -2, 2, -2, 0, 2, 0, -2, 2, 2, -2, 0, 0, 0, 2, 2, 0, -2, 0, -2, -1, -1, -1, -1, 1, 0, 0, 0, 0, -1, 0, 0, -1, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 5461574
    {'cdim': 2, 'counter': 53, 'faithful': False, 'group': '1296.3190', 'group_order': 1296, 'image': None, 'label': '1296.3190.2ak', 'multiplicity': 4, 'nt': [24, 67], 'qdim': 8, 'qvalues': [8, -8, -8, 8, 0, 0, 0, 0, -4, -4, 2, -4, -4, -4, -4, -4, 2, 8, 8, 2, 2, 2, -4, 2, -4, 8, -4, -4, -4, 2, 2, 0, 0, 4, 4, -2, -2, 4, 4, -8, 4, 4, 4, -8, 4, -4, -4, 4, -8, -2, -2, -2, 4, -2, 4, 4, 4, 0, 4, -4, -2, 0, 8, 0, 4, 2, 2, 4, 0, 0, 0, -4, -4, 0, -2, 0, -8, 4, -2, -2, 2, 4, 0, 0, 0, 0, -4, 0, 0, 2, 0, -2, 0, 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], 'schur_index': 1}
  • id: 5461575
    {'cdim': 2, 'counter': 54, 'faithful': False, 'group': '1296.3190', 'group_order': 1296, 'image': None, 'label': '1296.3190.2al', 'multiplicity': 4, 'nt': [24, 67], 'qdim': 8, 'qvalues': [8, -8, 8, -8, 0, 0, 0, 0, -4, -4, 2, -4, -4, -4, -4, -4, 2, 8, 8, 2, 2, 2, -4, 2, -4, 8, -4, -4, -4, 2, 2, 0, 0, 4, 4, -2, -2, 4, 4, -8, 4, 4, 4, -8, -4, 4, 4, -4, -8, -2, -2, -2, 4, -2, 4, 4, 4, 0, -4, 4, 2, 0, -8, 0, -4, -2, -2, -4, 0, 0, 0, 4, 4, 0, 2, 0, 8, 4, -2, -2, -2, -4, 0, 0, 0, 0, 4, 0, 0, -2, 0, 2, 0, 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], 'schur_index': 1}
  • id: 5461586
    {'cdim': 4, 'counter': 64, 'faithful': False, 'group': '1296.3190', 'group_order': 1296, 'image': None, 'label': '1296.3190.4j', 'multiplicity': 2, 'nt': [12, 70], 'qdim': 8, 'qvalues': [8, 8, 0, 0, 0, 0, 0, 0, -4, -4, 2, -4, -4, 2, -4, 2, 2, -4, 8, 2, -1, -1, -4, 2, 2, -4, 2, 2, 2, -1, -1, 8, 0, -4, -4, 2, 2, 2, -4, 8, -4, -4, 2, -4, 0, 0, 0, 0, -4, -1, 2, 2, -4, -1, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, -4, 2, -4, -4, 2, -4, 2, -4, -1, 2, 2, -1, -1, 2, -1, 2, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 5461587
    {'cdim': 4, 'counter': 65, 'faithful': False, 'group': '1296.3190', 'group_order': 1296, 'image': None, 'label': '1296.3190.4k', 'multiplicity': 2, 'nt': [12, 70], 'qdim': 8, 'qvalues': [8, 8, 0, 0, 8, 0, 0, 0, -4, -4, -4, 8, 2, 2, 2, 2, -4, -4, -4, 2, 2, 2, -4, 2, -1, 2, -4, -1, 2, -1, -1, 0, 0, -4, -4, -4, -4, 2, 2, -4, 2, 8, 2, -4, 0, 0, 0, 0, 2, 2, 2, 2, -4, 2, -1, -4, -1, -4, 0, 0, 0, -4, 0, 2, 0, 0, 0, 0, 2, -4, -4, 0, 0, 2, 0, 2, 0, 2, -1, -1, 0, 0, -1, -1, -4, -1, 0, 2, 2, 0, -1, 0, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 5461588
    {'cdim': 4, 'counter': 66, 'faithful': False, 'group': '1296.3190', 'group_order': 1296, 'image': None, 'label': '1296.3190.4l', 'multiplicity': 2, 'nt': [12, 70], 'qdim': 8, 'qvalues': [8, 8, 8, 8, 0, 0, 0, 0, -4, -4, 2, -4, 2, -4, 2, -4, 2, 8, -4, -1, 2, 2, 2, -1, 2, -4, -4, 2, 2, -1, -1, 0, 0, -4, -4, 2, 2, -4, 2, -4, 2, -4, -4, 8, -4, -4, -4, -4, -4, 2, -1, -1, 2, 2, 2, -4, 2, 0, -4, -4, 2, 0, -4, 0, 2, 2, 2, 2, 0, 0, 0, 2, 2, 0, 2, 0, -4, 2, -1, -1, -1, 2, 0, 0, 0, 0, 2, 0, 0, -1, 0, -1, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 5461589
    {'cdim': 4, 'counter': 67, 'faithful': False, 'group': '1296.3190', 'group_order': 1296, 'image': None, 'label': '1296.3190.4m', 'multiplicity': 2, 'nt': [24, 204], 'qdim': 8, 'qvalues': [8, -8, 0, 0, 0, 0, 0, 0, 8, 8, 8, 8, -4, -4, -4, -4, 8, -4, -4, -4, -4, -4, -4, -4, 2, 2, -4, 2, 2, 2, 2, 0, 0, -8, -8, -8, -8, 4, 4, 4, 4, -8, 4, 4, 0, 0, 0, 0, -2, 4, 4, 4, 4, 4, -2, 4, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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: 5461590
    {'cdim': 4, 'counter': 68, 'faithful': False, 'group': '1296.3190', 'group_order': 1296, 'image': None, 'label': '1296.3190.4n', 'multiplicity': 2, 'nt': [24, 208], 'qdim': 8, 'qvalues': [8, -8, 0, 0, 0, 0, 0, 0, -4, -4, -4, 8, -4, 2, -4, 2, -4, -4, 8, -4, 2, 2, 8, -4, 2, -4, -4, 2, -4, 2, 2, 0, 0, 4, 4, 4, 4, -2, 4, -8, 4, -8, -2, 4, 0, 0, 0, 0, 4, -2, 4, 4, -8, -2, -2, 4, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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: 5461591
    {'cdim': 4, 'counter': 69, 'faithful': False, 'group': '1296.3190', 'group_order': 1296, 'image': None, 'label': '1296.3190.4o', 'multiplicity': 2, 'nt': [24, 229], 'qdim': 8, 'qvalues': [8, -8, 0, 0, 0, 0, 0, 0, 8, 8, -4, -4, 8, -4, 8, -4, -4, -4, 8, -4, 2, 2, -4, -4, -4, -4, 2, -4, 2, 2, 2, 0, 0, -8, -8, 4, 4, 4, -8, -8, -8, 4, 4, 4, 0, 0, 0, 0, 4, -2, 4, 4, 4, -2, 4, -2, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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: 5461593
    {'cdim': 4, 'counter': 70, 'faithful': False, 'group': '1296.3190', 'group_order': 1296, 'image': None, 'label': '1296.3190.4p', 'multiplicity': 2, 'nt': [24, 543], 'qdim': 8, 'qvalues': [8, -8, -8, 8, 0, 0, 0, 0, -4, -4, 2, -4, 2, -4, 2, -4, 2, 8, -4, -1, 2, 2, 2, -1, 2, -4, -4, 2, 2, -1, -1, 0, 0, 4, 4, -2, -2, 4, -2, 4, -2, 4, 4, -8, 4, -4, -4, 4, 4, -2, 1, 1, -2, -2, -2, 4, -2, 0, 4, -4, -2, 0, -4, 0, -2, 2, 2, -2, 0, 0, 0, 2, 2, 0, -2, 0, 4, -2, 1, 1, -1, -2, 0, 0, 0, 0, 2, 0, 0, -1, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 5461594
    {'cdim': 4, 'counter': 71, 'faithful': False, 'group': '1296.3190', 'group_order': 1296, 'image': None, 'label': '1296.3190.4q', 'multiplicity': 2, 'nt': [24, 543], 'qdim': 8, 'qvalues': [8, -8, 8, -8, 0, 0, 0, 0, -4, -4, 2, -4, 2, -4, 2, -4, 2, 8, -4, -1, 2, 2, 2, -1, 2, -4, -4, 2, 2, -1, -1, 0, 0, 4, 4, -2, -2, 4, -2, 4, -2, 4, 4, -8, -4, 4, 4, -4, 4, -2, 1, 1, -2, -2, -2, 4, -2, 0, -4, 4, 2, 0, 4, 0, 2, -2, -2, 2, 0, 0, 0, -2, -2, 0, 2, 0, -4, -2, 1, 1, 1, 2, 0, 0, 0, 0, -2, 0, 0, 1, 0, -1, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 5461595
    {'cdim': 4, 'counter': 72, 'faithful': False, 'group': '1296.3190', 'group_order': 1296, 'image': None, 'label': '1296.3190.4r', 'multiplicity': 2, 'nt': [24, 547], 'qdim': 8, 'qvalues': [8, 8, -8, -8, 0, 0, 0, 0, -4, -4, 2, -4, 2, -4, 2, -4, 2, 8, -4, -1, 2, 2, 2, -1, 2, -4, -4, 2, 2, -1, -1, 0, 0, -4, -4, 2, 2, -4, 2, -4, 2, -4, -4, 8, 4, 4, 4, 4, -4, 2, -1, -1, 2, 2, 2, -4, 2, 0, 4, 4, -2, 0, 4, 0, -2, -2, -2, -2, 0, 0, 0, -2, -2, 0, -2, 0, 4, 2, -1, -1, 1, -2, 0, 0, 0, 0, -2, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 5461596
    {'cdim': 4, 'counter': 73, 'faithful': False, 'group': '1296.3190', 'group_order': 1296, 'image': None, 'label': '1296.3190.4s', 'multiplicity': 2, 'nt': [24, 547], 'qdim': 8, 'qvalues': [8, 8, 0, 0, -8, 0, 0, 0, -4, -4, -4, 8, 2, 2, 2, 2, -4, -4, -4, 2, 2, 2, -4, 2, -1, 2, -4, -1, 2, -1, -1, 0, 0, -4, -4, -4, -4, 2, 2, -4, 2, 8, 2, -4, 0, 0, 0, 0, 2, 2, 2, 2, -4, 2, -1, -4, -1, 4, 0, 0, 0, 4, 0, -2, 0, 0, 0, 0, -2, 4, 4, 0, 0, -2, 0, -2, 0, 2, -1, -1, 0, 0, 1, 1, 4, 1, 0, -2, -2, 0, 1, 0, -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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 5461597
    {'cdim': 4, 'counter': 74, 'faithful': False, 'group': '1296.3190', 'group_order': 1296, 'image': None, 'label': '1296.3190.4t', 'multiplicity': 2, 'nt': [24, 547], 'qdim': 8, 'qvalues': [8, 8, 0, 0, 0, 0, 0, 0, -4, -4, 2, -4, -4, 2, -4, 2, 2, -4, 8, 2, -1, -1, -4, 2, 2, -4, 2, 2, 2, -1, -1, -8, 0, -4, -4, 2, 2, 2, -4, 8, -4, -4, 2, -4, 0, 0, 0, 0, -4, -1, 2, 2, -4, -1, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 4, -2, 4, 4, -2, 4, -2, 4, 1, -2, -2, 1, 1, -2, 1, -2, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 5461598
    {'cdim': 4, 'counter': 75, 'faithful': False, 'group': '1296.3190', 'group_order': 1296, 'image': None, 'label': '1296.3190.4u', 'multiplicity': 2, 'nt': [24, 1280], 'qdim': 8, 'qvalues': [8, -8, 0, 0, 0, 0, 0, 0, -4, -4, -4, 8, 2, 2, 2, 2, -4, -4, -4, 2, 2, 2, -4, 2, -1, 2, -4, -1, 2, -1, -1, 0, 0, 4, 4, 4, 4, -2, -2, 4, -2, -8, -2, 4, 0, 0, 0, 0, -2, -2, -2, -2, 4, -2, 1, 4, 1, 0, 0, 0, 0, 0, 0, -6, 0, 0, 0, 0, 6, 0, 0, 0, 0, -6, 0, 6, 0, -2, 1, 1, 0, 0, 3, 3, 0, -3, 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], 'schur_index': 1}
  • id: 5461599
    {'cdim': 4, 'counter': 76, 'faithful': False, 'group': '1296.3190', 'group_order': 1296, 'image': None, 'label': '1296.3190.4v', 'multiplicity': 2, 'nt': [24, 1280], 'qdim': 8, 'qvalues': [8, -8, 0, 0, 0, 0, 0, 0, -4, -4, -4, 8, 2, 2, 2, 2, -4, -4, -4, 2, 2, 2, -4, 2, -1, 2, -4, -1, 2, -1, -1, 0, 0, 4, 4, 4, 4, -2, -2, 4, -2, -8, -2, 4, 0, 0, 0, 0, -2, -2, -2, -2, 4, -2, 1, 4, 1, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, -6, 0, 0, 0, 0, 6, 0, -6, 0, -2, 1, 1, 0, 0, -3, -3, 0, 3, 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], 'schur_index': 1}
  • id: 5461601
    {'cdim': 8, 'counter': 78, 'faithful': False, 'group': '1296.3190', 'group_order': 1296, 'image': None, 'label': '1296.3190.8a', 'multiplicity': 1, 'nt': [12, 117], 'qdim': 8, 'qvalues': [8, 8, 0, 0, 0, 0, 0, 0, 8, 8, -4, -4, -4, -4, -4, -4, -4, -4, -4, 2, 2, 2, 2, 2, 2, 2, 2, 2, -1, -1, -1, 0, 0, 8, 8, -4, -4, -4, -4, -4, -4, -4, -4, -4, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 5461602
    {'cdim': 8, 'counter': 79, 'faithful': False, 'group': '1296.3190', 'group_order': 1296, 'image': None, 'label': '1296.3190.8b', 'multiplicity': 1, 'nt': [24, 1295], 'qdim': 8, 'qvalues': [8, -8, 0, 0, 0, 0, 0, 0, 8, 8, -4, -4, -4, -4, -4, -4, -4, -4, -4, 2, 2, 2, 2, 2, 2, 2, 2, 2, -1, -1, -1, 0, 0, -8, -8, 4, 4, 4, 4, 4, 4, 4, 4, 4, 0, 0, 0, 0, -2, -2, -2, -2, -2, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 5461600
    {'cdim': 4, 'counter': 77, 'faithful': False, 'group': '1296.3190', 'group_order': 1296, 'image': None, 'label': '1296.3190.4w', 'multiplicity': 4, 'nt': [48, 0], 'qdim': 16, 'qvalues': [16, -16, 0, 0, 0, 0, 0, 0, -8, -8, 4, -8, -8, 4, -8, 4, 4, -8, 16, 4, -2, -2, -8, 4, 4, -8, 4, 4, 4, -2, -2, 0, 0, 8, 8, -4, -4, -4, 8, -16, 8, 8, -4, 8, 0, 0, 0, 0, 8, 2, -4, -4, 8, 2, -4, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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: 5461604
    {'cdim': 8, 'counter': 80, 'faithful': False, 'group': '1296.3190', 'group_order': 1296, 'image': None, 'label': '1296.3190.8c', 'multiplicity': 2, 'nt': [24, 1535], 'qdim': 16, 'qvalues': [16, 16, 0, 0, 0, 0, 0, 0, -8, -8, 4, -8, 4, 4, 4, 4, 4, -8, -8, -2, -2, -2, 4, -2, -2, 4, 4, -2, -2, 1, 1, 0, 0, -8, -8, 4, 4, 4, 4, -8, 4, -8, 4, -8, 0, 0, 0, 0, 4, -2, -2, -2, 4, -2, -2, 4, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 5461605
    {'cdim': 8, 'counter': 81, 'faithful': True, 'group': '1296.3190', 'group_order': 1296, 'image': None, 'label': '1296.3190.8d', 'multiplicity': 2, 'nt': [48, 0], 'qdim': 16, 'qvalues': [16, -16, 0, 0, 0, 0, 0, 0, -8, -8, 4, -8, 4, 4, 4, 4, 4, -8, -8, -2, -2, -2, 4, -2, -2, 4, 4, -2, -2, 1, 1, 0, 0, 8, 8, -4, -4, -4, -4, 8, -4, 8, -4, 8, 0, 0, 0, 0, -4, 2, 2, 2, -4, 2, 2, -4, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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: 10646957
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 1296, 'counter': 1, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '1296.3190', 'group_counter': 3190, 'group_order': 1296, 'image': None, 'image_isoclass': '1.1', 'image_order': 1, 'indicator': 1, 'kernel': '1.a1.a1', 'kernel_order': 1296, 'label': '1296.3190.1a', 'nt': [1, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[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: 10647004
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 1296, 'counter': 2, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '1296.3190', 'group_counter': 3190, 'group_order': 1296, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.g1.a1', 'kernel_order': 648, 'label': '1296.3190.1b', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[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: 10647015
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 1296, 'counter': 3, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '1296.3190', 'group_counter': 3190, 'group_order': 1296, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.f1.a1', 'kernel_order': 648, 'label': '1296.3190.1c', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-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: 10647026
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 1296, 'counter': 4, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '1296.3190', 'group_counter': 3190, 'group_order': 1296, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.e1.a1', 'kernel_order': 648, 'label': '1296.3190.1d', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-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: 10647037
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 1296, 'counter': 5, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '1296.3190', 'group_counter': 3190, 'group_order': 1296, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.d1.a1', 'kernel_order': 648, 'label': '1296.3190.1e', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[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: 10647048
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 1296, 'counter': 6, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '1296.3190', 'group_counter': 3190, 'group_order': 1296, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.c1.a1', 'kernel_order': 648, 'label': '1296.3190.1f', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[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: 10647059
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 1296, 'counter': 7, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '1296.3190', 'group_counter': 3190, 'group_order': 1296, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.b1.a1', 'kernel_order': 648, 'label': '1296.3190.1g', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-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: 10647070
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 1296, 'counter': 8, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '1296.3190', 'group_counter': 3190, 'group_order': 1296, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.a1.a1', 'kernel_order': 648, 'label': '1296.3190.1h', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-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: 10647081
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 1296, 'counter': 9, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '1296.3190', 'group_counter': 3190, 'group_order': 1296, 'image': None, 'image_isoclass': '3.1', 'image_order': 3, 'indicator': 0, 'kernel': '3.a1.a1', 'kernel_order': 432, 'label': '1296.3190.1i1', 'nt': [3, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 0]], [[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, 0]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]]]}
  • id: 10646958
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 1296, 'counter': 10, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '1296.3190', 'group_counter': 3190, 'group_order': 1296, 'image': None, 'image_isoclass': '3.1', 'image_order': 3, 'indicator': 0, 'kernel': '3.a1.a1', 'kernel_order': 432, 'label': '1296.3190.1i2', 'nt': [3, 2], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 0]], [[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, 0]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]]]}
  • id: 10646969
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 1296, 'counter': 11, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '1296.3190', 'group_counter': 3190, 'group_order': 1296, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': '6.j1.a1', 'kernel_order': 216, 'label': '1296.3190.1j1', '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, -1]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[-1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 0]], [[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, 0]], [[1, 1]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, -1]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[-1, 1]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[-1, 0]], [[-1, 1]], [[-1, 0]], [[-1, -1]], [[-1, 0]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, -1]], [[-1, 1]], [[1, 0]], [[-1, -1]], [[1, 0]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[-1, 1]], [[-1, 0]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 1]]]}
  • id: 10646980
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 1296, 'counter': 12, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '1296.3190', 'group_counter': 3190, 'group_order': 1296, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': '6.j1.a1', 'kernel_order': 216, 'label': '1296.3190.1j2', '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, 1]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[-1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 0]], [[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, 0]], [[1, -1]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[-1, 0]], [[-1, 0]], [[-1, -1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[-1, -1]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[-1, 0]], [[-1, -1]], [[-1, 0]], [[-1, 1]], [[-1, 0]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 1]], [[-1, -1]], [[1, 0]], [[-1, 1]], [[1, 0]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[-1, -1]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, -1]]]}
  • id: 10646991
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 1296, 'counter': 13, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '1296.3190', 'group_counter': 3190, 'group_order': 1296, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': '6.i1.a1', 'kernel_order': 216, 'label': '1296.3190.1k1', '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, -1]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, -1]], [[-1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 0]], [[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, 0]], [[1, 1]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, -1]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[-1, 1]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[-1, 0]], [[-1, 1]], [[-1, 0]], [[-1, -1]], [[-1, 0]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, 0]], [[-1, 1]], [[-1, 0]], [[-1, 1]], [[-1, 0]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]]]}
  • id: 10646998
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 1296, 'counter': 14, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '1296.3190', 'group_counter': 3190, 'group_order': 1296, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': '6.i1.a1', 'kernel_order': 216, 'label': '1296.3190.1k2', '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, 1]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 1]], [[-1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 0]], [[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, 0]], [[1, -1]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[-1, 0]], [[-1, 0]], [[-1, -1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[-1, -1]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[-1, 0]], [[-1, -1]], [[-1, 0]], [[-1, 1]], [[-1, 0]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 0]], [[-1, -1]], [[-1, 0]], [[-1, -1]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]]]}
  • id: 10646999
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 1296, 'counter': 15, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '1296.3190', 'group_counter': 3190, 'group_order': 1296, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': '6.h1.a1', 'kernel_order': 216, 'label': '1296.3190.1l1', '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, -1]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, -1]], [[-1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 0]], [[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, 0]], [[1, 1]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, -1]], [[1, 0]], [[-1, 0]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[-1, -1]], [[-1, 1]], [[1, -1]], [[-1, 1]], [[1, -1]], [[-1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[-1, 1]], [[-1, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 1]], [[-1, 0]], [[1, -1]], [[1, 0]], [[-1, -1]], [[1, -1]], [[-1, 1]], [[1, 0]], [[1, 1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, 0]], [[-1, -1]], [[-1, 0]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[1, 1]], [[1, -1]], [[-1, -1]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, 0]], [[-1, 1]], [[-1, 0]], [[-1, 1]], [[-1, 0]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]]]}
  • id: 10647000
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 1296, 'counter': 16, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '1296.3190', 'group_counter': 3190, 'group_order': 1296, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': '6.h1.a1', 'kernel_order': 216, 'label': '1296.3190.1l2', '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, 1]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 1]], [[-1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 0]], [[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, 0]], [[1, -1]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[1, 0]], [[-1, 0]], [[1, -1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[-1, 1]], [[-1, -1]], [[1, 1]], [[-1, -1]], [[1, 1]], [[-1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[-1, -1]], [[-1, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, -1]], [[-1, 0]], [[1, 1]], [[1, 0]], [[-1, 1]], [[1, 1]], [[-1, -1]], [[1, 0]], [[1, -1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, 0]], [[-1, 1]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[1, -1]], [[1, 1]], [[-1, 1]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 0]], [[-1, -1]], [[-1, 0]], [[-1, -1]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]]]}
  • id: 10647001
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 1296, 'counter': 17, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '1296.3190', 'group_counter': 3190, 'group_order': 1296, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': '6.g1.a1', 'kernel_order': 216, 'label': '1296.3190.1m1', '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, -1]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[-1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 0]], [[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, 0]], [[1, 1]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, -1]], [[1, 0]], [[-1, 0]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[-1, -1]], [[-1, 1]], [[1, -1]], [[-1, 1]], [[1, -1]], [[-1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[-1, 1]], [[-1, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 1]], [[-1, 0]], [[1, -1]], [[1, 0]], [[-1, -1]], [[1, -1]], [[-1, 1]], [[1, 0]], [[1, 1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, -1]], [[1, 1]], [[-1, 0]], [[1, -1]], [[-1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[-1, 1]], [[-1, -1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[-1, 1]], [[-1, 0]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 1]]]}
  • id: 10647002
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 1296, 'counter': 18, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '1296.3190', 'group_counter': 3190, 'group_order': 1296, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': '6.g1.a1', 'kernel_order': 216, 'label': '1296.3190.1m2', '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, 1]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[-1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 0]], [[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, 0]], [[1, -1]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[1, 0]], [[-1, 0]], [[1, -1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[-1, 1]], [[-1, -1]], [[1, 1]], [[-1, -1]], [[1, 1]], [[-1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[-1, -1]], [[-1, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, -1]], [[-1, 0]], [[1, 1]], [[1, 0]], [[-1, 1]], [[1, 1]], [[-1, -1]], [[1, 0]], [[1, -1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[1, -1]], [[-1, 0]], [[1, 1]], [[-1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[-1, -1]], [[-1, 1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[-1, -1]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, -1]]]}
  • id: 10647003
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 1296, 'counter': 19, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '1296.3190', 'group_counter': 3190, 'group_order': 1296, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': '6.e1.a1', 'kernel_order': 216, 'label': '1296.3190.1n1', 'nt': [6, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 0]], [[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, 0]], [[1, 1]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[-1, 0]], [[1, 0]], [[-1, 1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[1, -1]], [[1, 1]], [[-1, -1]], [[1, 1]], [[-1, -1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 0]], [[-1, -1]], [[-1, 1]], [[-1, 0]], [[-1, 1]], [[1, 0]], [[-1, -1]], [[-1, 0]], [[1, -1]], [[-1, -1]], [[1, 1]], [[-1, 0]], [[-1, 1]], [[1, -1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, 0]], [[-1, -1]], [[-1, 0]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]]]}
  • id: 10647005
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 1296, 'counter': 20, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '1296.3190', 'group_counter': 3190, 'group_order': 1296, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': '6.e1.a1', 'kernel_order': 216, 'label': '1296.3190.1n2', 'nt': [6, 2], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 0]], [[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, 0]], [[1, -1]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[-1, 0]], [[1, 0]], [[-1, -1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[1, 1]], [[1, -1]], [[-1, 1]], [[1, -1]], [[-1, 1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 0]], [[-1, 1]], [[-1, -1]], [[-1, 0]], [[-1, -1]], [[1, 0]], [[-1, 1]], [[-1, 0]], [[1, 1]], [[-1, 1]], [[1, -1]], [[-1, 0]], [[-1, -1]], [[1, 1]], [[-1, -1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, 0]], [[-1, 1]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]]]}
  • id: 10647006
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 1296, 'counter': 21, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '1296.3190', 'group_counter': 3190, 'group_order': 1296, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': '6.c1.a1', 'kernel_order': 216, 'label': '1296.3190.1o1', 'nt': [6, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, -1]], [[-1, 0]], [[-1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 0]], [[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, 0]], [[1, 1]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[-1, 0]], [[1, 0]], [[-1, 1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[1, -1]], [[1, 1]], [[-1, -1]], [[1, 1]], [[-1, -1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 0]], [[-1, -1]], [[-1, 1]], [[-1, 0]], [[-1, 1]], [[1, 0]], [[-1, -1]], [[-1, 0]], [[1, -1]], [[-1, -1]], [[1, 1]], [[-1, 0]], [[-1, 1]], [[1, -1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, -1]], [[1, 1]], [[-1, 0]], [[1, -1]], [[-1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[-1, -1]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, 0]], [[-1, 1]], [[-1, 0]], [[-1, 1]], [[-1, 0]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, 0]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 1]]]}
  • id: 10647007
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 1296, 'counter': 22, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '1296.3190', 'group_counter': 3190, 'group_order': 1296, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': '6.c1.a1', 'kernel_order': 216, 'label': '1296.3190.1o2', 'nt': [6, 2], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 1]], [[-1, 0]], [[-1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 0]], [[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, 0]], [[1, -1]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[-1, 0]], [[1, 0]], [[-1, -1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[1, 1]], [[1, -1]], [[-1, 1]], [[1, -1]], [[-1, 1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 0]], [[-1, 1]], [[-1, -1]], [[-1, 0]], [[-1, -1]], [[1, 0]], [[-1, 1]], [[-1, 0]], [[1, 1]], [[-1, 1]], [[1, -1]], [[-1, 0]], [[-1, -1]], [[1, 1]], [[-1, -1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[1, -1]], [[-1, 0]], [[1, 1]], [[-1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[-1, 1]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 0]], [[-1, -1]], [[-1, 0]], [[-1, -1]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, -1]]]}
  • id: 10647008
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 1296, 'counter': 23, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '1296.3190', 'group_counter': 3190, 'group_order': 1296, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': '6.b1.a1', 'kernel_order': 216, 'label': '1296.3190.1p1', 'nt': [6, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, -1]], [[-1, 0]], [[-1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 0]], [[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, 0]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, -1]], [[-1, 1]], [[1, 0]], [[-1, -1]], [[1, 0]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, 0]], [[-1, 1]], [[-1, 0]], [[-1, 1]], [[-1, 0]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, 0]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 1]]]}
  • id: 10647009
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 1296, 'counter': 24, 'cyclotomic_n': 3, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '1296.3190', 'group_counter': 3190, 'group_order': 1296, 'image': None, 'image_isoclass': '6.2', 'image_order': 6, 'indicator': 0, 'kernel': '6.b1.a1', 'kernel_order': 216, 'label': '1296.3190.1p2', 'nt': [6, 2], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 1]], [[-1, 0]], [[-1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 0]], [[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, 0]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 1]], [[-1, -1]], [[1, 0]], [[-1, 1]], [[1, 0]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, 0]], [[-1, -1]], [[-1, 0]], [[-1, -1]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, -1]]]}
  • id: 10647010
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  • id: 10647052
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  • id: 10647053
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  • id: 10647054
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  • id: 10647055
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  • id: 10647056
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  • id: 10647057
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  • id: 10647058
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  • id: 10647060
    {'center': '6.f1.a1', 'center_index': 6, 'center_order': 216, 'counter': 70, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '1296.3190', 'group_counter': 3190, 'group_order': 1296, 'image': None, 'image_isoclass': '36.12', 'image_order': 36, 'indicator': 0, 'kernel': '36.e1.a1', 'kernel_order': 36, 'label': '1296.3190.2ad2', 'nt': [12, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, 1]], [[2, -1]], [[2, 1]], [[2, 0]], [[2, -1]], [[-1, -1]], [[2, 1]], [[-1, 1]], [[2, -1]], [[-1, 0]], [[2, 0]], [[2, -1]], [[-1, -1]], [[-1, 1]], [[2, 0]], [[2, 1]], [[-1, -1]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[-2, 0]], [[0, 0]], [[2, -1]], [[2, 1]], [[2, -1]], [[2, 1]], [[-1, 1]], [[2, 1]], [[2, 0]], [[2, -1]], [[2, 0]], [[-1, -1]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, -1]], [[2, -1]], [[2, 1]], [[2, 0]], [[-1, 1]], [[-1, 1]], [[-1, 0]], [[-1, -1]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, -1]], [[2, 1]], [[2, -1]], [[0, 0]], [[0, 0]], [[2, 1]], [[0, 0]], [[2, 1]], [[0, 0]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[0, 0]], [[0, 0]], [[-1, 1]], [[-1, -1]], [[-1, 0]], [[-1, -1]], [[0, 0]], [[-1, 1]], [[-1, 0]], [[0, 0]], [[-1, 1]], [[0, 0]], [[-1, 0]], [[-1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, -1]], [[0, 0]], [[-2, 1]], [[0, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[0, 0]], [[0, 0]], [[-2, 1]], [[-2, 0]], [[-2, 1]], [[-2, -1]], [[-2, 1]], [[-2, -1]], [[-2, 0]], [[-2, -1]], [[1, 0]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 10647061
    {'center': '6.a1.a1', 'center_index': 6, 'center_order': 216, 'counter': 71, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '1296.3190', 'group_counter': 3190, 'group_order': 1296, 'image': None, 'image_isoclass': '36.12', 'image_order': 36, 'indicator': 0, 'kernel': '36.c1.a1', 'kernel_order': 36, 'label': '1296.3190.2ae1', 'nt': [12, 18], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, -1]], [[2, 1]], [[2, -1]], [[2, 0]], [[-1, 1]], [[2, 1]], [[-1, -1]], [[2, -1]], [[2, 1]], [[2, 0]], [[-1, 0]], [[-1, 1]], [[2, 1]], [[2, -1]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[-1, 0]], [[2, 0]], [[-1, -1]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[0, 0]], [[0, 0]], [[2, 1]], [[2, -1]], [[2, 1]], [[2, -1]], [[2, -1]], [[-1, -1]], [[-1, 0]], [[-1, 1]], [[2, 0]], [[2, 1]], [[2, 0]], [[2, -1]], [[2, -1]], [[2, 1]], [[2, 1]], [[-1, 0]], [[2, 1]], [[-1, 1]], [[-1, -1]], [[-1, 0]], [[2, -1]], [[-1, -1]], [[2, 0]], [[-1, 1]], [[1, 0]], [[2, 0]], [[2, 0]], [[2, -1]], [[1, 0]], [[-1, 0]], [[1, 1]], [[-1, 1]], [[2, 1]], [[2, -1]], [[-1, -1]], [[1, 1]], [[-2, -1]], [[-2, 1]], [[-1, -1]], [[-1, 1]], [[1, -1]], [[2, 1]], [[1, -1]], [[-1, 0]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, 0]], [[1, -1]], [[1, 1]], [[-2, 0]], [[1, 1]], [[-1, 0]], [[-2, -1]], [[1, 0]], [[-1, -1]], [[1, -1]], [[-1, 1]], [[1, 0]], [[-2, 1]], [[-1, -1]], [[-2, 1]], [[1, 1]], [[1, 1]], [[1, -1]], [[-2, -1]], [[1, -1]], [[0, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 10647062
    {'center': '6.a1.a1', 'center_index': 6, 'center_order': 216, 'counter': 72, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '1296.3190', 'group_counter': 3190, 'group_order': 1296, 'image': None, 'image_isoclass': '36.12', 'image_order': 36, 'indicator': 0, 'kernel': '36.c1.a1', 'kernel_order': 36, 'label': '1296.3190.2ae2', 'nt': [12, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 1]], [[2, -1]], [[2, 1]], [[2, 0]], [[-1, -1]], [[2, -1]], [[-1, 1]], [[2, 1]], [[2, -1]], [[2, 0]], [[-1, 0]], [[-1, -1]], [[2, -1]], [[2, 1]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[-1, 0]], [[2, 0]], [[-1, 1]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[0, 0]], [[0, 0]], [[2, -1]], [[2, 1]], [[2, -1]], [[2, 1]], [[2, 1]], [[-1, 1]], [[-1, 0]], [[-1, -1]], [[2, 0]], [[2, -1]], [[2, 0]], [[2, 1]], [[2, 1]], [[2, -1]], [[2, -1]], [[-1, 0]], [[2, -1]], [[-1, -1]], [[-1, 1]], [[-1, 0]], [[2, 1]], [[-1, 1]], [[2, 0]], [[-1, -1]], [[1, 0]], [[2, 0]], [[2, 0]], [[2, 1]], [[1, 0]], [[-1, 0]], [[1, -1]], [[-1, -1]], [[2, -1]], [[2, 1]], [[-1, 1]], [[1, -1]], [[-2, 1]], [[-2, -1]], [[-1, 1]], [[-1, -1]], [[1, 1]], [[2, -1]], [[1, 1]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 0]], [[1, 1]], [[1, -1]], [[-2, 0]], [[1, -1]], [[-1, 0]], [[-2, 1]], [[1, 0]], [[-1, 1]], [[1, 1]], [[-1, -1]], [[1, 0]], [[-2, -1]], [[-1, 1]], [[-2, -1]], [[1, -1]], [[1, -1]], [[1, 1]], [[-2, 1]], [[1, 1]], [[0, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 10647063
    {'center': '6.d1.a1', 'center_index': 6, 'center_order': 216, 'counter': 73, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '1296.3190', 'group_counter': 3190, 'group_order': 1296, 'image': None, 'image_isoclass': '36.12', 'image_order': 36, 'indicator': 0, 'kernel': '36.b1.a1', 'kernel_order': 36, 'label': '1296.3190.2af1', 'nt': [12, 18], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, -1]], [[2, 1]], [[-1, -1]], [[-1, 0]], [[2, 1]], [[2, 1]], [[2, -1]], [[2, -1]], [[-1, 1]], [[2, 0]], [[2, 0]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, 0]], [[-1, -1]], [[2, 1]], [[2, 0]], [[-1, 0]], [[2, -1]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[-2, 0]], [[-2, 0]], [[2, 1]], [[2, -1]], [[-1, 1]], [[-1, -1]], [[2, -1]], [[2, -1]], [[2, 0]], [[2, 1]], [[-1, 0]], [[2, 1]], [[2, 0]], [[2, -1]], [[2, -1]], [[2, 1]], [[2, 1]], [[2, 0]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, 0]], [[-1, -1]], [[2, -1]], [[-1, 0]], [[2, 1]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, -1]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 1]], [[-1, 1]], [[-1, -1]], [[2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, -1]], [[2, 1]], [[0, 0]], [[-1, 1]], [[0, 0]], [[2, 0]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-1, -1]], [[0, 0]], [[-1, 1]], [[0, 0]], [[0, 0]], [[-1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, -1]], [[1, 0]], [[1, -1]], [[-2, 1]], [[-2, -1]], [[1, 1]], [[1, 0]], [[1, 1]], [[-2, 0]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[-2, -1]], [[1, -1]], [[-2, 1]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[-2, -1]], [[-2, 1]]]}
  • id: 10647064
    {'center': '6.d1.a1', 'center_index': 6, 'center_order': 216, 'counter': 74, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '1296.3190', 'group_counter': 3190, 'group_order': 1296, 'image': None, 'image_isoclass': '36.12', 'image_order': 36, 'indicator': 0, 'kernel': '36.b1.a1', 'kernel_order': 36, 'label': '1296.3190.2af2', 'nt': [12, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1]], [[2, -1]], [[-1, 1]], [[-1, 0]], [[2, -1]], [[2, -1]], [[2, 1]], [[2, 1]], [[-1, -1]], [[2, 0]], [[2, 0]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, 0]], [[-1, 1]], [[2, -1]], [[2, 0]], [[-1, 0]], [[2, 1]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[-2, 0]], [[-2, 0]], [[2, -1]], [[2, 1]], [[-1, -1]], [[-1, 1]], [[2, 1]], [[2, 1]], [[2, 0]], [[2, -1]], [[-1, 0]], [[2, -1]], [[2, 0]], [[2, 1]], [[2, 1]], [[2, -1]], [[2, -1]], [[2, 0]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, 0]], [[-1, 1]], [[2, 1]], [[-1, 0]], [[2, -1]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, -1]], [[-1, -1]], [[-1, 1]], [[2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1]], [[2, -1]], [[0, 0]], [[-1, -1]], [[0, 0]], [[2, 0]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-1, 1]], [[0, 0]], [[-1, -1]], [[0, 0]], [[0, 0]], [[-1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1]], [[1, 0]], [[1, 1]], [[-2, -1]], [[-2, 1]], [[1, -1]], [[1, 0]], [[1, -1]], [[-2, 0]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[-2, 1]], [[1, 1]], [[-2, -1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[-2, 1]], [[-2, -1]]]}
  • id: 10647065
    {'center': '12.b1.a1', 'center_index': 12, 'center_order': 108, 'counter': 75, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '1296.3190', 'group_counter': 3190, 'group_order': 1296, 'image': None, 'image_isoclass': '72.30', 'image_order': 72, 'indicator': 0, 'kernel': '72.i1.b1', 'kernel_order': 18, 'label': '1296.3190.2ag1', 'nt': [12, 42], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, -1]], [[2, 1]], [[2, -1]], [[2, 0]], [[-1, 1]], [[2, 1]], [[-1, -1]], [[2, -1]], [[2, 1]], [[2, 0]], [[-1, 0]], [[-1, 1]], [[2, 1]], [[2, -1]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[-1, 0]], [[2, 0]], [[-1, -1]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[0, 0]], [[0, 0]], [[-2, 1]], [[-2, -1]], [[-2, 1]], [[-2, -1]], [[-2, -1]], [[1, -1]], [[1, 0]], [[1, 1]], [[-2, 0]], [[-2, 1]], [[-2, 0]], [[-2, -1]], [[2, -1]], [[2, 1]], [[-2, 1]], [[1, 0]], [[-2, 1]], [[1, 1]], [[1, -1]], [[1, 0]], [[-2, -1]], [[1, -1]], [[-2, 0]], [[1, 1]], [[1, 0], [2, 1]], [[-2, 0]], [[2, 0]], [[-2, -1]], [[-1, 0], [-2, 1]], [[-1, 0]], [[-2, 0], [-1, 1]], [[1, 1]], [[2, 1]], [[2, -1]], [[1, -1]], [[2, 0], [1, 1]], [[0, 0]], [[0, 0]], [[-1, -1]], [[-1, 1]], [[-1, 0], [1, 1]], [[-2, 1]], [[1, 0], [-1, 1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[-1, 1]], [[1, 0]], [[-1, 0], [1, 1]], [[-2, 0], [-1, 1]], [[0, 0]], [[2, 0], [1, 1]], [[-1, 0]], [[0, 0]], [[1, 0], [2, 1]], [[-1, -1]], [[1, 0], [-1, 1]], [[1, 1]], [[-1, 0], [-2, 1]], [[0, 0]], [[1, -1]], [[0, 0]], [[-2, 0], [-1, 1]], [[2, 0], [1, 1]], [[-1, 0], [1, 1]], [[0, 0]], [[1, 0], [-1, 1]], [[0, 0]], [[1, 0], [2, 1]], [[0, 0]], [[-1, 0], [-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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: 10647066
    {'center': '12.b1.a1', 'center_index': 12, 'center_order': 108, 'counter': 76, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '1296.3190', 'group_counter': 3190, 'group_order': 1296, 'image': None, 'image_isoclass': '72.30', 'image_order': 72, 'indicator': 0, 'kernel': '72.i1.b1', 'kernel_order': 18, 'label': '1296.3190.2ag2', 'nt': [12, 2], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1]], [[2, -1]], [[2, 1]], [[2, 0]], [[-1, -1]], [[2, -1]], [[-1, 1]], [[2, 1]], [[2, -1]], [[2, 0]], [[-1, 0]], [[-1, -1]], [[2, -1]], [[2, 1]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[-1, 0]], [[2, 0]], [[-1, 1]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[0, 0]], [[0, 0]], [[-2, -1]], [[-2, 1]], [[-2, -1]], [[-2, 1]], [[-2, 1]], [[1, 1]], [[1, 0]], [[1, -1]], [[-2, 0]], [[-2, -1]], [[-2, 0]], [[-2, 1]], [[2, 1]], [[2, -1]], [[-2, -1]], [[1, 0]], [[-2, -1]], [[1, -1]], [[1, 1]], [[1, 0]], [[-2, 1]], [[1, 1]], [[-2, 0]], [[1, -1]], [[-1, 0], [-2, 1]], [[-2, 0]], [[2, 0]], [[-2, 1]], [[1, 0], [2, 1]], [[-1, 0]], [[-1, 0], [1, 1]], [[1, -1]], [[2, -1]], [[2, 1]], [[1, 1]], [[1, 0], [-1, 1]], [[0, 0]], [[0, 0]], [[-1, 1]], [[-1, -1]], [[-2, 0], [-1, 1]], [[-2, -1]], [[2, 0], [1, 1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[-1, -1]], [[1, 0]], [[-2, 0], [-1, 1]], [[-1, 0], [1, 1]], [[0, 0]], [[1, 0], [-1, 1]], [[-1, 0]], [[0, 0]], [[-1, 0], [-2, 1]], [[-1, 1]], [[2, 0], [1, 1]], [[1, -1]], [[1, 0], [2, 1]], [[0, 0]], [[1, 1]], [[0, 0]], [[-1, 0], [1, 1]], [[1, 0], [-1, 1]], [[-2, 0], [-1, 1]], [[0, 0]], [[2, 0], [1, 1]], [[0, 0]], [[-1, 0], [-2, 1]], [[0, 0]], [[1, 0], [2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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: 10647067
    {'center': '12.b1.a1', 'center_index': 12, 'center_order': 108, 'counter': 77, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '1296.3190', 'group_counter': 3190, 'group_order': 1296, 'image': None, 'image_isoclass': '72.30', 'image_order': 72, 'indicator': 0, 'kernel': '72.i1.b1', 'kernel_order': 18, 'label': '1296.3190.2ah1', 'nt': [12, 42], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, -1]], [[2, 1]], [[2, -1]], [[2, 0]], [[-1, 1]], [[2, 1]], [[-1, -1]], [[2, -1]], [[2, 1]], [[2, 0]], [[-1, 0]], [[-1, 1]], [[2, 1]], [[2, -1]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[-1, 0]], [[2, 0]], [[-1, -1]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[0, 0]], [[0, 0]], [[-2, 1]], [[-2, -1]], [[-2, 1]], [[-2, -1]], [[-2, -1]], [[1, -1]], [[1, 0]], [[1, 1]], [[-2, 0]], [[-2, 1]], [[-2, 0]], [[-2, -1]], [[2, -1]], [[2, 1]], [[-2, 1]], [[1, 0]], [[-2, 1]], [[1, 1]], [[1, -1]], [[1, 0]], [[-2, -1]], [[1, -1]], [[-2, 0]], [[1, 1]], [[-1, 0], [-2, 1]], [[-2, 0]], [[2, 0]], [[-2, -1]], [[1, 0], [2, 1]], [[-1, 0]], [[2, 0], [1, 1]], [[1, 1]], [[2, 1]], [[2, -1]], [[1, -1]], [[-2, 0], [-1, 1]], [[0, 0]], [[0, 0]], [[-1, -1]], [[-1, 1]], [[1, 0], [-1, 1]], [[-2, 1]], [[-1, 0], [1, 1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[-1, 1]], [[1, 0]], [[1, 0], [-1, 1]], [[2, 0], [1, 1]], [[0, 0]], [[-2, 0], [-1, 1]], [[-1, 0]], [[0, 0]], [[-1, 0], [-2, 1]], [[-1, -1]], [[-1, 0], [1, 1]], [[1, 1]], [[1, 0], [2, 1]], [[0, 0]], [[1, -1]], [[0, 0]], [[2, 0], [1, 1]], [[-2, 0], [-1, 1]], [[1, 0], [-1, 1]], [[0, 0]], [[-1, 0], [1, 1]], [[0, 0]], [[-1, 0], [-2, 1]], [[0, 0]], [[1, 0], [2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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: 10647068
    {'center': '12.b1.a1', 'center_index': 12, 'center_order': 108, 'counter': 78, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '1296.3190', 'group_counter': 3190, 'group_order': 1296, 'image': None, 'image_isoclass': '72.30', 'image_order': 72, 'indicator': 0, 'kernel': '72.i1.b1', 'kernel_order': 18, 'label': '1296.3190.2ah2', 'nt': [12, 2], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1]], [[2, -1]], [[2, 1]], [[2, 0]], [[-1, -1]], [[2, -1]], [[-1, 1]], [[2, 1]], [[2, -1]], [[2, 0]], [[-1, 0]], [[-1, -1]], [[2, -1]], [[2, 1]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[-1, 0]], [[2, 0]], [[-1, 1]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[0, 0]], [[0, 0]], [[-2, -1]], [[-2, 1]], [[-2, -1]], [[-2, 1]], [[-2, 1]], [[1, 1]], [[1, 0]], [[1, -1]], [[-2, 0]], [[-2, -1]], [[-2, 0]], [[-2, 1]], [[2, 1]], [[2, -1]], [[-2, -1]], [[1, 0]], [[-2, -1]], [[1, -1]], [[1, 1]], [[1, 0]], [[-2, 1]], [[1, 1]], [[-2, 0]], [[1, -1]], [[1, 0], [2, 1]], [[-2, 0]], [[2, 0]], [[-2, 1]], [[-1, 0], [-2, 1]], [[-1, 0]], [[1, 0], [-1, 1]], [[1, -1]], [[2, -1]], [[2, 1]], [[1, 1]], [[-1, 0], [1, 1]], [[0, 0]], [[0, 0]], [[-1, 1]], [[-1, -1]], [[2, 0], [1, 1]], [[-2, -1]], [[-2, 0], [-1, 1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[-1, -1]], [[1, 0]], [[2, 0], [1, 1]], [[1, 0], [-1, 1]], [[0, 0]], [[-1, 0], [1, 1]], [[-1, 0]], [[0, 0]], [[1, 0], [2, 1]], [[-1, 1]], [[-2, 0], [-1, 1]], [[1, -1]], [[-1, 0], [-2, 1]], [[0, 0]], [[1, 1]], [[0, 0]], [[1, 0], [-1, 1]], [[-1, 0], [1, 1]], [[2, 0], [1, 1]], [[0, 0]], [[-2, 0], [-1, 1]], [[0, 0]], [[1, 0], [2, 1]], [[0, 0]], [[-1, 0], [-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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: 10647069
    {'center': '12.b1.a1', 'center_index': 12, 'center_order': 108, 'counter': 79, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '1296.3190', 'group_counter': 3190, 'group_order': 1296, 'image': None, 'image_isoclass': '72.30', 'image_order': 72, 'indicator': 0, 'kernel': '72.i1.a1', 'kernel_order': 18, 'label': '1296.3190.2ai1', 'nt': [12, 42], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, -1]], [[2, 1]], [[2, -1]], [[2, 0]], [[-1, 1]], [[2, 1]], [[-1, -1]], [[2, -1]], [[2, 1]], [[2, 0]], [[-1, 0]], [[-1, 1]], [[2, 1]], [[2, -1]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[-1, 0]], [[2, 0]], [[-1, -1]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[0, 0]], [[0, 0]], [[-2, 1]], [[-2, -1]], [[-2, 1]], [[-2, -1]], [[-2, -1]], [[1, -1]], [[1, 0]], [[1, 1]], [[-2, 0]], [[-2, 1]], [[-2, 0]], [[2, -1]], [[-2, -1]], [[-2, 1]], [[2, 1]], [[1, 0]], [[-2, 1]], [[1, 1]], [[1, -1]], [[1, 0]], [[-2, -1]], [[1, -1]], [[-2, 0]], [[1, 1]], [[1, 0], [2, 1]], [[2, 0]], [[-2, 0]], [[2, -1]], [[-1, 0], [-2, 1]], [[1, 0]], [[-2, 0], [-1, 1]], [[-1, 1]], [[-2, 1]], [[-2, -1]], [[-1, -1]], [[2, 0], [1, 1]], [[0, 0]], [[0, 0]], [[1, -1]], [[1, 1]], [[-1, 0], [1, 1]], [[2, 1]], [[1, 0], [-1, 1]], [[-1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[-1, 0]], [[-1, 0], [1, 1]], [[-2, 0], [-1, 1]], [[0, 0]], [[2, 0], [1, 1]], [[1, 0]], [[0, 0]], [[1, 0], [2, 1]], [[1, -1]], [[1, 0], [-1, 1]], [[-1, 1]], [[-1, 0], [-2, 1]], [[0, 0]], [[-1, -1]], [[0, 0]], [[2, 0], [1, 1]], [[-2, 0], [-1, 1]], [[1, 0], [-1, 1]], [[0, 0]], [[-1, 0], [1, 1]], [[0, 0]], [[-1, 0], [-2, 1]], [[0, 0]], [[1, 0], [2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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: 10647071
    {'center': '12.b1.a1', 'center_index': 12, 'center_order': 108, 'counter': 80, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '1296.3190', 'group_counter': 3190, 'group_order': 1296, 'image': None, 'image_isoclass': '72.30', 'image_order': 72, 'indicator': 0, 'kernel': '72.i1.a1', 'kernel_order': 18, 'label': '1296.3190.2ai2', 'nt': [12, 2], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1]], [[2, -1]], [[2, 1]], [[2, 0]], [[-1, -1]], [[2, -1]], [[-1, 1]], [[2, 1]], [[2, -1]], [[2, 0]], [[-1, 0]], [[-1, -1]], [[2, -1]], [[2, 1]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[-1, 0]], [[2, 0]], [[-1, 1]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[0, 0]], [[0, 0]], [[-2, -1]], [[-2, 1]], [[-2, -1]], [[-2, 1]], [[-2, 1]], [[1, 1]], [[1, 0]], [[1, -1]], [[-2, 0]], [[-2, -1]], [[-2, 0]], [[2, 1]], [[-2, 1]], [[-2, -1]], [[2, -1]], [[1, 0]], [[-2, -1]], [[1, -1]], [[1, 1]], [[1, 0]], [[-2, 1]], [[1, 1]], [[-2, 0]], [[1, -1]], [[-1, 0], [-2, 1]], [[2, 0]], [[-2, 0]], [[2, 1]], [[1, 0], [2, 1]], [[1, 0]], [[-1, 0], [1, 1]], [[-1, -1]], [[-2, -1]], [[-2, 1]], [[-1, 1]], [[1, 0], [-1, 1]], [[0, 0]], [[0, 0]], [[1, 1]], [[1, -1]], [[-2, 0], [-1, 1]], [[2, -1]], [[2, 0], [1, 1]], [[-1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[-1, 0]], [[-2, 0], [-1, 1]], [[-1, 0], [1, 1]], [[0, 0]], [[1, 0], [-1, 1]], [[1, 0]], [[0, 0]], [[-1, 0], [-2, 1]], [[1, 1]], [[2, 0], [1, 1]], [[-1, -1]], [[1, 0], [2, 1]], [[0, 0]], [[-1, 1]], [[0, 0]], [[1, 0], [-1, 1]], [[-1, 0], [1, 1]], [[2, 0], [1, 1]], [[0, 0]], [[-2, 0], [-1, 1]], [[0, 0]], [[1, 0], [2, 1]], [[0, 0]], [[-1, 0], [-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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: 10647072
    {'center': '12.b1.a1', 'center_index': 12, 'center_order': 108, 'counter': 81, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '1296.3190', 'group_counter': 3190, 'group_order': 1296, 'image': None, 'image_isoclass': '72.30', 'image_order': 72, 'indicator': 0, 'kernel': '72.i1.a1', 'kernel_order': 18, 'label': '1296.3190.2aj1', 'nt': [12, 42], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, -1]], [[2, 1]], [[2, -1]], [[2, 0]], [[-1, 1]], [[2, 1]], [[-1, -1]], [[2, -1]], [[2, 1]], [[2, 0]], [[-1, 0]], [[-1, 1]], [[2, 1]], [[2, -1]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[-1, 0]], [[2, 0]], [[-1, -1]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[0, 0]], [[0, 0]], [[-2, 1]], [[-2, -1]], [[-2, 1]], [[-2, -1]], [[-2, -1]], [[1, -1]], [[1, 0]], [[1, 1]], [[-2, 0]], [[-2, 1]], [[-2, 0]], [[2, -1]], [[-2, -1]], [[-2, 1]], [[2, 1]], [[1, 0]], [[-2, 1]], [[1, 1]], [[1, -1]], [[1, 0]], [[-2, -1]], [[1, -1]], [[-2, 0]], [[1, 1]], [[-1, 0], [-2, 1]], [[2, 0]], [[-2, 0]], [[2, -1]], [[1, 0], [2, 1]], [[1, 0]], [[2, 0], [1, 1]], [[-1, 1]], [[-2, 1]], [[-2, -1]], [[-1, -1]], [[-2, 0], [-1, 1]], [[0, 0]], [[0, 0]], [[1, -1]], [[1, 1]], [[1, 0], [-1, 1]], [[2, 1]], [[-1, 0], [1, 1]], [[-1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[-1, 0]], [[1, 0], [-1, 1]], [[2, 0], [1, 1]], [[0, 0]], [[-2, 0], [-1, 1]], [[1, 0]], [[0, 0]], [[-1, 0], [-2, 1]], [[1, -1]], [[-1, 0], [1, 1]], [[-1, 1]], [[1, 0], [2, 1]], [[0, 0]], [[-1, -1]], [[0, 0]], [[-2, 0], [-1, 1]], [[2, 0], [1, 1]], [[-1, 0], [1, 1]], [[0, 0]], [[1, 0], [-1, 1]], [[0, 0]], [[1, 0], [2, 1]], [[0, 0]], [[-1, 0], [-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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: 10647073
    {'center': '12.b1.a1', 'center_index': 12, 'center_order': 108, 'counter': 82, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '1296.3190', 'group_counter': 3190, 'group_order': 1296, 'image': None, 'image_isoclass': '72.30', 'image_order': 72, 'indicator': 0, 'kernel': '72.i1.a1', 'kernel_order': 18, 'label': '1296.3190.2aj2', 'nt': [12, 2], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1]], [[2, -1]], [[2, 1]], [[2, 0]], [[-1, -1]], [[2, -1]], [[-1, 1]], [[2, 1]], [[2, -1]], [[2, 0]], [[-1, 0]], [[-1, -1]], [[2, -1]], [[2, 1]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[-1, 0]], [[2, 0]], [[-1, 1]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[0, 0]], [[0, 0]], [[-2, -1]], [[-2, 1]], [[-2, -1]], [[-2, 1]], [[-2, 1]], [[1, 1]], [[1, 0]], [[1, -1]], [[-2, 0]], [[-2, -1]], [[-2, 0]], [[2, 1]], [[-2, 1]], [[-2, -1]], [[2, -1]], [[1, 0]], [[-2, -1]], [[1, -1]], [[1, 1]], [[1, 0]], [[-2, 1]], [[1, 1]], [[-2, 0]], [[1, -1]], [[1, 0], [2, 1]], [[2, 0]], [[-2, 0]], [[2, 1]], [[-1, 0], [-2, 1]], [[1, 0]], [[1, 0], [-1, 1]], [[-1, -1]], [[-2, -1]], [[-2, 1]], [[-1, 1]], [[-1, 0], [1, 1]], [[0, 0]], [[0, 0]], [[1, 1]], [[1, -1]], [[2, 0], [1, 1]], [[2, -1]], [[-2, 0], [-1, 1]], [[-1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[-1, 0]], [[2, 0], [1, 1]], [[1, 0], [-1, 1]], [[0, 0]], [[-1, 0], [1, 1]], [[1, 0]], [[0, 0]], [[1, 0], [2, 1]], [[1, 1]], [[-2, 0], [-1, 1]], [[-1, -1]], [[-1, 0], [-2, 1]], [[0, 0]], [[-1, 1]], [[0, 0]], [[-1, 0], [1, 1]], [[1, 0], [-1, 1]], [[-2, 0], [-1, 1]], [[0, 0]], [[2, 0], [1, 1]], [[0, 0]], [[-1, 0], [-2, 1]], [[0, 0]], [[1, 0], [2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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: 10647074
    {'center': '12.a1.a1', 'center_index': 12, 'center_order': 108, 'counter': 83, 'cyclotomic_n': 12, 'dim': 2, 'faithful': False, 'field': [1, 0, 1], 'group': '1296.3190', 'group_counter': 3190, 'group_order': 1296, 'image': None, 'image_isoclass': '72.28', 'image_order': 72, 'indicator': 0, 'kernel': '72.h1.b1', 'kernel_order': 18, 'label': '1296.3190.2ak1', 'nt': [24, 67], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 2]], [[2, 4]], [[1, 2]], [[-1, 0]], [[2, 4]], [[2, 4]], [[-2, 2]], [[-2, 2]], [[-1, 4]], [[2, 0]], [[2, 0]], [[-1, 4]], [[-1, 4]], [[1, 2]], [[-1, 0]], [[1, 2]], [[2, 4]], [[2, 0]], [[-1, 0]], [[-2, 2]], [[-1, 0]], [[-1, 4]], [[1, 2]], [[0, 0]], [[0, 0]], [[-2, 4]], [[2, 2]], [[1, 4]], [[-1, 2]], [[2, 2]], [[2, 2]], [[-2, 0]], [[-2, 4]], [[1, 0]], [[-2, 4]], [[-2, 0]], [[2, 2]], [[-2, 2]], [[2, 4]], [[-2, 4]], [[-2, 0]], [[1, 4]], [[1, 4]], [[-1, 2]], [[1, 0]], [[-1, 2]], [[2, 2]], [[1, 0]], [[-2, 4]], [[0, 0]], [[1, 0]], [[-1, 0]], [[-1, 2]], [[0, 0]], [[2, 0]], [[0, 0]], [[-2, 4]], [[-1, 4]], [[1, 2]], [[2, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 2]], [[2, 4]], [[0, 0]], [[1, 4]], [[0, 0]], [[-2, 0]], [[1, 0]], [[-1, 2]], [[1, 4]], [[-1, 4]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[1, 2]], [[0, 0]], [[1, 4]], [[0, 0]], [[0, 0]], [[-1, 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]], [[-1, 1], [-1, 3]], [[-1, 1], [-1, -1]], [[1, 1], [1, 3]], [[0, 0]], [[0, 0]], [[-1, 1], [2, 3]], [[1, 1], [1, -1]], [[1, 1], [-2, 3]], [[0, 0]], [[-1, 1], [2, 3]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, 3]], [[1, 1], [-2, 3]], [[0, 0]], [[-1, 1], [-1, 3]], [[0, 0]], [[1, 1], [-2, 3]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, 3]], [[-1, 1], [2, 3]], [[-1, 1], [-1, 3]], [[0, 0]], [[0, 0]]]}
  • id: 10647075
    {'center': '12.a1.a1', 'center_index': 12, 'center_order': 108, 'counter': 84, 'cyclotomic_n': 12, 'dim': 2, 'faithful': False, 'field': [1, 0, 1], 'group': '1296.3190', 'group_counter': 3190, 'group_order': 1296, 'image': None, 'image_isoclass': '72.28', 'image_order': 72, 'indicator': 0, 'kernel': '72.h1.b1', 'kernel_order': 18, 'label': '1296.3190.2ak2', 'nt': [24, 4], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 4]], [[-2, 2]], [[-1, 4]], [[-1, 0]], [[-2, 2]], [[-2, 2]], [[2, 4]], [[2, 4]], [[1, 2]], [[2, 0]], [[2, 0]], [[1, 2]], [[1, 2]], [[-1, 4]], [[-1, 0]], [[-1, 4]], [[-2, 2]], [[2, 0]], [[-1, 0]], [[2, 4]], [[-1, 0]], [[1, 2]], [[-1, 4]], [[0, 0]], [[0, 0]], [[2, 2]], [[-2, 4]], [[-1, 2]], [[1, 4]], [[-2, 4]], [[-2, 4]], [[-2, 0]], [[2, 2]], [[1, 0]], [[2, 2]], [[-2, 0]], [[-2, 4]], [[2, 4]], [[-2, 2]], [[2, 2]], [[-2, 0]], [[-1, 2]], [[-1, 2]], [[1, 4]], [[1, 0]], [[1, 4]], [[-2, 4]], [[1, 0]], [[2, 2]], [[0, 0]], [[1, 0]], [[-1, 0]], [[1, 4]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 2]], [[1, 2]], [[-1, 4]], [[-2, 4]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 4]], [[-2, 2]], [[0, 0]], [[-1, 2]], [[0, 0]], [[-2, 0]], [[1, 0]], [[1, 4]], [[-1, 2]], [[1, 2]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-1, 4]], [[0, 0]], [[-1, 2]], [[0, 0]], [[0, 0]], [[1, 4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1], [2, 3]], [[-1, 1], [-1, -1]], [[1, 1], [-2, 3]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, 3]], [[1, 1], [1, -1]], [[1, 1], [1, 3]], [[0, 0]], [[-1, 1], [-1, 3]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[1, 1], [-2, 3]], [[1, 1], [1, 3]], [[0, 0]], [[-1, 1], [2, 3]], [[0, 0]], [[1, 1], [1, 3]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[1, 1], [-2, 3]], [[-1, 1], [-1, 3]], [[-1, 1], [2, 3]], [[0, 0]], [[0, 0]]]}
  • id: 10647076
    {'center': '12.a1.a1', 'center_index': 12, 'center_order': 108, 'counter': 85, 'cyclotomic_n': 12, 'dim': 2, 'faithful': False, 'field': [1, 0, 1], 'group': '1296.3190', 'group_counter': 3190, 'group_order': 1296, 'image': None, 'image_isoclass': '72.28', 'image_order': 72, 'indicator': 0, 'kernel': '72.h1.b1', 'kernel_order': 18, 'label': '1296.3190.2ak3', 'nt': [24, 67], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 2]], [[2, 4]], [[1, 2]], [[-1, 0]], [[2, 4]], [[2, 4]], [[-2, 2]], [[-2, 2]], [[-1, 4]], [[2, 0]], [[2, 0]], [[-1, 4]], [[-1, 4]], [[1, 2]], [[-1, 0]], [[1, 2]], [[2, 4]], [[2, 0]], [[-1, 0]], [[-2, 2]], [[-1, 0]], [[-1, 4]], [[1, 2]], [[0, 0]], [[0, 0]], [[-2, 4]], [[2, 2]], [[1, 4]], [[-1, 2]], [[2, 2]], [[2, 2]], [[-2, 0]], [[-2, 4]], [[1, 0]], [[-2, 4]], [[-2, 0]], [[2, 2]], [[-2, 2]], [[2, 4]], [[-2, 4]], [[-2, 0]], [[1, 4]], [[1, 4]], [[-1, 2]], [[1, 0]], [[-1, 2]], [[2, 2]], [[1, 0]], [[-2, 4]], [[0, 0]], [[1, 0]], [[-1, 0]], [[-1, 2]], [[0, 0]], [[2, 0]], [[0, 0]], [[-2, 4]], [[-1, 4]], [[1, 2]], [[2, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 2]], [[2, 4]], [[0, 0]], [[1, 4]], [[0, 0]], [[-2, 0]], [[1, 0]], [[-1, 2]], [[1, 4]], [[-1, 4]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[1, 2]], [[0, 0]], [[1, 4]], [[0, 0]], [[0, 0]], [[-1, 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]], [[1, 1], [1, 3]], [[1, 1], [1, -1]], [[-1, 1], [-1, 3]], [[0, 0]], [[0, 0]], [[1, 1], [-2, 3]], [[-1, 1], [-1, -1]], [[-1, 1], [2, 3]], [[0, 0]], [[1, 1], [-2, 3]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, 3]], [[-1, 1], [2, 3]], [[0, 0]], [[1, 1], [1, 3]], [[0, 0]], [[-1, 1], [2, 3]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, 3]], [[1, 1], [-2, 3]], [[1, 1], [1, 3]], [[0, 0]], [[0, 0]]]}
  • id: 10647077
    {'center': '12.a1.a1', 'center_index': 12, 'center_order': 108, 'counter': 86, 'cyclotomic_n': 12, 'dim': 2, 'faithful': False, 'field': [1, 0, 1], 'group': '1296.3190', 'group_counter': 3190, 'group_order': 1296, 'image': None, 'image_isoclass': '72.28', 'image_order': 72, 'indicator': 0, 'kernel': '72.h1.b1', 'kernel_order': 18, 'label': '1296.3190.2ak4', 'nt': [24, 4], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 4]], [[-2, 2]], [[-1, 4]], [[-1, 0]], [[-2, 2]], [[-2, 2]], [[2, 4]], [[2, 4]], [[1, 2]], [[2, 0]], [[2, 0]], [[1, 2]], [[1, 2]], [[-1, 4]], [[-1, 0]], [[-1, 4]], [[-2, 2]], [[2, 0]], [[-1, 0]], [[2, 4]], [[-1, 0]], [[1, 2]], [[-1, 4]], [[0, 0]], [[0, 0]], [[2, 2]], [[-2, 4]], [[-1, 2]], [[1, 4]], [[-2, 4]], [[-2, 4]], [[-2, 0]], [[2, 2]], [[1, 0]], [[2, 2]], [[-2, 0]], [[-2, 4]], [[2, 4]], [[-2, 2]], [[2, 2]], [[-2, 0]], [[-1, 2]], [[-1, 2]], [[1, 4]], [[1, 0]], [[1, 4]], [[-2, 4]], [[1, 0]], [[2, 2]], [[0, 0]], [[1, 0]], [[-1, 0]], [[1, 4]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 2]], [[1, 2]], [[-1, 4]], [[-2, 4]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 4]], [[-2, 2]], [[0, 0]], [[-1, 2]], [[0, 0]], [[-2, 0]], [[1, 0]], [[1, 4]], [[-1, 2]], [[1, 2]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-1, 4]], [[0, 0]], [[-1, 2]], [[0, 0]], [[0, 0]], [[1, 4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [-2, 3]], [[1, 1], [1, -1]], [[-1, 1], [2, 3]], [[0, 0]], [[0, 0]], [[1, 1], [1, 3]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, 3]], [[0, 0]], [[1, 1], [1, 3]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[-1, 1], [2, 3]], [[-1, 1], [-1, 3]], [[0, 0]], [[1, 1], [-2, 3]], [[0, 0]], [[-1, 1], [-1, 3]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[-1, 1], [2, 3]], [[1, 1], [1, 3]], [[1, 1], [-2, 3]], [[0, 0]], [[0, 0]]]}
  • id: 10647078
    {'center': '12.a1.a1', 'center_index': 12, 'center_order': 108, 'counter': 87, 'cyclotomic_n': 12, 'dim': 2, 'faithful': False, 'field': [1, 0, 1], 'group': '1296.3190', 'group_counter': 3190, 'group_order': 1296, 'image': None, 'image_isoclass': '72.28', 'image_order': 72, 'indicator': 0, 'kernel': '72.h1.a1', 'kernel_order': 18, 'label': '1296.3190.2al1', 'nt': [24, 67], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 2]], [[2, 4]], [[1, 2]], [[-1, 0]], [[2, 4]], [[2, 4]], [[-2, 2]], [[-2, 2]], [[-1, 4]], [[2, 0]], [[2, 0]], [[-1, 4]], [[-1, 4]], [[1, 2]], [[-1, 0]], [[1, 2]], [[2, 4]], [[2, 0]], [[-1, 0]], [[-2, 2]], [[-1, 0]], [[-1, 4]], [[1, 2]], [[0, 0]], [[0, 0]], [[-2, 4]], [[2, 2]], [[1, 4]], [[-1, 2]], [[2, 2]], [[2, 2]], [[-2, 0]], [[-2, 4]], [[1, 0]], [[-2, 4]], [[-2, 0]], [[-2, 2]], [[2, 2]], [[-2, 4]], [[2, 4]], [[-2, 0]], [[1, 4]], [[1, 4]], [[-1, 2]], [[1, 0]], [[-1, 2]], [[2, 2]], [[1, 0]], [[-2, 4]], [[0, 0]], [[-1, 0]], [[1, 0]], [[1, 2]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, 4]], [[1, 4]], [[-1, 2]], [[-2, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 2]], [[-2, 4]], [[0, 0]], [[-1, 4]], [[0, 0]], [[2, 0]], [[1, 0]], [[-1, 2]], [[1, 4]], [[1, 4]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-1, 2]], [[0, 0]], [[-1, 4]], [[0, 0]], [[0, 0]], [[1, 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]], [[-1, 1], [-1, 3]], [[-1, 1], [-1, -1]], [[1, 1], [1, 3]], [[0, 0]], [[0, 0]], [[-1, 1], [2, 3]], [[1, 1], [1, -1]], [[1, 1], [-2, 3]], [[0, 0]], [[-1, 1], [2, 3]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, 3]], [[1, 1], [-2, 3]], [[0, 0]], [[-1, 1], [-1, 3]], [[0, 0]], [[-1, 1], [2, 3]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, 3]], [[1, 1], [-2, 3]], [[1, 1], [1, 3]], [[0, 0]], [[0, 0]]]}
  • id: 10647079
    {'center': '12.a1.a1', 'center_index': 12, 'center_order': 108, 'counter': 88, 'cyclotomic_n': 12, 'dim': 2, 'faithful': False, 'field': [1, 0, 1], 'group': '1296.3190', 'group_counter': 3190, 'group_order': 1296, 'image': None, 'image_isoclass': '72.28', 'image_order': 72, 'indicator': 0, 'kernel': '72.h1.a1', 'kernel_order': 18, 'label': '1296.3190.2al2', 'nt': [24, 4], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 4]], [[-2, 2]], [[-1, 4]], [[-1, 0]], [[-2, 2]], [[-2, 2]], [[2, 4]], [[2, 4]], [[1, 2]], [[2, 0]], [[2, 0]], [[1, 2]], [[1, 2]], [[-1, 4]], [[-1, 0]], [[-1, 4]], [[-2, 2]], [[2, 0]], [[-1, 0]], [[2, 4]], [[-1, 0]], [[1, 2]], [[-1, 4]], [[0, 0]], [[0, 0]], [[2, 2]], [[-2, 4]], [[-1, 2]], [[1, 4]], [[-2, 4]], [[-2, 4]], [[-2, 0]], [[2, 2]], [[1, 0]], [[2, 2]], [[-2, 0]], [[2, 4]], [[-2, 4]], [[2, 2]], [[-2, 2]], [[-2, 0]], [[-1, 2]], [[-1, 2]], [[1, 4]], [[1, 0]], [[1, 4]], [[-2, 4]], [[1, 0]], [[2, 2]], [[0, 0]], [[-1, 0]], [[1, 0]], [[-1, 4]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-2, 2]], [[-1, 2]], [[1, 4]], [[2, 4]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 4]], [[2, 2]], [[0, 0]], [[1, 2]], [[0, 0]], [[2, 0]], [[1, 0]], [[1, 4]], [[-1, 2]], [[-1, 2]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[1, 4]], [[0, 0]], [[1, 2]], [[0, 0]], [[0, 0]], [[-1, 4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1], [2, 3]], [[-1, 1], [-1, -1]], [[1, 1], [-2, 3]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, 3]], [[1, 1], [1, -1]], [[1, 1], [1, 3]], [[0, 0]], [[-1, 1], [-1, 3]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[1, 1], [-2, 3]], [[1, 1], [1, 3]], [[0, 0]], [[-1, 1], [2, 3]], [[0, 0]], [[-1, 1], [-1, 3]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[-1, 1], [2, 3]], [[1, 1], [1, 3]], [[1, 1], [-2, 3]], [[0, 0]], [[0, 0]]]}
  • id: 10647080
    {'center': '12.a1.a1', 'center_index': 12, 'center_order': 108, 'counter': 89, 'cyclotomic_n': 12, 'dim': 2, 'faithful': False, 'field': [1, 0, 1], 'group': '1296.3190', 'group_counter': 3190, 'group_order': 1296, 'image': None, 'image_isoclass': '72.28', 'image_order': 72, 'indicator': 0, 'kernel': '72.h1.a1', 'kernel_order': 18, 'label': '1296.3190.2al3', 'nt': [24, 67], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 2]], [[2, 4]], [[1, 2]], [[-1, 0]], [[2, 4]], [[2, 4]], [[-2, 2]], [[-2, 2]], [[-1, 4]], [[2, 0]], [[2, 0]], [[-1, 4]], [[-1, 4]], [[1, 2]], [[-1, 0]], [[1, 2]], [[2, 4]], [[2, 0]], [[-1, 0]], [[-2, 2]], [[-1, 0]], [[-1, 4]], [[1, 2]], [[0, 0]], [[0, 0]], [[-2, 4]], [[2, 2]], [[1, 4]], [[-1, 2]], [[2, 2]], [[2, 2]], [[-2, 0]], [[-2, 4]], [[1, 0]], [[-2, 4]], [[-2, 0]], [[-2, 2]], [[2, 2]], [[-2, 4]], [[2, 4]], [[-2, 0]], [[1, 4]], [[1, 4]], [[-1, 2]], [[1, 0]], [[-1, 2]], [[2, 2]], [[1, 0]], [[-2, 4]], [[0, 0]], [[-1, 0]], [[1, 0]], [[1, 2]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, 4]], [[1, 4]], [[-1, 2]], [[-2, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 2]], [[-2, 4]], [[0, 0]], [[-1, 4]], [[0, 0]], [[2, 0]], [[1, 0]], [[-1, 2]], [[1, 4]], [[1, 4]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-1, 2]], [[0, 0]], [[-1, 4]], [[0, 0]], [[0, 0]], [[1, 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]], [[1, 1], [1, 3]], [[1, 1], [1, -1]], [[-1, 1], [-1, 3]], [[0, 0]], [[0, 0]], [[1, 1], [-2, 3]], [[-1, 1], [-1, -1]], [[-1, 1], [2, 3]], [[0, 0]], [[1, 1], [-2, 3]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, 3]], [[-1, 1], [2, 3]], [[0, 0]], [[1, 1], [1, 3]], [[0, 0]], [[1, 1], [-2, 3]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, 3]], [[-1, 1], [2, 3]], [[-1, 1], [-1, 3]], [[0, 0]], [[0, 0]]]}
  • id: 10647082
    {'center': '12.a1.a1', 'center_index': 12, 'center_order': 108, 'counter': 90, 'cyclotomic_n': 12, 'dim': 2, 'faithful': False, 'field': [1, 0, 1], 'group': '1296.3190', 'group_counter': 3190, 'group_order': 1296, 'image': None, 'image_isoclass': '72.28', 'image_order': 72, 'indicator': 0, 'kernel': '72.h1.a1', 'kernel_order': 18, 'label': '1296.3190.2al4', 'nt': [24, 4], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 4]], [[-2, 2]], [[-1, 4]], [[-1, 0]], [[-2, 2]], [[-2, 2]], [[2, 4]], [[2, 4]], [[1, 2]], [[2, 0]], [[2, 0]], [[1, 2]], [[1, 2]], [[-1, 4]], [[-1, 0]], [[-1, 4]], [[-2, 2]], [[2, 0]], [[-1, 0]], [[2, 4]], [[-1, 0]], [[1, 2]], [[-1, 4]], [[0, 0]], [[0, 0]], [[2, 2]], [[-2, 4]], [[-1, 2]], [[1, 4]], [[-2, 4]], [[-2, 4]], [[-2, 0]], [[2, 2]], [[1, 0]], [[2, 2]], [[-2, 0]], [[2, 4]], [[-2, 4]], [[2, 2]], [[-2, 2]], [[-2, 0]], [[-1, 2]], [[-1, 2]], [[1, 4]], [[1, 0]], [[1, 4]], [[-2, 4]], [[1, 0]], [[2, 2]], [[0, 0]], [[-1, 0]], [[1, 0]], [[-1, 4]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-2, 2]], [[-1, 2]], [[1, 4]], [[2, 4]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 4]], [[2, 2]], [[0, 0]], [[1, 2]], [[0, 0]], [[2, 0]], [[1, 0]], [[1, 4]], [[-1, 2]], [[-1, 2]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[1, 4]], [[0, 0]], [[1, 2]], [[0, 0]], [[0, 0]], [[-1, 4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [-2, 3]], [[1, 1], [1, -1]], [[-1, 1], [2, 3]], [[0, 0]], [[0, 0]], [[1, 1], [1, 3]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, 3]], [[0, 0]], [[1, 1], [1, 3]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[-1, 1], [2, 3]], [[-1, 1], [-1, 3]], [[0, 0]], [[1, 1], [-2, 3]], [[0, 0]], [[1, 1], [1, 3]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[1, 1], [-2, 3]], [[-1, 1], [-1, 3]], [[-1, 1], [2, 3]], [[0, 0]], [[0, 0]]]}
  • id: 10647011
    {'center': '6.d1.a1', 'center_index': 6, 'center_order': 216, 'counter': 26, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '1296.3190', 'group_counter': 3190, 'group_order': 1296, 'image': None, 'image_isoclass': '6.1', 'image_order': 6, 'indicator': 1, 'kernel': '6.d1.a1', 'kernel_order': 216, 'label': '1296.3190.2b', 'nt': [3, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]]]}
  • id: 10647012
    {'center': '6.a1.a1', 'center_index': 6, 'center_order': 216, 'counter': 27, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '1296.3190', 'group_counter': 3190, 'group_order': 1296, 'image': None, 'image_isoclass': '6.1', 'image_order': 6, 'indicator': 1, 'kernel': '6.a1.a1', 'kernel_order': 216, 'label': '1296.3190.2c', 'nt': [3, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 10647013
    {'center': '4.a1.a1', 'center_index': 4, 'center_order': 324, 'counter': 28, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '1296.3190', 'group_counter': 3190, 'group_order': 1296, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.b1.b1', 'kernel_order': 162, 'label': '1296.3190.2d', 'nt': [4, 3], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[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]], [[-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]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 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]], [[0, 0]], [[0, 0]], [[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: 10647014
    {'center': '4.a1.a1', 'center_index': 4, 'center_order': 324, 'counter': 29, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '1296.3190', 'group_counter': 3190, 'group_order': 1296, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.b1.a1', 'kernel_order': 162, 'label': '1296.3190.2e', 'nt': [4, 3], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[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]], [[-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]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 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]], [[0, 0]], [[0, 0]], [[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: 10647016
    {'center': '6.a1.a1', 'center_index': 6, 'center_order': 216, 'counter': 30, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '1296.3190', 'group_counter': 3190, 'group_order': 1296, 'image': None, 'image_isoclass': '12.4', 'image_order': 12, 'indicator': 1, 'kernel': '12.g1.a1', 'kernel_order': 108, 'label': '1296.3190.2f', 'nt': [6, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 10647017
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  • id: 10647018
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  • id: 10647019
    {'center': '6.a1.a1', 'center_index': 6, 'center_order': 216, 'counter': 33, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '1296.3190', 'group_counter': 3190, 'group_order': 1296, 'image': None, 'image_isoclass': '12.4', 'image_order': 12, 'indicator': 1, 'kernel': '12.e1.a1', 'kernel_order': 108, 'label': '1296.3190.2i', 'nt': [6, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-2, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[1, 0]], [[2, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[2, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 10647020
    {'center': '6.f1.a1', 'center_index': 6, 'center_order': 216, 'counter': 34, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '1296.3190', 'group_counter': 3190, 'group_order': 1296, 'image': None, 'image_isoclass': '12.4', 'image_order': 12, 'indicator': 1, 'kernel': '12.l1.a1', 'kernel_order': 108, 'label': '1296.3190.2j', 'nt': [6, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 10647021
    {'center': '6.f1.a1', 'center_index': 6, 'center_order': 216, 'counter': 35, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '1296.3190', 'group_counter': 3190, 'group_order': 1296, 'image': None, 'image_isoclass': '12.4', 'image_order': 12, 'indicator': 1, 'kernel': '12.i1.a1', 'kernel_order': 108, 'label': '1296.3190.2k', 'nt': [6, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 10647022
    {'center': '6.f1.a1', 'center_index': 6, 'center_order': 216, 'counter': 36, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '1296.3190', 'group_counter': 3190, 'group_order': 1296, 'image': None, 'image_isoclass': '12.4', 'image_order': 12, 'indicator': 1, 'kernel': '12.d1.a1', 'kernel_order': 108, 'label': '1296.3190.2l', 'nt': [6, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 10647023
    {'center': '6.a1.a1', 'center_index': 6, 'center_order': 216, 'counter': 37, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '1296.3190', 'group_counter': 3190, 'group_order': 1296, 'image': None, 'image_isoclass': '12.4', 'image_order': 12, 'indicator': 1, 'kernel': '12.b1.a1', 'kernel_order': 108, 'label': '1296.3190.2m', 'nt': [6, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[2, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[-1, 0]], [[-2, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-2, 0]], [[-1, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 10647024
    {'center': '6.d1.a1', 'center_index': 6, 'center_order': 216, 'counter': 38, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '1296.3190', 'group_counter': 3190, 'group_order': 1296, 'image': None, 'image_isoclass': '12.4', 'image_order': 12, 'indicator': 1, 'kernel': '12.a1.a1', 'kernel_order': 108, 'label': '1296.3190.2n', 'nt': [6, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]]]}
  • id: 10647025
    {'center': '6.f1.a1', 'center_index': 6, 'center_order': 216, 'counter': 39, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '1296.3190', 'group_counter': 3190, 'group_order': 1296, 'image': None, 'image_isoclass': '18.3', 'image_order': 18, 'indicator': 0, 'kernel': '18.c1.a1', 'kernel_order': 72, 'label': '1296.3190.2o1', 'nt': [6, 5], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, -1]], [[2, 1]], [[2, -1]], [[2, 0]], [[2, 1]], [[-1, 1]], [[2, -1]], [[-1, -1]], [[2, 1]], [[-1, 0]], [[2, 0]], [[2, 1]], [[-1, 1]], [[-1, -1]], [[2, 0]], [[2, -1]], [[-1, 1]], [[-1, 0]], [[-1, 0]], [[-1, -1]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[2, 0]], [[0, 0]], [[2, 1]], [[2, -1]], [[2, 1]], [[2, -1]], [[-1, -1]], [[2, -1]], [[2, 0]], [[2, 1]], [[2, 0]], [[-1, 1]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 1]], [[2, 1]], [[2, -1]], [[2, 0]], [[-1, -1]], [[-1, -1]], [[-1, 0]], [[-1, 1]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1]], [[2, -1]], [[2, 1]], [[0, 0]], [[0, 0]], [[2, -1]], [[0, 0]], [[2, -1]], [[0, 0]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[0, 0]], [[0, 0]], [[-1, -1]], [[-1, 1]], [[-1, 0]], [[-1, 1]], [[0, 0]], [[-1, -1]], [[-1, 0]], [[0, 0]], [[-1, -1]], [[0, 0]], [[-1, 0]], [[-1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1]], [[0, 0]], [[2, -1]], [[0, 0]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[0, 0]], [[0, 0]], [[2, -1]], [[2, 0]], [[2, -1]], [[2, 1]], [[2, -1]], [[2, 1]], [[2, 0]], [[2, 1]], [[-1, 0]], [[-1, 1]], [[-1, 0]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 10647027
    {'center': '6.f1.a1', 'center_index': 6, 'center_order': 216, 'counter': 40, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '1296.3190', 'group_counter': 3190, 'group_order': 1296, 'image': None, 'image_isoclass': '18.3', 'image_order': 18, 'indicator': 0, 'kernel': '18.c1.a1', 'kernel_order': 72, 'label': '1296.3190.2o2', 'nt': [6, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 1]], [[2, -1]], [[2, 1]], [[2, 0]], [[2, -1]], [[-1, -1]], [[2, 1]], [[-1, 1]], [[2, -1]], [[-1, 0]], [[2, 0]], [[2, -1]], [[-1, -1]], [[-1, 1]], [[2, 0]], [[2, 1]], [[-1, -1]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[2, 0]], [[0, 0]], [[2, -1]], [[2, 1]], [[2, -1]], [[2, 1]], [[-1, 1]], [[2, 1]], [[2, 0]], [[2, -1]], [[2, 0]], [[-1, -1]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, -1]], [[2, -1]], [[2, 1]], [[2, 0]], [[-1, 1]], [[-1, 1]], [[-1, 0]], [[-1, -1]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, -1]], [[2, 1]], [[2, -1]], [[0, 0]], [[0, 0]], [[2, 1]], [[0, 0]], [[2, 1]], [[0, 0]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[0, 0]], [[0, 0]], [[-1, 1]], [[-1, -1]], [[-1, 0]], [[-1, -1]], [[0, 0]], [[-1, 1]], [[-1, 0]], [[0, 0]], [[-1, 1]], [[0, 0]], [[-1, 0]], [[-1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, -1]], [[0, 0]], [[2, 1]], [[0, 0]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[0, 0]], [[0, 0]], [[2, 1]], [[2, 0]], [[2, 1]], [[2, -1]], [[2, 1]], [[2, -1]], [[2, 0]], [[2, -1]], [[-1, 0]], [[-1, -1]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 10647028
    {'center': '6.d1.a1', 'center_index': 6, 'center_order': 216, 'counter': 41, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '1296.3190', 'group_counter': 3190, 'group_order': 1296, 'image': None, 'image_isoclass': '18.3', 'image_order': 18, 'indicator': 0, 'kernel': '18.b1.a1', 'kernel_order': 72, 'label': '1296.3190.2p1', 'nt': [6, 5], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, -1]], [[2, 1]], [[-1, -1]], [[-1, 0]], [[2, 1]], [[2, 1]], [[2, -1]], [[2, -1]], [[-1, 1]], [[2, 0]], [[2, 0]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, 0]], [[-1, -1]], [[2, 1]], [[2, 0]], [[-1, 0]], [[2, -1]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[2, 0]], [[2, 0]], [[2, 1]], [[2, -1]], [[-1, 1]], [[-1, -1]], [[2, -1]], [[2, -1]], [[2, 0]], [[2, 1]], [[-1, 0]], [[2, 1]], [[2, 0]], [[2, -1]], [[2, -1]], [[2, 1]], [[2, 1]], [[2, 0]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, 0]], [[-1, -1]], [[2, -1]], [[-1, 0]], [[2, 1]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, -1]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 1]], [[-1, 1]], [[-1, -1]], [[2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, -1]], [[2, 1]], [[0, 0]], [[-1, 1]], [[0, 0]], [[2, 0]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-1, -1]], [[0, 0]], [[-1, 1]], [[0, 0]], [[0, 0]], [[-1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, -1]], [[-1, 0]], [[-1, -1]], [[2, 1]], [[2, -1]], [[-1, 1]], [[-1, 0]], [[-1, 1]], [[2, 0]], [[-1, 1]], [[-1, 0]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[2, -1]], [[-1, -1]], [[2, 1]], [[-1, 1]], [[-1, 0]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[2, -1]], [[2, 1]]]}
  • id: 10647029
    {'center': '6.d1.a1', 'center_index': 6, 'center_order': 216, 'counter': 42, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '1296.3190', 'group_counter': 3190, 'group_order': 1296, 'image': None, 'image_isoclass': '18.3', 'image_order': 18, 'indicator': 0, 'kernel': '18.b1.a1', 'kernel_order': 72, 'label': '1296.3190.2p2', 'nt': [6, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1]], [[2, -1]], [[-1, 1]], [[-1, 0]], [[2, -1]], [[2, -1]], [[2, 1]], [[2, 1]], [[-1, -1]], [[2, 0]], [[2, 0]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, 0]], [[-1, 1]], [[2, -1]], [[2, 0]], [[-1, 0]], [[2, 1]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[2, 0]], [[2, 0]], [[2, -1]], [[2, 1]], [[-1, -1]], [[-1, 1]], [[2, 1]], [[2, 1]], [[2, 0]], [[2, -1]], [[-1, 0]], [[2, -1]], [[2, 0]], [[2, 1]], [[2, 1]], [[2, -1]], [[2, -1]], [[2, 0]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, 0]], [[-1, 1]], [[2, 1]], [[-1, 0]], [[2, -1]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, -1]], [[-1, -1]], [[-1, 1]], [[2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1]], [[2, -1]], [[0, 0]], [[-1, -1]], [[0, 0]], [[2, 0]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-1, 1]], [[0, 0]], [[-1, -1]], [[0, 0]], [[0, 0]], [[-1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1]], [[-1, 0]], [[-1, 1]], [[2, -1]], [[2, 1]], [[-1, -1]], [[-1, 0]], [[-1, -1]], [[2, 0]], [[-1, -1]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[2, 1]], [[-1, 1]], [[2, -1]], [[-1, -1]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[2, 1]], [[2, -1]]]}
  • id: 10647030
    {'center': '6.a1.a1', 'center_index': 6, 'center_order': 216, 'counter': 43, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '1296.3190', 'group_counter': 3190, 'group_order': 1296, 'image': None, 'image_isoclass': '18.3', 'image_order': 18, 'indicator': 0, 'kernel': '18.a1.a1', 'kernel_order': 72, 'label': '1296.3190.2q1', 'nt': [6, 5], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, -1]], [[2, 1]], [[2, -1]], [[2, 0]], [[-1, 1]], [[2, 1]], [[-1, -1]], [[2, -1]], [[2, 1]], [[2, 0]], [[-1, 0]], [[-1, 1]], [[2, 1]], [[2, -1]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[-1, 0]], [[2, 0]], [[-1, -1]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[0, 0]], [[0, 0]], [[2, 1]], [[2, -1]], [[2, 1]], [[2, -1]], [[2, -1]], [[-1, -1]], [[-1, 0]], [[-1, 1]], [[2, 0]], [[2, 1]], [[2, 0]], [[2, -1]], [[2, -1]], [[2, 1]], [[2, 1]], [[-1, 0]], [[2, 1]], [[-1, 1]], [[-1, -1]], [[-1, 0]], [[2, -1]], [[-1, -1]], [[2, 0]], [[-1, 1]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, -1]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[-1, 1]], [[2, 1]], [[2, -1]], [[-1, -1]], [[-1, 1]], [[2, -1]], [[2, 1]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[2, 1]], [[-1, -1]], [[-1, 0]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[2, 0]], [[-1, 1]], [[-1, 0]], [[2, -1]], [[-1, 0]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, 0]], [[2, 1]], [[-1, -1]], [[2, 1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[2, -1]], [[-1, -1]], [[0, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 10647031
    {'center': '6.a1.a1', 'center_index': 6, 'center_order': 216, 'counter': 44, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '1296.3190', 'group_counter': 3190, 'group_order': 1296, 'image': None, 'image_isoclass': '18.3', 'image_order': 18, 'indicator': 0, 'kernel': '18.a1.a1', 'kernel_order': 72, 'label': '1296.3190.2q2', 'nt': [6, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 1]], [[2, -1]], [[2, 1]], [[2, 0]], [[-1, -1]], [[2, -1]], [[-1, 1]], [[2, 1]], [[2, -1]], [[2, 0]], [[-1, 0]], [[-1, -1]], [[2, -1]], [[2, 1]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[-1, 0]], [[2, 0]], [[-1, 1]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[0, 0]], [[0, 0]], [[2, -1]], [[2, 1]], [[2, -1]], [[2, 1]], [[2, 1]], [[-1, 1]], [[-1, 0]], [[-1, -1]], [[2, 0]], [[2, -1]], [[2, 0]], [[2, 1]], [[2, 1]], [[2, -1]], [[2, -1]], [[-1, 0]], [[2, -1]], [[-1, -1]], [[-1, 1]], [[-1, 0]], [[2, 1]], [[-1, 1]], [[2, 0]], [[-1, -1]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 1]], [[-1, 0]], [[-1, 0]], [[-1, -1]], [[-1, -1]], [[2, -1]], [[2, 1]], [[-1, 1]], [[-1, -1]], [[2, 1]], [[2, -1]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[2, -1]], [[-1, 1]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[2, 0]], [[-1, -1]], [[-1, 0]], [[2, 1]], [[-1, 0]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, 0]], [[2, -1]], [[-1, 1]], [[2, -1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[2, 1]], [[-1, 1]], [[0, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 10647032
    {'center': '12.a1.a1', 'center_index': 12, 'center_order': 108, 'counter': 45, 'cyclotomic_n': 12, 'dim': 2, 'faithful': False, 'field': [-3, 0, 1], 'group': '1296.3190', 'group_counter': 3190, 'group_order': 1296, 'image': None, 'image_isoclass': '24.6', 'image_order': 24, 'indicator': 1, 'kernel': '24.e1.b1', 'kernel_order': 54, 'label': '1296.3190.2r1', 'nt': [12, 12], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[-1, 0]], [[-1, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[0, 0]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[0, 0]], [[-1, 1], [-1, -1]], [[0, 0]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[0, 0]], [[0, 0]]]}
  • id: 10647033
    {'center': '12.a1.a1', 'center_index': 12, 'center_order': 108, 'counter': 46, 'cyclotomic_n': 12, 'dim': 2, 'faithful': False, 'field': [-3, 0, 1], 'group': '1296.3190', 'group_counter': 3190, 'group_order': 1296, 'image': None, 'image_isoclass': '24.6', 'image_order': 24, 'indicator': 1, 'kernel': '24.e1.b1', 'kernel_order': 54, 'label': '1296.3190.2r2', 'nt': [12, 12], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[-1, 0]], [[-1, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[0, 0]], [[0, 0]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[0, 0]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[0, 0]], [[1, 1], [1, -1]], [[0, 0]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[0, 0]], [[0, 0]]]}
  • id: 10647034
    {'center': '12.a1.a1', 'center_index': 12, 'center_order': 108, 'counter': 47, 'cyclotomic_n': 12, 'dim': 2, 'faithful': False, 'field': [-3, 0, 1], 'group': '1296.3190', 'group_counter': 3190, 'group_order': 1296, 'image': None, 'image_isoclass': '24.6', 'image_order': 24, 'indicator': 1, 'kernel': '24.e1.a1', 'kernel_order': 54, 'label': '1296.3190.2s1', 'nt': [12, 12], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[1, 0]], [[1, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[0, 0]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[0, 0]], [[-1, 1], [-1, -1]], [[0, 0]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[0, 0]], [[0, 0]]]}
  • id: 10647035
    {'center': '12.a1.a1', 'center_index': 12, 'center_order': 108, 'counter': 48, 'cyclotomic_n': 12, 'dim': 2, 'faithful': False, 'field': [-3, 0, 1], 'group': '1296.3190', 'group_counter': 3190, 'group_order': 1296, 'image': None, 'image_isoclass': '24.6', 'image_order': 24, 'indicator': 1, 'kernel': '24.e1.a1', 'kernel_order': 54, 'label': '1296.3190.2s2', 'nt': [12, 12], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[1, 0]], [[1, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[0, 0]], [[0, 0]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[0, 0]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[0, 0]], [[1, 1], [1, -1]], [[0, 0]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[0, 0]], [[0, 0]]]}
  • id: 10647036
    {'center': '12.b1.a1', 'center_index': 12, 'center_order': 108, 'counter': 49, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '1296.3190', 'group_counter': 3190, 'group_order': 1296, 'image': None, 'image_isoclass': '24.8', 'image_order': 24, 'indicator': 0, 'kernel': '24.f1.b1', 'kernel_order': 54, 'label': '1296.3190.2t1', 'nt': [12, 13], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[-1, 0], [-2, 1]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[1, 0], [2, 1]], [[-1, 0]], [[-1, 0], [-2, 1]], [[1, 0]], [[2, 0]], [[2, 0]], [[1, 0]], [[1, 0], [2, 1]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[1, 0], [2, 1]], [[-2, 0]], [[-1, 0], [-2, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[0, 0]], [[1, 0], [2, 1]], [[-1, 0]], [[0, 0]], [[-1, 0], [-2, 1]], [[-1, 0]], [[-1, 0], [-2, 1]], [[1, 0]], [[1, 0], [2, 1]], [[0, 0]], [[1, 0]], [[0, 0]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[1, 0], [2, 1]], [[0, 0]], [[-1, 0], [-2, 1]], [[0, 0]], [[-1, 0], [-2, 1]], [[0, 0]], [[1, 0], [2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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: 10647038
    {'center': '12.b1.a1', 'center_index': 12, 'center_order': 108, 'counter': 50, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '1296.3190', 'group_counter': 3190, 'group_order': 1296, 'image': None, 'image_isoclass': '24.8', 'image_order': 24, 'indicator': 0, 'kernel': '24.f1.b1', 'kernel_order': 54, 'label': '1296.3190.2t2', 'nt': [12, 2], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[1, 0], [2, 1]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-1, 0], [-2, 1]], [[-1, 0]], [[1, 0], [2, 1]], [[1, 0]], [[2, 0]], [[2, 0]], [[1, 0]], [[-1, 0], [-2, 1]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0], [-2, 1]], [[-2, 0]], [[1, 0], [2, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[0, 0]], [[-1, 0], [-2, 1]], [[-1, 0]], [[0, 0]], [[1, 0], [2, 1]], [[-1, 0]], [[1, 0], [2, 1]], [[1, 0]], [[-1, 0], [-2, 1]], [[0, 0]], [[1, 0]], [[0, 0]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[-1, 0], [-2, 1]], [[0, 0]], [[1, 0], [2, 1]], [[0, 0]], [[1, 0], [2, 1]], [[0, 0]], [[-1, 0], [-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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: 10647039
    {'center': '12.b1.a1', 'center_index': 12, 'center_order': 108, 'counter': 51, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '1296.3190', 'group_counter': 3190, 'group_order': 1296, 'image': None, 'image_isoclass': '24.8', 'image_order': 24, 'indicator': 0, 'kernel': '24.f1.a1', 'kernel_order': 54, 'label': '1296.3190.2u1', 'nt': [12, 13], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[-1, 0], [-2, 1]], [[2, 0]], [[-2, 0]], [[2, 0]], [[1, 0], [2, 1]], [[1, 0]], [[-1, 0], [-2, 1]], [[-1, 0]], [[-2, 0]], [[-2, 0]], [[-1, 0]], [[1, 0], [2, 1]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0], [2, 1]], [[2, 0]], [[-1, 0], [-2, 1]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[0, 0]], [[1, 0], [2, 1]], [[1, 0]], [[0, 0]], [[-1, 0], [-2, 1]], [[1, 0]], [[-1, 0], [-2, 1]], [[-1, 0]], [[1, 0], [2, 1]], [[0, 0]], [[-1, 0]], [[0, 0]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[-1, 0], [-2, 1]], [[0, 0]], [[1, 0], [2, 1]], [[0, 0]], [[1, 0], [2, 1]], [[0, 0]], [[-1, 0], [-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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: 10647040
    {'center': '12.b1.a1', 'center_index': 12, 'center_order': 108, 'counter': 52, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '1296.3190', 'group_counter': 3190, 'group_order': 1296, 'image': None, 'image_isoclass': '24.8', 'image_order': 24, 'indicator': 0, 'kernel': '24.f1.a1', 'kernel_order': 54, 'label': '1296.3190.2u2', 'nt': [12, 2], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[1, 0], [2, 1]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-1, 0], [-2, 1]], [[1, 0]], [[1, 0], [2, 1]], [[-1, 0]], [[-2, 0]], [[-2, 0]], [[-1, 0]], [[-1, 0], [-2, 1]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[-1, 0], [-2, 1]], [[2, 0]], [[1, 0], [2, 1]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[0, 0]], [[-1, 0], [-2, 1]], [[1, 0]], [[0, 0]], [[1, 0], [2, 1]], [[1, 0]], [[1, 0], [2, 1]], [[-1, 0]], [[-1, 0], [-2, 1]], [[0, 0]], [[-1, 0]], [[0, 0]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[1, 0], [2, 1]], [[0, 0]], [[-1, 0], [-2, 1]], [[0, 0]], [[-1, 0], [-2, 1]], [[0, 0]], [[1, 0], [2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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: 10647041
    {'center': '4.a1.a1', 'center_index': 4, 'center_order': 324, 'counter': 53, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '1296.3190', 'group_counter': 3190, 'group_order': 1296, 'image': None, 'image_isoclass': '24.10', 'image_order': 24, 'indicator': 0, 'kernel': '24.g1.b1', 'kernel_order': 54, 'label': '1296.3190.2v1', 'nt': [12, 14], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, -1]], [[2, 1]], [[2, -1]], [[2, 0]], [[2, 1]], [[2, 1]], [[2, -1]], [[2, -1]], [[2, 1]], [[2, 0]], [[2, 0]], [[2, 1]], [[2, 1]], [[2, -1]], [[2, 0]], [[2, -1]], [[2, 1]], [[2, 0]], [[2, 0]], [[2, -1]], [[2, 0]], [[2, 1]], [[2, -1]], [[0, 0]], [[0, 0]], [[-2, 1]], [[-2, -1]], [[-2, 1]], [[-2, -1]], [[-2, -1]], [[-2, -1]], [[-2, 0]], [[-2, 1]], [[-2, 0]], [[-2, 1]], [[-2, 0]], [[-2, -1]], [[2, -1]], [[2, 1]], [[-2, 1]], [[-2, 0]], [[-2, 1]], [[-2, 1]], [[-2, -1]], [[-2, 0]], [[-2, -1]], [[-2, -1]], [[-2, 0]], [[-2, 1]], [[0, 0]], [[-2, 0]], [[2, 0]], [[-2, -1]], [[0, 0]], [[2, 0]], [[0, 0]], [[-2, 1]], [[2, 1]], [[2, -1]], [[-2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, -1]], [[2, 1]], [[0, 0]], [[-2, 1]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, -1]], [[-2, 1]], [[2, 1]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, -1]], [[0, 0]], [[-2, 1]], [[0, 0]], [[0, 0]], [[-2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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: 10647042
    {'center': '4.a1.a1', 'center_index': 4, 'center_order': 324, 'counter': 54, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '1296.3190', 'group_counter': 3190, 'group_order': 1296, 'image': None, 'image_isoclass': '24.10', 'image_order': 24, 'indicator': 0, 'kernel': '24.g1.b1', 'kernel_order': 54, 'label': '1296.3190.2v2', 'nt': [12, 2], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1]], [[2, -1]], [[2, 1]], [[2, 0]], [[2, -1]], [[2, -1]], [[2, 1]], [[2, 1]], [[2, -1]], [[2, 0]], [[2, 0]], [[2, -1]], [[2, -1]], [[2, 1]], [[2, 0]], [[2, 1]], [[2, -1]], [[2, 0]], [[2, 0]], [[2, 1]], [[2, 0]], [[2, -1]], [[2, 1]], [[0, 0]], [[0, 0]], [[-2, -1]], [[-2, 1]], [[-2, -1]], [[-2, 1]], [[-2, 1]], [[-2, 1]], [[-2, 0]], [[-2, -1]], [[-2, 0]], [[-2, -1]], [[-2, 0]], [[-2, 1]], [[2, 1]], [[2, -1]], [[-2, -1]], [[-2, 0]], [[-2, -1]], [[-2, -1]], [[-2, 1]], [[-2, 0]], [[-2, 1]], [[-2, 1]], [[-2, 0]], [[-2, -1]], [[0, 0]], [[-2, 0]], [[2, 0]], [[-2, 1]], [[0, 0]], [[2, 0]], [[0, 0]], [[-2, -1]], [[2, -1]], [[2, 1]], [[-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1]], [[2, -1]], [[0, 0]], [[-2, -1]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 1]], [[-2, -1]], [[2, -1]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 1]], [[0, 0]], [[-2, -1]], [[0, 0]], [[0, 0]], [[-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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: 10647043
    {'center': '4.a1.a1', 'center_index': 4, 'center_order': 324, 'counter': 55, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '1296.3190', 'group_counter': 3190, 'group_order': 1296, 'image': None, 'image_isoclass': '24.10', 'image_order': 24, 'indicator': 0, 'kernel': '24.g1.a1', 'kernel_order': 54, 'label': '1296.3190.2w1', 'nt': [12, 14], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, -1]], [[2, 1]], [[2, -1]], [[2, 0]], [[2, 1]], [[2, 1]], [[2, -1]], [[2, -1]], [[2, 1]], [[2, 0]], [[2, 0]], [[2, 1]], [[2, 1]], [[2, -1]], [[2, 0]], [[2, -1]], [[2, 1]], [[2, 0]], [[2, 0]], [[2, -1]], [[2, 0]], [[2, 1]], [[2, -1]], [[0, 0]], [[0, 0]], [[-2, 1]], [[-2, -1]], [[-2, 1]], [[-2, -1]], [[-2, -1]], [[-2, -1]], [[-2, 0]], [[-2, 1]], [[-2, 0]], [[-2, 1]], [[-2, 0]], [[2, -1]], [[-2, -1]], [[-2, 1]], [[2, 1]], [[-2, 0]], [[-2, 1]], [[-2, 1]], [[-2, -1]], [[-2, 0]], [[-2, -1]], [[-2, -1]], [[-2, 0]], [[-2, 1]], [[0, 0]], [[2, 0]], [[-2, 0]], [[2, -1]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, 1]], [[-2, 1]], [[-2, -1]], [[2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, -1]], [[-2, 1]], [[0, 0]], [[2, 1]], [[0, 0]], [[2, 0]], [[-2, 0]], [[-2, -1]], [[-2, 1]], [[-2, 1]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, -1]], [[0, 0]], [[2, 1]], [[0, 0]], [[0, 0]], [[2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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: 10647044
    {'center': '4.a1.a1', 'center_index': 4, 'center_order': 324, 'counter': 56, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '1296.3190', 'group_counter': 3190, 'group_order': 1296, 'image': None, 'image_isoclass': '24.10', 'image_order': 24, 'indicator': 0, 'kernel': '24.g1.a1', 'kernel_order': 54, 'label': '1296.3190.2w2', 'nt': [12, 2], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1]], [[2, -1]], [[2, 1]], [[2, 0]], [[2, -1]], [[2, -1]], [[2, 1]], [[2, 1]], [[2, -1]], [[2, 0]], [[2, 0]], [[2, -1]], [[2, -1]], [[2, 1]], [[2, 0]], [[2, 1]], [[2, -1]], [[2, 0]], [[2, 0]], [[2, 1]], [[2, 0]], [[2, -1]], [[2, 1]], [[0, 0]], [[0, 0]], [[-2, -1]], [[-2, 1]], [[-2, -1]], [[-2, 1]], [[-2, 1]], [[-2, 1]], [[-2, 0]], [[-2, -1]], [[-2, 0]], [[-2, -1]], [[-2, 0]], [[2, 1]], [[-2, 1]], [[-2, -1]], [[2, -1]], [[-2, 0]], [[-2, -1]], [[-2, -1]], [[-2, 1]], [[-2, 0]], [[-2, 1]], [[-2, 1]], [[-2, 0]], [[-2, -1]], [[0, 0]], [[2, 0]], [[-2, 0]], [[2, 1]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, -1]], [[-2, -1]], [[-2, 1]], [[2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1]], [[-2, -1]], [[0, 0]], [[2, -1]], [[0, 0]], [[2, 0]], [[-2, 0]], [[-2, 1]], [[-2, -1]], [[-2, -1]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 1]], [[0, 0]], [[2, -1]], [[0, 0]], [[0, 0]], [[2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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: 10647045
    {'center': '6.a1.a1', 'center_index': 6, 'center_order': 216, 'counter': 57, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '1296.3190', 'group_counter': 3190, 'group_order': 1296, 'image': None, 'image_isoclass': '36.12', 'image_order': 36, 'indicator': 0, 'kernel': '36.g1.a1', 'kernel_order': 36, 'label': '1296.3190.2x1', 'nt': [12, 18], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, -1]], [[2, 1]], [[2, -1]], [[2, 0]], [[-1, 1]], [[2, 1]], [[-1, -1]], [[2, -1]], [[2, 1]], [[2, 0]], [[-1, 0]], [[-1, 1]], [[2, 1]], [[2, -1]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[-1, 0]], [[2, 0]], [[-1, -1]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[0, 0]], [[0, 0]], [[2, 1]], [[2, -1]], [[2, 1]], [[2, -1]], [[2, -1]], [[-1, -1]], [[-1, 0]], [[-1, 1]], [[2, 0]], [[2, 1]], [[2, 0]], [[-2, -1]], [[-2, -1]], [[-2, 1]], [[-2, 1]], [[-1, 0]], [[2, 1]], [[-1, 1]], [[-1, -1]], [[-1, 0]], [[2, -1]], [[-1, -1]], [[2, 0]], [[-1, 1]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[-2, -1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, 1]], [[-2, 1]], [[-2, -1]], [[1, -1]], [[1, 1]], [[-2, -1]], [[-2, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[-2, 1]], [[1, -1]], [[1, 0]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 1]], [[-2, 0]], [[1, 1]], [[1, 0]], [[-2, -1]], [[1, 0]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 0]], [[-2, 1]], [[1, -1]], [[2, 1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[2, -1]], [[-1, -1]], [[0, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 10647046
    {'center': '6.a1.a1', 'center_index': 6, 'center_order': 216, 'counter': 58, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '1296.3190', 'group_counter': 3190, 'group_order': 1296, 'image': None, 'image_isoclass': '36.12', 'image_order': 36, 'indicator': 0, 'kernel': '36.g1.a1', 'kernel_order': 36, 'label': '1296.3190.2x2', 'nt': [12, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 1]], [[2, -1]], [[2, 1]], [[2, 0]], [[-1, -1]], [[2, -1]], [[-1, 1]], [[2, 1]], [[2, -1]], [[2, 0]], [[-1, 0]], [[-1, -1]], [[2, -1]], [[2, 1]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[-1, 0]], [[2, 0]], [[-1, 1]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[0, 0]], [[0, 0]], [[2, -1]], [[2, 1]], [[2, -1]], [[2, 1]], [[2, 1]], [[-1, 1]], [[-1, 0]], [[-1, -1]], [[2, 0]], [[2, -1]], [[2, 0]], [[-2, 1]], [[-2, 1]], [[-2, -1]], [[-2, -1]], [[-1, 0]], [[2, -1]], [[-1, -1]], [[-1, 1]], [[-1, 0]], [[2, 1]], [[-1, 1]], [[2, 0]], [[-1, -1]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[-2, 1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, -1]], [[-2, -1]], [[-2, 1]], [[1, 1]], [[1, -1]], [[-2, 1]], [[-2, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[-2, -1]], [[1, 1]], [[1, 0]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, -1]], [[-2, 0]], [[1, -1]], [[1, 0]], [[-2, 1]], [[1, 0]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, 0]], [[-2, -1]], [[1, 1]], [[2, -1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[2, 1]], [[-1, 1]], [[0, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 10647047
    {'center': '6.d1.a1', 'center_index': 6, 'center_order': 216, 'counter': 59, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '1296.3190', 'group_counter': 3190, 'group_order': 1296, 'image': None, 'image_isoclass': '36.12', 'image_order': 36, 'indicator': 0, 'kernel': '36.l1.a1', 'kernel_order': 36, 'label': '1296.3190.2y1', 'nt': [12, 18], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, -1]], [[2, 1]], [[-1, -1]], [[-1, 0]], [[2, 1]], [[2, 1]], [[2, -1]], [[2, -1]], [[-1, 1]], [[2, 0]], [[2, 0]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, 0]], [[-1, -1]], [[2, 1]], [[2, 0]], [[-1, 0]], [[2, -1]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[-2, 0]], [[2, 0]], [[2, 1]], [[2, -1]], [[-1, 1]], [[-1, -1]], [[2, -1]], [[2, -1]], [[2, 0]], [[2, 1]], [[-1, 0]], [[2, 1]], [[2, 0]], [[-2, -1]], [[-2, -1]], [[-2, 1]], [[-2, 1]], [[2, 0]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, 0]], [[-1, -1]], [[2, -1]], [[-1, 0]], [[2, 1]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-2, 1]], [[1, 1]], [[1, -1]], [[-2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, -1]], [[-2, 1]], [[0, 0]], [[1, 1]], [[0, 0]], [[-2, 0]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[1, 1]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[1, -1]], [[0, 0]], [[1, 1]], [[0, 0]], [[0, 0]], [[1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, -1]], [[1, 0]], [[1, -1]], [[-2, 1]], [[-2, -1]], [[1, 1]], [[1, 0]], [[1, 1]], [[-2, 0]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[-2, -1]], [[1, -1]], [[-2, 1]], [[-1, 1]], [[-1, 0]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[-1, -1]], [[2, -1]], [[2, 1]]]}
  • id: 10647049
    {'center': '6.d1.a1', 'center_index': 6, 'center_order': 216, 'counter': 60, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '1296.3190', 'group_counter': 3190, 'group_order': 1296, 'image': None, 'image_isoclass': '36.12', 'image_order': 36, 'indicator': 0, 'kernel': '36.l1.a1', 'kernel_order': 36, 'label': '1296.3190.2y2', 'nt': [12, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1]], [[2, -1]], [[-1, 1]], [[-1, 0]], [[2, -1]], [[2, -1]], [[2, 1]], [[2, 1]], [[-1, -1]], [[2, 0]], [[2, 0]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, 0]], [[-1, 1]], [[2, -1]], [[2, 0]], [[-1, 0]], [[2, 1]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[-2, 0]], [[2, 0]], [[2, -1]], [[2, 1]], [[-1, -1]], [[-1, 1]], [[2, 1]], [[2, 1]], [[2, 0]], [[2, -1]], [[-1, 0]], [[2, -1]], [[2, 0]], [[-2, 1]], [[-2, 1]], [[-2, -1]], [[-2, -1]], [[2, 0]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, 0]], [[-1, 1]], [[2, 1]], [[-1, 0]], [[2, -1]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-2, -1]], [[1, -1]], [[1, 1]], [[-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1]], [[-2, -1]], [[0, 0]], [[1, -1]], [[0, 0]], [[-2, 0]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[1, -1]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[1, 1]], [[0, 0]], [[1, -1]], [[0, 0]], [[0, 0]], [[1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1]], [[1, 0]], [[1, 1]], [[-2, -1]], [[-2, 1]], [[1, -1]], [[1, 0]], [[1, -1]], [[-2, 0]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[-2, 1]], [[1, 1]], [[-2, -1]], [[-1, -1]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[-1, 1]], [[2, 1]], [[2, -1]]]}
  • id: 10647050
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  • id: 10647051
    {'center': '6.d1.a1', 'center_index': 6, 'center_order': 216, 'counter': 62, 'cyclotomic_n': 3, 'dim': 2, 'faithful': False, 'field': [1, -1, 1], 'group': '1296.3190', 'group_counter': 3190, 'group_order': 1296, 'image': None, 'image_isoclass': '36.12', 'image_order': 36, 'indicator': 0, 'kernel': '36.k1.a1', 'kernel_order': 36, 'label': '1296.3190.2z2', 'nt': [12, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1]], [[2, -1]], [[-1, 1]], [[-1, 0]], [[2, -1]], [[2, -1]], [[2, 1]], [[2, 1]], [[-1, -1]], [[2, 0]], [[2, 0]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, 0]], [[-1, 1]], [[2, -1]], [[2, 0]], [[-1, 0]], [[2, 1]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[2, 0]], [[-2, 0]], [[2, -1]], [[2, 1]], [[-1, -1]], [[-1, 1]], [[2, 1]], [[2, 1]], [[2, 0]], [[2, -1]], [[-1, 0]], [[2, -1]], [[2, 0]], [[-2, 1]], [[-2, 1]], [[-2, -1]], [[-2, -1]], [[2, 0]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, 0]], [[-1, 1]], [[2, 1]], [[-1, 0]], [[2, -1]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-2, -1]], [[1, -1]], [[1, 1]], [[-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1]], [[-2, -1]], [[0, 0]], [[1, -1]], [[0, 0]], [[-2, 0]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[1, -1]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[1, 1]], [[0, 0]], [[1, -1]], [[0, 0]], [[0, 0]], [[1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1]], [[-1, 0]], [[-1, 1]], [[2, -1]], [[2, 1]], [[-1, -1]], [[-1, 0]], [[-1, -1]], [[2, 0]], [[-1, -1]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[2, 1]], [[-1, 1]], [[2, -1]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[-2, 1]], [[-2, -1]]]}
  • id: 10647083
    {'center': '36.i1.a1', 'center_index': 36, 'center_order': 36, 'counter': 91, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '1296.3190', 'group_counter': 3190, 'group_order': 1296, 'image': None, 'image_isoclass': '36.10', 'image_order': 36, 'indicator': 1, 'kernel': '36.i1.a1', 'kernel_order': 36, 'label': '1296.3190.4a', 'nt': [6, 9], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[4, 0]], [[-2, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[4, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[4, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[1, 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]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[4, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 10647084
    {'center': '36.d1.a1', 'center_index': 36, 'center_order': 36, 'counter': 92, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '1296.3190', 'group_counter': 3190, 'group_order': 1296, 'image': None, 'image_isoclass': '36.10', 'image_order': 36, 'indicator': 1, 'kernel': '36.d1.a1', 'kernel_order': 36, 'label': '1296.3190.4b', 'nt': [6, 9], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[0, 0]], [[-2, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[1, 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]], [[0, 0]], [[0, 0]], [[0, 0]], [[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: 10647085
    {'center': '36.a1.a1', 'center_index': 36, 'center_order': 36, 'counter': 93, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '1296.3190', 'group_counter': 3190, 'group_order': 1296, 'image': None, 'image_isoclass': '36.10', 'image_order': 36, 'indicator': 1, 'kernel': '36.a1.a1', 'kernel_order': 36, 'label': '1296.3190.4c', 'nt': [6, 9], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[4, 0]], [[-2, 0]], [[4, 0]], [[-2, 0]], [[4, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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: 10647086
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  • id: 10647087
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  • id: 10647088
    {'center': '36.d1.a1', 'center_index': 36, 'center_order': 36, 'counter': 96, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '1296.3190', 'group_counter': 3190, 'group_order': 1296, 'image': None, 'image_isoclass': '72.46', 'image_order': 72, 'indicator': 1, 'kernel': '72.b1.a1', 'kernel_order': 18, 'label': '1296.3190.4f', 'nt': [12, 37], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[0, 0]], [[2, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[-1, 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]], [[0, 0]], [[0, 0]], [[0, 0]], [[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: 10647089
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  • id: 10647090
    {'center': '36.a1.a1', 'center_index': 36, 'center_order': 36, 'counter': 98, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '1296.3190', 'group_counter': 3190, 'group_order': 1296, 'image': None, 'image_isoclass': '72.23', 'image_order': 72, 'indicator': 1, 'kernel': '72.g1.b1', 'kernel_order': 18, 'label': '1296.3190.4h', 'nt': [12, 38], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[4, 0]], [[-2, 0]], [[4, 0]], [[-2, 0]], [[4, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[-4, 0]], [[2, 0]], [[2, 0]], [[-4, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[4, 0]], [[-4, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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: 10647091
    {'center': '36.a1.a1', 'center_index': 36, 'center_order': 36, 'counter': 99, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '1296.3190', 'group_counter': 3190, 'group_order': 1296, 'image': None, 'image_isoclass': '72.23', 'image_order': 72, 'indicator': 1, 'kernel': '72.g1.a1', 'kernel_order': 18, 'label': '1296.3190.4i', 'nt': [12, 38], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[4, 0]], [[-2, 0]], [[4, 0]], [[-2, 0]], [[4, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[-4, 0]], [[2, 0]], [[2, 0]], [[-4, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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: 10646959
    {'center': '36.i1.a1', 'center_index': 36, 'center_order': 36, 'counter': 100, 'cyclotomic_n': 3, 'dim': 4, 'faithful': False, 'field': [1, -1, 1], 'group': '1296.3190', 'group_counter': 3190, 'group_order': 1296, 'image': None, 'image_isoclass': '108.38', 'image_order': 108, 'indicator': 0, 'kernel': '108.c1.a1', 'kernel_order': 12, 'label': '1296.3190.4j1', 'nt': [12, 70], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, -1]], [[4, 1]], [[-2, -1]], [[-2, 0]], [[4, 1]], [[-2, 1]], [[4, -1]], [[-2, -1]], [[-2, 1]], [[-2, 0]], [[4, 0]], [[-2, 1]], [[1, 1]], [[1, -1]], [[-2, 0]], [[-2, -1]], [[-2, 1]], [[-2, 0]], [[1, 0]], [[-2, -1]], [[1, 0]], [[1, 1]], [[1, -1]], [[4, 0]], [[0, 0]], [[4, 1]], [[4, -1]], [[-2, 1]], [[-2, -1]], [[-2, -1]], [[4, -1]], [[4, 0]], [[4, 1]], [[-2, 0]], [[-2, 1]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[1, 1]], [[-2, 1]], [[-2, -1]], [[-2, 0]], [[1, -1]], [[-2, -1]], [[1, 0]], [[-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, -1]], [[-2, 0]], [[-2, -1]], [[4, 1]], [[4, -1]], [[-2, 1]], [[-2, 0]], [[-2, 1]], [[-2, 0]], [[1, 1]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[-2, -1]], [[1, -1]], [[-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 10646960
    {'center': '36.i1.a1', 'center_index': 36, 'center_order': 36, 'counter': 101, 'cyclotomic_n': 3, 'dim': 4, 'faithful': False, 'field': [1, -1, 1], 'group': '1296.3190', 'group_counter': 3190, 'group_order': 1296, 'image': None, 'image_isoclass': '108.38', 'image_order': 108, 'indicator': 0, 'kernel': '108.c1.a1', 'kernel_order': 12, 'label': '1296.3190.4j2', 'nt': [12, 2], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 1]], [[4, -1]], [[-2, 1]], [[-2, 0]], [[4, -1]], [[-2, -1]], [[4, 1]], [[-2, 1]], [[-2, -1]], [[-2, 0]], [[4, 0]], [[-2, -1]], [[1, -1]], [[1, 1]], [[-2, 0]], [[-2, 1]], [[-2, -1]], [[-2, 0]], [[1, 0]], [[-2, 1]], [[1, 0]], [[1, -1]], [[1, 1]], [[4, 0]], [[0, 0]], [[4, -1]], [[4, 1]], [[-2, -1]], [[-2, 1]], [[-2, 1]], [[4, 1]], [[4, 0]], [[4, -1]], [[-2, 0]], [[-2, -1]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[1, -1]], [[-2, -1]], [[-2, 1]], [[-2, 0]], [[1, 1]], [[-2, 1]], [[1, 0]], [[-2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1]], [[-2, 0]], [[-2, 1]], [[4, -1]], [[4, 1]], [[-2, -1]], [[-2, 0]], [[-2, -1]], [[-2, 0]], [[1, -1]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[-2, 1]], [[1, 1]], [[-2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 10646961
    {'center': '36.d1.a1', 'center_index': 36, 'center_order': 36, 'counter': 102, 'cyclotomic_n': 3, 'dim': 4, 'faithful': False, 'field': [1, -1, 1], 'group': '1296.3190', 'group_counter': 3190, 'group_order': 1296, 'image': None, 'image_isoclass': '108.38', 'image_order': 108, 'indicator': 0, 'kernel': '108.b1.a1', 'kernel_order': 12, 'label': '1296.3190.4k1', 'nt': [12, 70], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, -1]], [[4, 1]], [[4, -1]], [[4, 0]], [[-2, 1]], [[-2, 1]], [[-2, -1]], [[-2, -1]], [[4, 1]], [[-2, 0]], [[-2, 0]], [[-2, 1]], [[-2, 1]], [[-2, -1]], [[-2, 0]], [[-2, -1]], [[1, 1]], [[1, 0]], [[-2, 0]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, -1]], [[0, 0]], [[0, 0]], [[4, 1]], [[4, -1]], [[4, 1]], [[4, -1]], [[-2, -1]], [[-2, -1]], [[-2, 0]], [[-2, 1]], [[4, 0]], [[-2, 1]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-2, 1]], [[-2, 1]], [[-2, -1]], [[-2, 0]], [[-2, -1]], [[1, -1]], [[-2, 0]], [[1, 1]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1]], [[4, -1]], [[4, 1]], [[0, 0]], [[0, 0]], [[-2, -1]], [[0, 0]], [[-2, -1]], [[0, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[0, 0]], [[0, 0]], [[1, -1]], [[1, 1]], [[-2, 0]], [[1, 1]], [[0, 0]], [[-2, -1]], [[1, 0]], [[0, 0]], [[1, -1]], [[0, 0]], [[1, 0]], [[-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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: 10646962
    {'center': '36.d1.a1', 'center_index': 36, 'center_order': 36, 'counter': 103, 'cyclotomic_n': 3, 'dim': 4, 'faithful': False, 'field': [1, -1, 1], 'group': '1296.3190', 'group_counter': 3190, 'group_order': 1296, 'image': None, 'image_isoclass': '108.38', 'image_order': 108, 'indicator': 0, 'kernel': '108.b1.a1', 'kernel_order': 12, 'label': '1296.3190.4k2', 'nt': [12, 2], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 1]], [[4, -1]], [[4, 1]], [[4, 0]], [[-2, -1]], [[-2, -1]], [[-2, 1]], [[-2, 1]], [[4, -1]], [[-2, 0]], [[-2, 0]], [[-2, -1]], [[-2, -1]], [[-2, 1]], [[-2, 0]], [[-2, 1]], [[1, -1]], [[1, 0]], [[-2, 0]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 1]], [[0, 0]], [[0, 0]], [[4, -1]], [[4, 1]], [[4, -1]], [[4, 1]], [[-2, 1]], [[-2, 1]], [[-2, 0]], [[-2, -1]], [[4, 0]], [[-2, -1]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-2, -1]], [[-2, -1]], [[-2, 1]], [[-2, 0]], [[-2, 1]], [[1, 1]], [[-2, 0]], [[1, -1]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, -1]], [[4, 1]], [[4, -1]], [[0, 0]], [[0, 0]], [[-2, 1]], [[0, 0]], [[-2, 1]], [[0, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[0, 0]], [[0, 0]], [[1, 1]], [[1, -1]], [[-2, 0]], [[1, -1]], [[0, 0]], [[-2, 1]], [[1, 0]], [[0, 0]], [[1, 1]], [[0, 0]], [[1, 0]], [[-2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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: 10646963
    {'center': '36.a1.a1', 'center_index': 36, 'center_order': 36, 'counter': 104, 'cyclotomic_n': 3, 'dim': 4, 'faithful': False, 'field': [1, -1, 1], 'group': '1296.3190', 'group_counter': 3190, 'group_order': 1296, 'image': None, 'image_isoclass': '108.38', 'image_order': 108, 'indicator': 0, 'kernel': '108.a1.a1', 'kernel_order': 12, 'label': '1296.3190.4l1', 'nt': [12, 70], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, -1]], [[4, 1]], [[-2, -1]], [[-2, 0]], [[-2, 1]], [[4, 1]], [[-2, -1]], [[4, -1]], [[-2, 1]], [[4, 0]], [[-2, 0]], [[1, 1]], [[-2, 1]], [[-2, -1]], [[1, 0]], [[1, -1]], [[-2, 1]], [[-2, 0]], [[-2, 0]], [[-2, -1]], [[1, 0]], [[1, 1]], [[1, -1]], [[0, 0]], [[0, 0]], [[4, 1]], [[4, -1]], [[-2, 1]], [[-2, -1]], [[4, -1]], [[-2, -1]], [[-2, 0]], [[-2, 1]], [[-2, 0]], [[4, 1]], [[4, 0]], [[4, -1]], [[4, -1]], [[4, 1]], [[4, 1]], [[-2, 0]], [[-2, 1]], [[1, 1]], [[1, -1]], [[1, 0]], [[-2, -1]], [[-2, -1]], [[-2, 0]], [[-2, 1]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, -1]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-2, 1]], [[-2, 1]], [[-2, -1]], [[-2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, -1]], [[-2, 1]], [[0, 0]], [[-2, 1]], [[0, 0]], [[-2, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[1, -1]], [[0, 0]], [[1, 1]], [[0, 0]], [[0, 0]], [[1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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: 10646964
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  • id: 10646965
    {'center': '72.b1.a1', 'center_index': 72, 'center_order': 18, 'counter': 106, 'cyclotomic_n': 3, 'dim': 4, 'faithful': False, 'field': [1, -1, 1], 'group': '1296.3190', 'group_counter': 3190, 'group_order': 1296, 'image': None, 'image_isoclass': '144.153', 'image_order': 144, 'indicator': 0, 'kernel': '144.b1.a1', 'kernel_order': 9, 'label': '1296.3190.4m1', 'nt': [24, 204], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-4, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-2, 0], [-4, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0], [4, 1]], [[0, 0]], [[-2, 0], [-4, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0], [4, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0], [4, 1]], [[0, 0]], [[-2, 0], [-4, 1]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-1, 0], [-2, 1]], [[1, 0], [2, 1]], [[0, 0]], [[-1, 0], [-2, 1]], [[0, 0]], [[0, 0]], [[1, 0], [2, 1]], [[0, 0]], [[1, 0], [2, 1]], [[0, 0]], [[-1, 0], [-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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: 10646966
    {'center': '72.b1.a1', 'center_index': 72, 'center_order': 18, 'counter': 107, 'cyclotomic_n': 3, 'dim': 4, 'faithful': False, 'field': [1, -1, 1], 'group': '1296.3190', 'group_counter': 3190, 'group_order': 1296, 'image': None, 'image_isoclass': '144.153', 'image_order': 144, 'indicator': 0, 'kernel': '144.b1.a1', 'kernel_order': 9, 'label': '1296.3190.4m2', 'nt': [24, 2], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-4, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0], [4, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0], [-4, 1]], [[0, 0]], [[2, 0], [4, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0], [-4, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0], [-4, 1]], [[0, 0]], [[2, 0], [4, 1]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[1, 0], [2, 1]], [[-1, 0], [-2, 1]], [[0, 0]], [[1, 0], [2, 1]], [[0, 0]], [[0, 0]], [[-1, 0], [-2, 1]], [[0, 0]], [[-1, 0], [-2, 1]], [[0, 0]], [[1, 0], [2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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: 10646967
    {'center': '24.a1.a1', 'center_index': 24, 'center_order': 54, 'counter': 108, 'cyclotomic_n': 3, 'dim': 4, 'faithful': False, 'field': [1, -1, 1], 'group': '1296.3190', 'group_counter': 3190, 'group_order': 1296, 'image': None, 'image_isoclass': '144.162', 'image_order': 144, 'indicator': 0, 'kernel': '144.d1.a1', 'kernel_order': 9, 'label': '1296.3190.4n1', 'nt': [24, 208], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, -1]], [[4, 1]], [[4, -1]], [[4, 0]], [[4, 1]], [[-2, 1]], [[4, -1]], [[-2, -1]], [[4, 1]], [[-2, 0]], [[4, 0]], [[4, 1]], [[-2, 1]], [[-2, -1]], [[4, 0]], [[4, -1]], [[-2, 1]], [[-2, 0]], [[-2, 0]], [[-2, -1]], [[-2, 0]], [[-2, 1]], [[-2, -1]], [[0, 0]], [[0, 0]], [[-4, 1]], [[-4, -1]], [[-4, 1]], [[-4, -1]], [[2, -1]], [[-4, -1]], [[-4, 0]], [[-4, 1]], [[-4, 0]], [[2, 1]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 1]], [[-4, 1]], [[-4, -1]], [[-4, 0]], [[2, -1]], [[2, -1]], [[2, 0]], [[2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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: 10646968
    {'center': '24.a1.a1', 'center_index': 24, 'center_order': 54, 'counter': 109, 'cyclotomic_n': 3, 'dim': 4, 'faithful': False, 'field': [1, -1, 1], 'group': '1296.3190', 'group_counter': 3190, 'group_order': 1296, 'image': None, 'image_isoclass': '144.162', 'image_order': 144, 'indicator': 0, 'kernel': '144.d1.a1', 'kernel_order': 9, 'label': '1296.3190.4n2', 'nt': [24, 2], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 1]], [[4, -1]], [[4, 1]], [[4, 0]], [[4, -1]], [[-2, -1]], [[4, 1]], [[-2, 1]], [[4, -1]], [[-2, 0]], [[4, 0]], [[4, -1]], [[-2, -1]], [[-2, 1]], [[4, 0]], [[4, 1]], [[-2, -1]], [[-2, 0]], [[-2, 0]], [[-2, 1]], [[-2, 0]], [[-2, -1]], [[-2, 1]], [[0, 0]], [[0, 0]], [[-4, -1]], [[-4, 1]], [[-4, -1]], [[-4, 1]], [[2, 1]], [[-4, 1]], [[-4, 0]], [[-4, -1]], [[-4, 0]], [[2, -1]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, -1]], [[-4, -1]], [[-4, 1]], [[-4, 0]], [[2, 1]], [[2, 1]], [[2, 0]], [[2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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: 10646970
    {'center': '72.a1.a1', 'center_index': 72, 'center_order': 18, 'counter': 110, 'cyclotomic_n': 12, 'dim': 4, 'faithful': False, 'field': [-3, 0, 1], 'group': '1296.3190', 'group_counter': 3190, 'group_order': 1296, 'image': None, 'image_isoclass': '144.144', 'image_order': 144, 'indicator': 1, 'kernel': '144.a1.a1', 'kernel_order': 9, 'label': '1296.3190.4o1', 'nt': [24, 229], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[4, 0]], [[-2, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[4, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[-4, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 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]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1], [-2, -1]], [[2, 1], [2, -1]], [[2, 1], [2, -1]], [[0, 0]], [[0, 0]], [[-2, 1], [-2, -1]], [[-2, 1], [-2, -1]], [[2, 1], [2, -1]], [[0, 0]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[0, 0]], [[1, 1], [1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 10646971
    {'center': '72.a1.a1', 'center_index': 72, 'center_order': 18, 'counter': 111, 'cyclotomic_n': 12, 'dim': 4, 'faithful': False, 'field': [-3, 0, 1], 'group': '1296.3190', 'group_counter': 3190, 'group_order': 1296, 'image': None, 'image_isoclass': '144.144', 'image_order': 144, 'indicator': 1, 'kernel': '144.a1.a1', 'kernel_order': 9, 'label': '1296.3190.4o2', 'nt': [24, 229], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[4, 0]], [[-2, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[4, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[-4, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 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]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1], [2, -1]], [[-2, 1], [-2, -1]], [[-2, 1], [-2, -1]], [[0, 0]], [[0, 0]], [[2, 1], [2, -1]], [[2, 1], [2, -1]], [[-2, 1], [-2, -1]], [[0, 0]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[0, 0]], [[-1, 1], [-1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 10646972
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  • id: 10646973
    {'center': '36.a1.a1', 'center_index': 36, 'center_order': 36, 'counter': 113, 'cyclotomic_n': 3, 'dim': 4, 'faithful': False, 'field': [1, -1, 1], 'group': '1296.3190', 'group_counter': 3190, 'group_order': 1296, 'image': None, 'image_isoclass': '216.122', 'image_order': 216, 'indicator': 0, 'kernel': '216.e1.b1', 'kernel_order': 6, 'label': '1296.3190.4p2', 'nt': [24, 2], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 1]], [[4, -1]], [[-2, 1]], [[-2, 0]], [[-2, -1]], [[4, -1]], [[-2, 1]], [[4, 1]], [[-2, -1]], [[4, 0]], [[-2, 0]], [[1, -1]], [[-2, -1]], [[-2, 1]], [[1, 0]], [[1, 1]], [[-2, -1]], [[-2, 0]], [[-2, 0]], [[-2, 1]], [[1, 0]], [[1, -1]], [[1, 1]], [[0, 0]], [[0, 0]], [[-4, -1]], [[-4, 1]], [[2, -1]], [[2, 1]], [[-4, 1]], [[2, 1]], [[2, 0]], [[2, -1]], [[2, 0]], [[-4, -1]], [[-4, 0]], [[-4, 1]], [[4, 1]], [[4, -1]], [[-4, -1]], [[2, 0]], [[2, -1]], [[-1, -1]], [[-1, 1]], [[-1, 0]], [[2, 1]], [[2, 1]], [[2, 0]], [[2, -1]], [[0, 0]], [[2, 0]], [[-2, 0]], [[2, 1]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, -1]], [[-2, -1]], [[-2, 1]], [[2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1]], [[-2, -1]], [[0, 0]], [[2, -1]], [[0, 0]], [[2, 0]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[1, -1]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[1, 1]], [[0, 0]], [[-1, -1]], [[0, 0]], [[0, 0]], [[-1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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: 10646974
    {'center': '36.a1.a1', 'center_index': 36, 'center_order': 36, 'counter': 114, 'cyclotomic_n': 3, 'dim': 4, 'faithful': False, 'field': [1, -1, 1], 'group': '1296.3190', 'group_counter': 3190, 'group_order': 1296, 'image': None, 'image_isoclass': '216.122', 'image_order': 216, 'indicator': 0, 'kernel': '216.e1.a1', 'kernel_order': 6, 'label': '1296.3190.4q1', 'nt': [24, 543], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, -1]], [[4, 1]], [[-2, -1]], [[-2, 0]], [[-2, 1]], [[4, 1]], [[-2, -1]], [[4, -1]], [[-2, 1]], [[4, 0]], [[-2, 0]], [[1, 1]], [[-2, 1]], [[-2, -1]], [[1, 0]], [[1, -1]], [[-2, 1]], [[-2, 0]], [[-2, 0]], [[-2, -1]], [[1, 0]], [[1, 1]], [[1, -1]], [[0, 0]], [[0, 0]], [[-4, 1]], [[-4, -1]], [[2, 1]], [[2, -1]], [[-4, -1]], [[2, -1]], [[2, 0]], [[2, 1]], [[2, 0]], [[-4, 1]], [[-4, 0]], [[4, -1]], [[-4, -1]], [[-4, 1]], [[4, 1]], [[2, 0]], [[2, 1]], [[-1, 1]], [[-1, -1]], [[-1, 0]], [[2, -1]], [[2, -1]], [[2, 0]], [[2, 1]], [[0, 0]], [[-2, 0]], [[2, 0]], [[-2, -1]], [[0, 0]], [[2, 0]], [[0, 0]], [[-2, 1]], [[2, 1]], [[2, -1]], [[-2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, -1]], [[2, 1]], [[0, 0]], [[-2, 1]], [[0, 0]], [[-2, 0]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-1, -1]], [[0, 0]], [[1, 1]], [[0, 0]], [[0, 0]], [[1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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: 10646975
    {'center': '36.a1.a1', 'center_index': 36, 'center_order': 36, 'counter': 115, 'cyclotomic_n': 3, 'dim': 4, 'faithful': False, 'field': [1, -1, 1], 'group': '1296.3190', 'group_counter': 3190, 'group_order': 1296, 'image': None, 'image_isoclass': '216.122', 'image_order': 216, 'indicator': 0, 'kernel': '216.e1.a1', 'kernel_order': 6, 'label': '1296.3190.4q2', 'nt': [24, 2], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 1]], [[4, -1]], [[-2, 1]], [[-2, 0]], [[-2, -1]], [[4, -1]], [[-2, 1]], [[4, 1]], [[-2, -1]], [[4, 0]], [[-2, 0]], [[1, -1]], [[-2, -1]], [[-2, 1]], [[1, 0]], [[1, 1]], [[-2, -1]], [[-2, 0]], [[-2, 0]], [[-2, 1]], [[1, 0]], [[1, -1]], [[1, 1]], [[0, 0]], [[0, 0]], [[-4, -1]], [[-4, 1]], [[2, -1]], [[2, 1]], [[-4, 1]], [[2, 1]], [[2, 0]], [[2, -1]], [[2, 0]], [[-4, -1]], [[-4, 0]], [[4, 1]], [[-4, 1]], [[-4, -1]], [[4, -1]], [[2, 0]], [[2, -1]], [[-1, -1]], [[-1, 1]], [[-1, 0]], [[2, 1]], [[2, 1]], [[2, 0]], [[2, -1]], [[0, 0]], [[-2, 0]], [[2, 0]], [[-2, 1]], [[0, 0]], [[2, 0]], [[0, 0]], [[-2, -1]], [[2, -1]], [[2, 1]], [[-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1]], [[2, -1]], [[0, 0]], [[-2, -1]], [[0, 0]], [[-2, 0]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-1, 1]], [[0, 0]], [[1, -1]], [[0, 0]], [[0, 0]], [[1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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: 10646976
    {'center': '36.a1.a1', 'center_index': 36, 'center_order': 36, 'counter': 116, 'cyclotomic_n': 3, 'dim': 4, 'faithful': False, 'field': [1, -1, 1], 'group': '1296.3190', 'group_counter': 3190, 'group_order': 1296, 'image': None, 'image_isoclass': '216.170', 'image_order': 216, 'indicator': 0, 'kernel': '216.d1.a1', 'kernel_order': 6, 'label': '1296.3190.4r1', 'nt': [24, 547], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, -1]], [[4, 1]], [[-2, -1]], [[-2, 0]], [[-2, 1]], [[4, 1]], [[-2, -1]], [[4, -1]], [[-2, 1]], [[4, 0]], [[-2, 0]], [[1, 1]], [[-2, 1]], [[-2, -1]], [[1, 0]], [[1, -1]], [[-2, 1]], [[-2, 0]], [[-2, 0]], [[-2, -1]], [[1, 0]], [[1, 1]], [[1, -1]], [[0, 0]], [[0, 0]], [[4, 1]], [[4, -1]], [[-2, 1]], [[-2, -1]], [[4, -1]], [[-2, -1]], [[-2, 0]], [[-2, 1]], [[-2, 0]], [[4, 1]], [[4, 0]], [[-4, -1]], [[-4, -1]], [[-4, 1]], [[-4, 1]], [[-2, 0]], [[-2, 1]], [[1, 1]], [[1, -1]], [[1, 0]], [[-2, -1]], [[-2, -1]], [[-2, 0]], [[-2, 1]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, -1]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 1]], [[2, 1]], [[2, -1]], [[2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, -1]], [[2, 1]], [[0, 0]], [[2, 1]], [[0, 0]], [[2, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[-1, 1]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-1, -1]], [[0, 0]], [[-1, 1]], [[0, 0]], [[0, 0]], [[-1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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: 10646977
    {'center': '36.a1.a1', 'center_index': 36, 'center_order': 36, 'counter': 117, 'cyclotomic_n': 3, 'dim': 4, 'faithful': False, 'field': [1, -1, 1], 'group': '1296.3190', 'group_counter': 3190, 'group_order': 1296, 'image': None, 'image_isoclass': '216.170', 'image_order': 216, 'indicator': 0, 'kernel': '216.d1.a1', 'kernel_order': 6, 'label': '1296.3190.4r2', 'nt': [24, 2], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 1]], [[4, -1]], [[-2, 1]], [[-2, 0]], [[-2, -1]], [[4, -1]], [[-2, 1]], [[4, 1]], [[-2, -1]], [[4, 0]], [[-2, 0]], [[1, -1]], [[-2, -1]], [[-2, 1]], [[1, 0]], [[1, 1]], [[-2, -1]], [[-2, 0]], [[-2, 0]], [[-2, 1]], [[1, 0]], [[1, -1]], [[1, 1]], [[0, 0]], [[0, 0]], [[4, -1]], [[4, 1]], [[-2, -1]], [[-2, 1]], [[4, 1]], [[-2, 1]], [[-2, 0]], [[-2, -1]], [[-2, 0]], [[4, -1]], [[4, 0]], [[-4, 1]], [[-4, 1]], [[-4, -1]], [[-4, -1]], [[-2, 0]], [[-2, -1]], [[1, -1]], [[1, 1]], [[1, 0]], [[-2, 1]], [[-2, 1]], [[-2, 0]], [[-2, -1]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 1]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, -1]], [[2, -1]], [[2, 1]], [[2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1]], [[2, -1]], [[0, 0]], [[2, -1]], [[0, 0]], [[2, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[-1, -1]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-1, 1]], [[0, 0]], [[-1, -1]], [[0, 0]], [[0, 0]], [[-1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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: 10646978
    {'center': '36.d1.a1', 'center_index': 36, 'center_order': 36, 'counter': 118, 'cyclotomic_n': 3, 'dim': 4, 'faithful': False, 'field': [1, -1, 1], 'group': '1296.3190', 'group_counter': 3190, 'group_order': 1296, 'image': None, 'image_isoclass': '216.170', 'image_order': 216, 'indicator': 0, 'kernel': '216.c1.a1', 'kernel_order': 6, 'label': '1296.3190.4s1', 'nt': [24, 547], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, -1]], [[4, 1]], [[4, -1]], [[4, 0]], [[-2, 1]], [[-2, 1]], [[-2, -1]], [[-2, -1]], [[4, 1]], [[-2, 0]], [[-2, 0]], [[-2, 1]], [[-2, 1]], [[-2, -1]], [[-2, 0]], [[-2, -1]], [[1, 1]], [[1, 0]], [[-2, 0]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, -1]], [[0, 0]], [[0, 0]], [[4, 1]], [[4, -1]], [[4, 1]], [[4, -1]], [[-2, -1]], [[-2, -1]], [[-2, 0]], [[-2, 1]], [[4, 0]], [[-2, 1]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-2, 1]], [[-2, 1]], [[-2, -1]], [[-2, 0]], [[-2, -1]], [[1, -1]], [[-2, 0]], [[1, 1]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1]], [[-4, -1]], [[-4, 1]], [[0, 0]], [[0, 0]], [[2, -1]], [[0, 0]], [[2, -1]], [[0, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[0, 0]], [[0, 0]], [[-1, -1]], [[-1, 1]], [[2, 0]], [[-1, 1]], [[0, 0]], [[2, -1]], [[-1, 0]], [[0, 0]], [[-1, -1]], [[0, 0]], [[-1, 0]], [[2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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: 10646979
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  • id: 10646981
    {'center': '36.i1.a1', 'center_index': 36, 'center_order': 36, 'counter': 120, 'cyclotomic_n': 3, 'dim': 4, 'faithful': False, 'field': [1, -1, 1], 'group': '1296.3190', 'group_counter': 3190, 'group_order': 1296, 'image': None, 'image_isoclass': '216.170', 'image_order': 216, 'indicator': 0, 'kernel': '216.b1.a1', 'kernel_order': 6, 'label': '1296.3190.4t1', 'nt': [24, 547], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, -1]], [[4, 1]], [[-2, -1]], [[-2, 0]], [[4, 1]], [[-2, 1]], [[4, -1]], [[-2, -1]], [[-2, 1]], [[-2, 0]], [[4, 0]], [[-2, 1]], [[1, 1]], [[1, -1]], [[-2, 0]], [[-2, -1]], [[-2, 1]], [[-2, 0]], [[1, 0]], [[-2, -1]], [[1, 0]], [[1, 1]], [[1, -1]], [[-4, 0]], [[0, 0]], [[4, 1]], [[4, -1]], [[-2, 1]], [[-2, -1]], [[-2, -1]], [[4, -1]], [[4, 0]], [[4, 1]], [[-2, 0]], [[-2, 1]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[1, 1]], [[-2, 1]], [[-2, -1]], [[-2, 0]], [[1, -1]], [[-2, -1]], [[1, 0]], [[-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, -1]], [[2, 0]], [[2, -1]], [[-4, 1]], [[-4, -1]], [[2, 1]], [[2, 0]], [[2, 1]], [[2, 0]], [[-1, 1]], [[-1, 0]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[2, -1]], [[-1, -1]], [[2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 10646982
    {'center': '36.i1.a1', 'center_index': 36, 'center_order': 36, 'counter': 121, 'cyclotomic_n': 3, 'dim': 4, 'faithful': False, 'field': [1, -1, 1], 'group': '1296.3190', 'group_counter': 3190, 'group_order': 1296, 'image': None, 'image_isoclass': '216.170', 'image_order': 216, 'indicator': 0, 'kernel': '216.b1.a1', 'kernel_order': 6, 'label': '1296.3190.4t2', 'nt': [24, 2], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 1]], [[4, -1]], [[-2, 1]], [[-2, 0]], [[4, -1]], [[-2, -1]], [[4, 1]], [[-2, 1]], [[-2, -1]], [[-2, 0]], [[4, 0]], [[-2, -1]], [[1, -1]], [[1, 1]], [[-2, 0]], [[-2, 1]], [[-2, -1]], [[-2, 0]], [[1, 0]], [[-2, 1]], [[1, 0]], [[1, -1]], [[1, 1]], [[-4, 0]], [[0, 0]], [[4, -1]], [[4, 1]], [[-2, -1]], [[-2, 1]], [[-2, 1]], [[4, 1]], [[4, 0]], [[4, -1]], [[-2, 0]], [[-2, -1]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[1, -1]], [[-2, -1]], [[-2, 1]], [[-2, 0]], [[1, 1]], [[-2, 1]], [[1, 0]], [[-2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1]], [[2, 0]], [[2, 1]], [[-4, -1]], [[-4, 1]], [[2, -1]], [[2, 0]], [[2, -1]], [[2, 0]], [[-1, -1]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[2, 1]], [[-1, 1]], [[2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 10646983
    {'center': '72.b1.a1', 'center_index': 72, 'center_order': 18, 'counter': 122, 'cyclotomic_n': 3, 'dim': 4, 'faithful': False, 'field': [1, -1, 1], 'group': '1296.3190', 'group_counter': 3190, 'group_order': 1296, 'image': None, 'image_isoclass': '432.658', 'image_order': 432, 'indicator': 0, 'kernel': '432.c1.a1', 'kernel_order': 3, 'label': '1296.3190.4u1', 'nt': [24, 1280], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, -1]], [[4, 1]], [[4, -1]], [[4, 0]], [[-2, 1]], [[-2, 1]], [[-2, -1]], [[-2, -1]], [[4, 1]], [[-2, 0]], [[-2, 0]], [[-2, 1]], [[-2, 1]], [[-2, -1]], [[-2, 0]], [[-2, -1]], [[1, 1]], [[1, 0]], [[-2, 0]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, -1]], [[0, 0]], [[0, 0]], [[-4, 1]], [[-4, -1]], [[-4, 1]], [[-4, -1]], [[2, -1]], [[2, -1]], [[2, 0]], [[2, 1]], [[-4, 0]], [[2, 1]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[2, 1]], [[2, 1]], [[2, -1]], [[2, 0]], [[2, -1]], [[-1, -1]], [[2, 0]], [[-1, 1]], [[2, 0], [4, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0], [-4, 1]], [[0, 0]], [[-4, 0], [-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0], [2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0], [2, 1]], [[0, 0]], [[2, 0], [-2, 1]], [[0, 0]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[0, 0]], [[0, 0]], [[1, 0], [-1, 1]], [[2, 0], [1, 1]], [[0, 0]], [[-2, 0], [-1, 1]], [[0, 0]], [[0, 0]], [[-1, 0], [-2, 1]], [[0, 0]], [[-1, 0], [1, 1]], [[0, 0]], [[1, 0], [2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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: 10646984
    {'center': '72.b1.a1', 'center_index': 72, 'center_order': 18, 'counter': 123, 'cyclotomic_n': 3, 'dim': 4, 'faithful': False, 'field': [1, -1, 1], 'group': '1296.3190', 'group_counter': 3190, 'group_order': 1296, 'image': None, 'image_isoclass': '432.658', 'image_order': 432, 'indicator': 0, 'kernel': '432.c1.a1', 'kernel_order': 3, 'label': '1296.3190.4u2', 'nt': [24, 2], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 1]], [[4, -1]], [[4, 1]], [[4, 0]], [[-2, -1]], [[-2, -1]], [[-2, 1]], [[-2, 1]], [[4, -1]], [[-2, 0]], [[-2, 0]], [[-2, -1]], [[-2, -1]], [[-2, 1]], [[-2, 0]], [[-2, 1]], [[1, -1]], [[1, 0]], [[-2, 0]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 1]], [[0, 0]], [[0, 0]], [[-4, -1]], [[-4, 1]], [[-4, -1]], [[-4, 1]], [[2, 1]], [[2, 1]], [[2, 0]], [[2, -1]], [[-4, 0]], [[2, -1]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[2, -1]], [[2, -1]], [[2, 1]], [[2, 0]], [[2, 1]], [[-1, 1]], [[2, 0]], [[-1, -1]], [[-2, 0], [-4, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0], [4, 1]], [[0, 0]], [[-2, 0], [2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0], [-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0], [-2, 1]], [[0, 0]], [[4, 0], [2, 1]], [[0, 0]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[0, 0]], [[0, 0]], [[2, 0], [1, 1]], [[1, 0], [-1, 1]], [[0, 0]], [[-1, 0], [1, 1]], [[0, 0]], [[0, 0]], [[1, 0], [2, 1]], [[0, 0]], [[-2, 0], [-1, 1]], [[0, 0]], [[-1, 0], [-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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: 10646985
    {'center': '72.b1.a1', 'center_index': 72, 'center_order': 18, 'counter': 124, 'cyclotomic_n': 3, 'dim': 4, 'faithful': False, 'field': [1, -1, 1], 'group': '1296.3190', 'group_counter': 3190, 'group_order': 1296, 'image': None, 'image_isoclass': '432.658', 'image_order': 432, 'indicator': 0, 'kernel': '432.c1.a1', 'kernel_order': 3, 'label': '1296.3190.4v1', 'nt': [24, 1280], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, -1]], [[4, 1]], [[4, -1]], [[4, 0]], [[-2, 1]], [[-2, 1]], [[-2, -1]], [[-2, -1]], [[4, 1]], [[-2, 0]], [[-2, 0]], [[-2, 1]], [[-2, 1]], [[-2, -1]], [[-2, 0]], [[-2, -1]], [[1, 1]], [[1, 0]], [[-2, 0]], [[1, -1]], [[1, 0]], [[1, 1]], [[1, -1]], [[0, 0]], [[0, 0]], [[-4, 1]], [[-4, -1]], [[-4, 1]], [[-4, -1]], [[2, -1]], [[2, -1]], [[2, 0]], [[2, 1]], [[-4, 0]], [[2, 1]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[2, 1]], [[2, 1]], [[2, -1]], [[2, 0]], [[2, -1]], [[-1, -1]], [[2, 0]], [[-1, 1]], [[-2, 0], [-4, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0], [4, 1]], [[0, 0]], [[4, 0], [2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0], [-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0], [-2, 1]], [[0, 0]], [[-2, 0], [2, 1]], [[0, 0]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[0, 0]], [[0, 0]], [[-1, 0], [1, 1]], [[-2, 0], [-1, 1]], [[0, 0]], [[2, 0], [1, 1]], [[0, 0]], [[0, 0]], [[1, 0], [2, 1]], [[0, 0]], [[1, 0], [-1, 1]], [[0, 0]], [[-1, 0], [-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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: 10646986
    {'center': '72.b1.a1', 'center_index': 72, 'center_order': 18, 'counter': 125, 'cyclotomic_n': 3, 'dim': 4, 'faithful': False, 'field': [1, -1, 1], 'group': '1296.3190', 'group_counter': 3190, 'group_order': 1296, 'image': None, 'image_isoclass': '432.658', 'image_order': 432, 'indicator': 0, 'kernel': '432.c1.a1', 'kernel_order': 3, 'label': '1296.3190.4v2', 'nt': [24, 2], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 1]], [[4, -1]], [[4, 1]], [[4, 0]], [[-2, -1]], [[-2, -1]], [[-2, 1]], [[-2, 1]], [[4, -1]], [[-2, 0]], [[-2, 0]], [[-2, -1]], [[-2, -1]], [[-2, 1]], [[-2, 0]], [[-2, 1]], [[1, -1]], [[1, 0]], [[-2, 0]], [[1, 1]], [[1, 0]], [[1, -1]], [[1, 1]], [[0, 0]], [[0, 0]], [[-4, -1]], [[-4, 1]], [[-4, -1]], [[-4, 1]], [[2, 1]], [[2, 1]], [[2, 0]], [[2, -1]], [[-4, 0]], [[2, -1]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[2, -1]], [[2, -1]], [[2, 1]], [[2, 0]], [[2, 1]], [[-1, 1]], [[2, 0]], [[-1, -1]], [[2, 0], [4, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0], [-4, 1]], [[0, 0]], [[2, 0], [-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0], [2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0], [2, 1]], [[0, 0]], [[-4, 0], [-2, 1]], [[0, 0]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[0, 0]], [[0, 0]], [[-2, 0], [-1, 1]], [[-1, 0], [1, 1]], [[0, 0]], [[1, 0], [-1, 1]], [[0, 0]], [[0, 0]], [[-1, 0], [-2, 1]], [[0, 0]], [[2, 0], [1, 1]], [[0, 0]], [[1, 0], [2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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: 10646987
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  • id: 10646988
    {'center': '72.a1.a1', 'center_index': 72, 'center_order': 18, 'counter': 127, 'cyclotomic_n': 12, 'dim': 4, 'faithful': False, 'field': [1, 0, 1], 'group': '1296.3190', 'group_counter': 3190, 'group_order': 1296, 'image': None, 'image_isoclass': '432.649', 'image_order': 432, 'indicator': 0, 'kernel': '432.b1.a1', 'kernel_order': 3, 'label': '1296.3190.4w2', 'nt': [48, 4], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 4]], [[-4, 2]], [[-2, 4]], [[-2, 0]], [[-4, 2]], [[2, 2]], [[4, 4]], [[-2, 4]], [[2, 2]], [[-2, 0]], [[4, 0]], [[2, 2]], [[-1, 2]], [[1, 4]], [[-2, 0]], [[-2, 4]], [[2, 2]], [[-2, 0]], [[1, 0]], [[-2, 4]], [[1, 0]], [[-1, 2]], [[1, 4]], [[0, 0]], [[0, 0]], [[4, 2]], [[-4, 4]], [[-2, 2]], [[2, 4]], [[2, 4]], [[-4, 4]], [[-4, 0]], [[4, 2]], [[2, 0]], [[-2, 2]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[1, 2]], [[-2, 2]], [[2, 4]], [[2, 0]], [[-1, 4]], [[2, 4]], [[-1, 0]], [[-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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 4]], [[1, 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, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1], [4, 3]], [[-2, 1], [-2, -1]], [[2, 1], [-4, 3]], [[0, 0]], [[0, 0]], [[-2, 1], [-2, 3]], [[2, 1], [2, -1]], [[2, 1], [2, 3]], [[0, 0]], [[1, 1], [1, 3]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[-1, 1], [2, 3]], [[-1, 1], [-1, 3]], [[0, 0]], [[1, 1], [-2, 3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 10646989
    {'center': '72.a1.a1', 'center_index': 72, 'center_order': 18, 'counter': 128, 'cyclotomic_n': 12, 'dim': 4, 'faithful': False, 'field': [1, 0, 1], 'group': '1296.3190', 'group_counter': 3190, 'group_order': 1296, 'image': None, 'image_isoclass': '432.649', 'image_order': 432, 'indicator': 0, 'kernel': '432.b1.a1', 'kernel_order': 3, 'label': '1296.3190.4w3', 'nt': [48, 0], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 2]], [[4, 4]], [[2, 2]], [[-2, 0]], [[4, 4]], [[-2, 4]], [[-4, 2]], [[2, 2]], [[-2, 4]], [[-2, 0]], [[4, 0]], [[-2, 4]], [[1, 4]], [[-1, 2]], [[-2, 0]], [[2, 2]], [[-2, 4]], [[-2, 0]], [[1, 0]], [[2, 2]], [[1, 0]], [[1, 4]], [[-1, 2]], [[0, 0]], [[0, 0]], [[-4, 4]], [[4, 2]], [[2, 4]], [[-2, 2]], [[-2, 2]], [[4, 2]], [[-4, 0]], [[-4, 4]], [[2, 0]], [[2, 4]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-1, 4]], [[2, 4]], [[-2, 2]], [[2, 0]], [[1, 2]], [[-2, 2]], [[-1, 0]], [[2, 4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 2]], [[-1, 4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1], [2, 3]], [[2, 1], [2, -1]], [[-2, 1], [-2, 3]], [[0, 0]], [[0, 0]], [[2, 1], [-4, 3]], [[-2, 1], [-2, -1]], [[-2, 1], [4, 3]], [[0, 0]], [[-1, 1], [2, 3]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, 3]], [[1, 1], [-2, 3]], [[0, 0]], [[-1, 1], [-1, 3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 10646990
    {'center': '72.a1.a1', 'center_index': 72, 'center_order': 18, 'counter': 129, 'cyclotomic_n': 12, 'dim': 4, 'faithful': False, 'field': [1, 0, 1], 'group': '1296.3190', 'group_counter': 3190, 'group_order': 1296, 'image': None, 'image_isoclass': '432.649', 'image_order': 432, 'indicator': 0, 'kernel': '432.b1.a1', 'kernel_order': 3, 'label': '1296.3190.4w4', 'nt': [48, 4], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 4]], [[-4, 2]], [[-2, 4]], [[-2, 0]], [[-4, 2]], [[2, 2]], [[4, 4]], [[-2, 4]], [[2, 2]], [[-2, 0]], [[4, 0]], [[2, 2]], [[-1, 2]], [[1, 4]], [[-2, 0]], [[-2, 4]], [[2, 2]], [[-2, 0]], [[1, 0]], [[-2, 4]], [[1, 0]], [[-1, 2]], [[1, 4]], [[0, 0]], [[0, 0]], [[4, 2]], [[-4, 4]], [[-2, 2]], [[2, 4]], [[2, 4]], [[-4, 4]], [[-4, 0]], [[4, 2]], [[2, 0]], [[-2, 2]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[1, 2]], [[-2, 2]], [[2, 4]], [[2, 0]], [[-1, 4]], [[2, 4]], [[-1, 0]], [[-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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 4]], [[1, 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, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1], [-4, 3]], [[2, 1], [2, -1]], [[-2, 1], [4, 3]], [[0, 0]], [[0, 0]], [[2, 1], [2, 3]], [[-2, 1], [-2, -1]], [[-2, 1], [-2, 3]], [[0, 0]], [[-1, 1], [-1, 3]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[1, 1], [-2, 3]], [[1, 1], [1, 3]], [[0, 0]], [[-1, 1], [2, 3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 10646992
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  • id: 10646993
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  • id: 10646994
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  • id: 10646995
    {'center': '216.a1.a1', 'center_index': 216, 'center_order': 6, 'counter': 133, 'cyclotomic_n': 3, 'dim': 8, 'faithful': False, 'field': [1, -1, 1], 'group': '1296.3190', 'group_counter': 3190, 'group_order': 1296, 'image': None, 'image_isoclass': '648.731', 'image_order': 648, 'indicator': 0, 'kernel': '648.a1.a1', 'kernel_order': 2, 'label': '1296.3190.8c2', 'nt': [24, 2], 'q_character': None, 'values': [[[8, 0]], [[8, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[8, 1]], [[8, -1]], [[-4, 1]], [[-4, 0]], [[-4, -1]], [[-4, -1]], [[-4, 1]], [[-4, 1]], [[-4, -1]], [[-4, 0]], [[-4, 0]], [[2, -1]], [[2, -1]], [[2, 1]], [[2, 0]], [[2, 1]], [[2, -1]], [[2, 0]], [[2, 0]], [[2, 1]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[0, 0]], [[0, 0]], [[8, -1]], [[8, 1]], [[-4, -1]], [[-4, 1]], [[-4, 1]], [[-4, 1]], [[-4, 0]], [[-4, -1]], [[-4, 0]], [[-4, -1]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, -1]], [[2, -1]], [[2, 1]], [[2, 0]], [[2, 1]], [[2, 1]], [[2, 0]], [[2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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: 10646996
    {'center': '216.a1.a1', 'center_index': 216, 'center_order': 6, 'counter': 134, 'cyclotomic_n': 3, 'dim': 8, 'faithful': True, 'field': [1, -1, 1], 'group': '1296.3190', 'group_counter': 3190, 'group_order': 1296, 'image': None, 'image_isoclass': '1296.3190', 'image_order': 1296, 'indicator': 0, 'kernel': '1296.a1.a1', 'kernel_order': 1, 'label': '1296.3190.8d1', 'nt': [48, 0], 'q_character': None, 'values': [[[8, 0]], [[-8, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[8, -1]], [[8, 1]], [[-4, -1]], [[-4, 0]], [[-4, 1]], [[-4, 1]], [[-4, -1]], [[-4, -1]], [[-4, 1]], [[-4, 0]], [[-4, 0]], [[2, 1]], [[2, 1]], [[2, -1]], [[2, 0]], [[2, -1]], [[2, 1]], [[2, 0]], [[2, 0]], [[2, -1]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[0, 0]], [[0, 0]], [[-8, 1]], [[-8, -1]], [[4, 1]], [[4, -1]], [[4, -1]], [[4, -1]], [[4, 0]], [[4, 1]], [[4, 0]], [[4, 1]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 1]], [[-2, 1]], [[-2, -1]], [[-2, 0]], [[-2, -1]], [[-2, -1]], [[-2, 0]], [[-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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: 10646997
    {'center': '216.a1.a1', 'center_index': 216, 'center_order': 6, 'counter': 135, 'cyclotomic_n': 3, 'dim': 8, 'faithful': True, 'field': [1, -1, 1], 'group': '1296.3190', 'group_counter': 3190, 'group_order': 1296, 'image': None, 'image_isoclass': '1296.3190', 'image_order': 1296, 'indicator': 0, 'kernel': '1296.a1.a1', 'kernel_order': 1, 'label': '1296.3190.8d2', 'nt': [48, 2], 'q_character': None, 'values': [[[8, 0]], [[-8, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[8, 1]], [[8, -1]], [[-4, 1]], [[-4, 0]], [[-4, -1]], [[-4, -1]], [[-4, 1]], [[-4, 1]], [[-4, -1]], [[-4, 0]], [[-4, 0]], [[2, -1]], [[2, -1]], [[2, 1]], [[2, 0]], [[2, 1]], [[2, -1]], [[2, 0]], [[2, 0]], [[2, 1]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[0, 0]], [[0, 0]], [[-8, -1]], [[-8, 1]], [[4, -1]], [[4, 1]], [[4, 1]], [[4, 1]], [[4, 0]], [[4, -1]], [[4, 0]], [[4, -1]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, -1]], [[-2, -1]], [[-2, 1]], [[-2, 0]], [[-2, 1]], [[-2, 1]], [[-2, 0]], [[-2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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: 71059842
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': True, 'core_order': 1296, 'counter': 1, 'cyclic': False, 'direct': True, 'hall': 6, 'label': '1296.3190.1.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '1.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': False, 'quotient': '1.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 1, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_1', 'simple': False, 'solvable': True, 'special_labels': ['R', 'L0', 'D0', 'C0'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '1296.3190', 'subgroup_hash': 3190, 'subgroup_order': 1296, 'subgroup_tex': 'C_6.S_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 71059953
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': True, 'core_order': 648, 'counter': 2, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1296.3190.2.a1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '648.746', 'subgroup_hash': 746, 'subgroup_order': 648, 'subgroup_tex': 'C_3^4:C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 71060064
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': True, 'core_order': 648, 'counter': 3, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1296.3190.2.b1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, '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': '648.747', 'subgroup_hash': 747, 'subgroup_order': 648, 'subgroup_tex': 'C_3^4:C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 71060175
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': True, 'core_order': 648, 'counter': 4, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1296.3190.2.c1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, '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': '648.646', 'subgroup_hash': 646, 'subgroup_order': 648, 'subgroup_tex': 'S_3\\times C_3^2:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 71060286
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': True, 'core_order': 648, 'counter': 5, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1296.3190.2.d1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': ['C1'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '648.649', 'subgroup_hash': 649, 'subgroup_order': 648, 'subgroup_tex': 'C_3^3:D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 71060397
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': True, 'core_order': 648, 'counter': 6, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1296.3190.2.e1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.e1.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': '648.655', 'subgroup_hash': 655, 'subgroup_order': 648, 'subgroup_tex': 'C_3^3:D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 71060508
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': True, 'core_order': 648, 'counter': 7, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1296.3190.2.f1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.f1.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': '648.659', 'subgroup_hash': 659, 'subgroup_order': 648, 'subgroup_tex': 'C_3^3:D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 71060611
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': True, 'core_order': 648, 'counter': 8, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1296.3190.2.g1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.g1.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': '648.656', 'subgroup_hash': 656, 'subgroup_order': 648, 'subgroup_tex': 'C_3^3:D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 71060622
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': True, 'centralizer_order': 6, 'characteristic': True, 'core_order': 432, 'counter': 9, 'cyclic': False, 'direct': True, 'hall': 0, 'label': '1296.3190.3.a1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '3.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '3.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 3, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '432.598', 'subgroup_hash': 598, 'subgroup_order': 432, 'subgroup_tex': 'D_6:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 71059843
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 216, 'counter': 10, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.3.b1.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '432.656', 'subgroup_hash': 656, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 71059854
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 216, 'counter': 11, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.3.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: 71059865
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 216, 'counter': 12, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.3.d1.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3.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': 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': '432.649', 'subgroup_hash': 649, 'subgroup_order': 432, 'subgroup_tex': 'C_{12}:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 71059876
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': True, 'core_order': 324, 'counter': 13, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1296.3190.4.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': False, 'standard_generators': False, 'stem': False, 'subgroup': '324.172', 'subgroup_hash': 172, 'subgroup_order': 324, 'subgroup_tex': 'D_6\\times C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 71059887
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': True, 'core_order': 324, 'counter': 14, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1296.3190.4.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', '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': '324.172', 'subgroup_hash': 172, 'subgroup_order': 324, 'subgroup_tex': 'D_6\\times C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 71059898
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': True, 'core_order': 324, 'counter': 15, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1296.3190.4.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '324.173', 'subgroup_hash': 173, 'subgroup_order': 324, 'subgroup_tex': 'C_3^2:C_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 71059909
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': True, 'core_order': 324, 'counter': 16, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1296.3190.4.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '324.173', 'subgroup_hash': 173, 'subgroup_order': 324, 'subgroup_tex': 'C_3^2:C_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 71059920
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': True, 'core_order': 324, 'counter': 17, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1296.3190.4.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '324.174', 'subgroup_hash': 174, 'subgroup_order': 324, 'subgroup_tex': 'C_3^3:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 71059931
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': True, 'core_order': 324, 'counter': 18, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1296.3190.4.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.f1.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': '324.155', 'subgroup_hash': 155, 'subgroup_order': 324, 'subgroup_tex': 'C_3^3:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 71059942
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': True, 'core_order': 324, 'counter': 19, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1296.3190.4.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.g1.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': '324.156', 'subgroup_hash': 156, 'subgroup_order': 324, 'subgroup_tex': 'C_3^3:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 71059954
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 162, 'counter': 20, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.4.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4.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': 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': '324.165', 'subgroup_hash': 165, 'subgroup_order': 324, 'subgroup_tex': 'C_3^2\\times S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 71059965
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 162, 'counter': 21, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.4.h1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4.h1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '324.165', 'subgroup_hash': 165, 'subgroup_order': 324, 'subgroup_tex': 'C_3^2\\times S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 71059976
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 162, 'counter': 22, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.4.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4.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': 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': '324.166', 'subgroup_hash': 166, 'subgroup_order': 324, 'subgroup_tex': 'C_3^2:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 71059987
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 162, 'counter': 23, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.4.i1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4.i1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '324.166', 'subgroup_hash': 166, 'subgroup_order': 324, 'subgroup_tex': 'C_3^2:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 71059998
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': True, 'core_order': 216, 'counter': 24, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1296.3190.6.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': True, '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: 71060009
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': True, 'core_order': 216, 'counter': 25, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1296.3190.6.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': [], 'split': True, '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: 71060020
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': True, 'core_order': 216, 'counter': 26, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1296.3190.6.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, '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': '216.171', 'subgroup_hash': 171, 'subgroup_order': 216, 'subgroup_tex': 'C_6:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 71060031
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': True, 'core_order': 216, 'counter': 27, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1296.3190.6.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, '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': '216.119', 'subgroup_hash': 119, 'subgroup_order': 216, 'subgroup_tex': 'C_6.S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 71060042
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': True, 'core_order': 216, 'counter': 28, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1296.3190.6.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, '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': '216.119', 'subgroup_hash': 119, 'subgroup_order': 216, 'subgroup_tex': 'C_6.S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 71060053
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': True, 'centralizer_order': 36, 'characteristic': True, 'core_order': 216, 'counter': 29, 'cyclic': False, 'direct': True, 'hall': 0, 'label': '1296.3190.6.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '6.f1.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': '216.122', 'subgroup_hash': 122, 'subgroup_order': 216, 'subgroup_tex': 'C_3^2:D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 71060065
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': True, 'core_order': 216, 'counter': 30, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1296.3190.6.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '6.g1.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': '216.122', 'subgroup_hash': 122, 'subgroup_order': 216, 'subgroup_tex': 'C_3^2:D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 71060076
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': True, 'core_order': 216, 'counter': 31, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1296.3190.6.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '6.h1.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': '216.128', 'subgroup_hash': 128, 'subgroup_order': 216, 'subgroup_tex': 'C_3^2:D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 71060087
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': True, 'core_order': 216, 'counter': 32, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1296.3190.6.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '6.i1.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': '216.132', 'subgroup_hash': 132, 'subgroup_order': 216, 'subgroup_tex': 'C_3^2:D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 71060098
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': True, 'core_order': 216, 'counter': 33, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1296.3190.6.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '6.j1.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': '216.129', 'subgroup_hash': 129, 'subgroup_order': 216, 'subgroup_tex': 'C_3^2:D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 71060109
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 108, 'counter': 34, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.6.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': '216.174', 'subgroup_hash': 174, 'subgroup_order': 216, 'subgroup_tex': 'S_3\\times C_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 71060120
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 108, 'counter': 35, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.6.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '216.175', 'subgroup_hash': 175, 'subgroup_order': 216, 'subgroup_tex': 'C_6^2:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 71060131
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 108, 'counter': 36, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.6.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, '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': '216.138', 'subgroup_hash': 138, 'subgroup_order': 216, 'subgroup_tex': 'C_6.C_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 71060142
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 108, 'counter': 37, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.6.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': '216.174', 'subgroup_hash': 174, 'subgroup_order': 216, 'subgroup_tex': 'S_3\\times C_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 71060153
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 72, 'counter': 38, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.6.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, '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': '216.170', 'subgroup_hash': 170, 'subgroup_order': 216, 'subgroup_tex': 'C_6\\times S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 71060164
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 108, 'counter': 39, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.6.p1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, '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': '216.170', 'subgroup_hash': 170, 'subgroup_order': 216, 'subgroup_tex': 'C_6\\times S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 71060176
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 108, 'counter': 40, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.6.q1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.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': 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: 71060187
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 36, 'counter': 41, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.6.r1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.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': 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: 71060198
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 108, 'counter': 42, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.6.s1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.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': 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': '216.136', 'subgroup_hash': 136, 'subgroup_order': 216, 'subgroup_tex': 'C_6.C_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 71060209
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 72, 'counter': 43, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.6.t1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.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': 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: 71060220
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 108, 'counter': 44, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.6.u1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.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': 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: 71060231
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 108, 'counter': 45, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.6.v1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.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': 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: 71060242
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 108, 'counter': 46, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.6.w1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.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': 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': '216.137', 'subgroup_hash': 137, 'subgroup_order': 216, 'subgroup_tex': 'C_3^2\\times D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 71060253
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 72, 'counter': 47, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.6.x1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.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': 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: 71060264
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 108, 'counter': 48, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.6.y1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.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': 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: 71060275
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 108, 'counter': 49, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.6.z1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.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': 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: 71060287
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 36, 'counter': 50, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.6.ba1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.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': 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: 71060298
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 108, 'counter': 51, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.6.bb1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.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': 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: 71060309
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 108, 'counter': 52, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.6.bc1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.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': 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: 71060320
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 108, 'counter': 53, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.6.bd1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.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': 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: 71060331
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 108, 'counter': 54, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.6.be1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.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': 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: 71060342
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 36, 'counter': 55, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.6.bf1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.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': 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: 71060353
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 108, 'counter': 56, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.6.bg1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.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': 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: 71060364
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 108, 'counter': 57, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.6.bh1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.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': 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': '216.142', 'subgroup_hash': 142, 'subgroup_order': 216, 'subgroup_tex': 'C_3^2:D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 71060375
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': True, 'core_order': 162, 'counter': 58, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1296.3190.8.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': ['F', 'S'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '162.55', 'subgroup_hash': 55, 'subgroup_order': 162, 'subgroup_tex': 'C_3^3\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 71060386
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 162, 'counter': 59, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1296.3190.8.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.3', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '162.51', 'subgroup_hash': 51, 'subgroup_order': 162, 'subgroup_tex': 'S_3\\times C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 71060398
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 162, 'counter': 60, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1296.3190.8.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.3', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '162.51', 'subgroup_hash': 51, 'subgroup_order': 162, 'subgroup_tex': 'S_3\\times C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 71060409
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 81, 'counter': 61, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.8.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': '162.51', 'subgroup_hash': 51, 'subgroup_order': 162, 'subgroup_tex': 'S_3\\times C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 71060420
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 81, 'counter': 62, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.8.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.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': 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': '162.52', 'subgroup_hash': 52, 'subgroup_order': 162, 'subgroup_tex': 'C_3^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 71060431
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 81, 'counter': 63, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.8.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.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': 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': '162.52', 'subgroup_hash': 52, 'subgroup_order': 162, 'subgroup_tex': 'C_3^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 71060442
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 81, 'counter': 64, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.8.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.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': 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': '162.53', 'subgroup_hash': 53, 'subgroup_order': 162, 'subgroup_tex': 'C_3^3:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 71060453
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 36, 'counter': 65, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.9.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: 71060464
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 36, 'counter': 66, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.9.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '9.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 9, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.160', 'subgroup_hash': 160, 'subgroup_order': 144, 'subgroup_tex': 'C_6\\times D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 71060475
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 72, 'counter': 67, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.9.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': '144.151', 'subgroup_hash': 151, 'subgroup_order': 144, 'subgroup_tex': 'C_6:D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 71060486
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 36, 'counter': 68, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.9.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': '144.162', 'subgroup_hash': 162, 'subgroup_order': 144, 'subgroup_tex': 'C_{12}:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 71060497
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 72, 'counter': 69, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.9.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '9.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': 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: 71060509
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 72, 'counter': 70, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.9.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '9.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': 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': '144.144', 'subgroup_hash': 144, 'subgroup_order': 144, 'subgroup_tex': 'S_3\\times D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 71060520
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': True, 'core_order': 108, 'counter': 71, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1296.3190.12.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '12.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '12.4', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '108.42', 'subgroup_hash': 42, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 71060531
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': True, 'core_order': 108, 'counter': 72, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1296.3190.12.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '12.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '12.4', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '108.42', 'subgroup_hash': 42, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 71060542
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': True, 'core_order': 108, 'counter': 73, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1296.3190.12.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '12.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '12.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '108.42', 'subgroup_hash': 42, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 71060553
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': True, 'core_order': 108, 'counter': 74, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1296.3190.12.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '12.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '12.4', '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': '108.42', 'subgroup_hash': 42, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 71060564
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': True, 'core_order': 108, 'counter': 75, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1296.3190.12.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '12.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '12.4', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, '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: 71060575
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': True, 'core_order': 108, 'counter': 76, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1296.3190.12.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '12.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '12.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '108.42', 'subgroup_hash': 42, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 71060586
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': True, 'core_order': 108, 'counter': 77, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1296.3190.12.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '12.g1.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': '108.43', 'subgroup_hash': 43, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 71060597
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': True, 'core_order': 108, 'counter': 78, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1296.3190.12.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '12.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '12.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '108.43', 'subgroup_hash': 43, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 71060608
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': True, 'core_order': 108, 'counter': 79, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1296.3190.12.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '12.i1.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': '108.43', 'subgroup_hash': 43, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 71060612
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': True, 'core_order': 108, 'counter': 80, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1296.3190.12.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '12.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '12.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '108.43', 'subgroup_hash': 43, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 71060613
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': True, 'core_order': 108, 'counter': 81, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1296.3190.12.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '12.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '12.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '108.44', 'subgroup_hash': 44, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 71060614
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': True, 'core_order': 108, 'counter': 82, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1296.3190.12.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '12.l1.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': '108.32', 'subgroup_hash': 32, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 71060615
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': True, 'core_order': 108, 'counter': 83, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1296.3190.12.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '12.m1.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': '108.32', 'subgroup_hash': 32, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 71060616
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': True, 'core_order': 108, 'counter': 84, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1296.3190.12.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '12.n1.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': '108.33', 'subgroup_hash': 33, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 71060617
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': True, 'core_order': 108, 'counter': 85, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1296.3190.12.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '12.o1.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': ['C3'], 'split': True, '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: 71060618
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': True, 'core_order': 108, 'counter': 86, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1296.3190.12.p1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '12.p1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '12.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '108.33', 'subgroup_hash': 33, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 71060619
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 54, 'counter': 87, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.12.q1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '108.45', 'subgroup_hash': 45, 'subgroup_order': 108, 'subgroup_tex': 'C_3\\times C_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 71060620
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 36, 'counter': 88, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.12.r1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.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': 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: 71060621
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 36, 'counter': 89, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.12.s1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.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': 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: 71060623
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 36, 'counter': 90, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.12.t1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.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': 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: 71060624
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 12, 'counter': 91, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.12.u1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.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': 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: 71060625
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 54, 'counter': 92, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.12.v1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.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': 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': '108.45', 'subgroup_hash': 45, 'subgroup_order': 108, 'subgroup_tex': 'C_3\\times C_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 71060626
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 36, 'counter': 93, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.12.w1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.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': 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: 71060627
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 36, 'counter': 94, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.12.x1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.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': 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: 71060628
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 36, 'counter': 95, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.12.y1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.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': 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: 71060629
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 12, 'counter': 96, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.12.z1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.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': 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: 71060630
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 54, 'counter': 97, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.12.ba1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.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': 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: 71060631
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 54, 'counter': 98, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.12.bb1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.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': 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: 71060632
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 18, 'counter': 99, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.12.bc1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.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': 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: 71059844
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 36, 'counter': 100, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.12.bd1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.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': 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: 71059845
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 54, 'counter': 101, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.12.be1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.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': 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: 71059846
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 54, 'counter': 102, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.12.bf1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.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': 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: 71059847
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 18, 'counter': 103, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.12.bg1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.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': 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: 71059848
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 36, 'counter': 104, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.12.bh1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.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': 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: 71059849
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 54, 'counter': 105, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.12.bi1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.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': 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: 71059850
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 54, 'counter': 106, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.12.bj1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.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': 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: 71059851
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 18, 'counter': 107, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.12.bk1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.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': 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: 71059852
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 54, 'counter': 108, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.12.bl1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.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': 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: 71059853
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 18, 'counter': 109, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.12.bm1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.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': 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: 71059855
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 18, 'counter': 110, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.12.bn1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.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': 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: 71059856
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 6, 'counter': 111, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.12.bo1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.bo1.a1', 'outer_equivalence': False, 'perfect': False, '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: 71059857
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 54, 'counter': 112, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.12.bp1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.bp1.a1', 'outer_equivalence': False, 'perfect': False, '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: 71059858
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 36, 'counter': 113, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.12.bq1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.bq1.a1', 'outer_equivalence': False, 'perfect': False, '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: 71059859
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 54, 'counter': 114, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.12.br1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.br1.a1', 'outer_equivalence': False, 'perfect': False, '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': '108.35', 'subgroup_hash': 35, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 71059860
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 54, 'counter': 115, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.12.bs1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.bs1.a1', 'outer_equivalence': False, 'perfect': False, '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: 71059861
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 18, 'counter': 116, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.12.bt1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.bt1.a1', 'outer_equivalence': False, 'perfect': False, '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: 71059862
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 36, 'counter': 117, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.12.bu1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.bu1.a1', 'outer_equivalence': False, 'perfect': False, '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: 71059863
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 36, 'counter': 118, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.12.bv1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.bv1.a1', 'outer_equivalence': False, 'perfect': False, '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: 71059864
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 36, 'counter': 119, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.12.bw1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.bw1.a1', 'outer_equivalence': False, 'perfect': False, '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: 71059866
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 12, 'counter': 120, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.12.bx1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.bx1.a1', 'outer_equivalence': False, 'perfect': False, '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: 71059867
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 27, 'counter': 121, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.12.by1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.by1.a1', 'outer_equivalence': False, 'perfect': False, '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: 71059868
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 27, 'counter': 122, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.12.by1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.by1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.42', 'subgroup_hash': 42, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 71059869
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 27, 'counter': 123, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.12.bz1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.bz1.a1', 'outer_equivalence': False, 'perfect': False, '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: 71059870
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 27, 'counter': 124, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.12.bz1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.bz1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.43', 'subgroup_hash': 43, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 71059871
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 54, 'counter': 125, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.12.ca1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.ca1.a1', 'outer_equivalence': False, 'perfect': False, '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: 71059872
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 54, 'counter': 126, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.12.ca1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.ca1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.42', 'subgroup_hash': 42, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 71059873
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 54, 'counter': 127, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.12.cb1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.cb1.a1', 'outer_equivalence': False, 'perfect': False, '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: 71059874
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 54, 'counter': 128, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.12.cb1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.cb1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.38', 'subgroup_hash': 38, 'subgroup_order': 108, 'subgroup_tex': 'C_3\\times S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 71059875
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 54, 'counter': 129, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.12.cc1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.cc1.a1', 'outer_equivalence': False, 'perfect': False, '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: 71059877
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 54, 'counter': 130, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.12.cc1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.cc1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.38', 'subgroup_hash': 38, 'subgroup_order': 108, 'subgroup_tex': 'C_3\\times S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 71059878
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 18, 'counter': 131, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.12.cd1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.cd1.a1', 'outer_equivalence': False, 'perfect': False, '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: 71059879
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 18, 'counter': 132, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.12.cd1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.cd1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.38', 'subgroup_hash': 38, 'subgroup_order': 108, 'subgroup_tex': 'C_3\\times S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 71059880
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 18, 'counter': 133, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.12.cd1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.cd1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.38', 'subgroup_hash': 38, 'subgroup_order': 108, 'subgroup_tex': 'C_3\\times S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 71059881
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 18, 'counter': 134, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.12.cd1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.cd1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.38', 'subgroup_hash': 38, 'subgroup_order': 108, 'subgroup_tex': 'C_3\\times S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 71059882
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 54, 'counter': 135, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.12.ce1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.ce1.a1', 'outer_equivalence': False, 'perfect': False, '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: 71059883
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 54, 'counter': 136, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.12.ce1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.ce1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.38', 'subgroup_hash': 38, 'subgroup_order': 108, 'subgroup_tex': 'C_3\\times S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 71059884
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 54, 'counter': 137, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.12.cf1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.cf1.a1', 'outer_equivalence': False, 'perfect': False, '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: 71059885
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 54, 'counter': 138, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.12.cf1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.cf1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.38', 'subgroup_hash': 38, 'subgroup_order': 108, 'subgroup_tex': 'C_3\\times S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 71059886
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 18, 'counter': 139, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.12.cg1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.cg1.a1', 'outer_equivalence': False, 'perfect': False, '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: 71059888
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 18, 'counter': 140, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.12.cg1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.cg1.a2', 'outer_equivalence': False, 'perfect': False, '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: 71059889
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 18, 'counter': 141, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.12.cg1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.cg1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.38', 'subgroup_hash': 38, 'subgroup_order': 108, 'subgroup_tex': 'C_3\\times S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 71059890
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 18, 'counter': 142, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.12.cg1.b2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.cg1.b2', 'outer_equivalence': False, 'perfect': False, '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: 71059891
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 54, 'counter': 143, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.12.ch1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.ch1.a1', 'outer_equivalence': False, 'perfect': False, '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': '108.39', 'subgroup_hash': 39, 'subgroup_order': 108, 'subgroup_tex': 'C_3:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 71059892
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 54, 'counter': 144, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.12.ch1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.ch1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.39', 'subgroup_hash': 39, 'subgroup_order': 108, 'subgroup_tex': 'C_3:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 71059893
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': True, 'core_order': 81, 'counter': 145, 'cyclic': False, 'direct': False, 'hall': 3, 'label': '1296.3190.16.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.11', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 11, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '81.15', 'subgroup_hash': 15, 'subgroup_order': 81, 'subgroup_tex': 'C_3^4', 'supersolvable': True, 'sylow': 3}
  • id: 71059894
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': True, 'core_order': 72, 'counter': 146, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1296.3190.18.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': True, '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: 71059895
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': True, 'core_order': 72, 'counter': 147, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1296.3190.18.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, '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': '72.20', 'subgroup_hash': 20, 'subgroup_order': 72, 'subgroup_tex': 'C_6.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 71059896
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': True, 'centralizer_order': 36, 'characteristic': True, 'core_order': 72, 'counter': 148, 'cyclic': False, 'direct': True, 'hall': 0, 'label': '1296.3190.18.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '18.c1.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': '72.23', 'subgroup_hash': 23, 'subgroup_order': 72, 'subgroup_tex': 'C_3:D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 71059897
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 18, 'counter': 149, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.18.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '72.50', 'subgroup_hash': 50, 'subgroup_order': 72, 'subgroup_tex': 'C_2\\times C_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 71059899
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 36, 'counter': 150, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.18.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: 71059900
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 36, 'counter': 151, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.18.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': '72.48', 'subgroup_hash': 48, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 71059901
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 12, 'counter': 152, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.18.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': '72.48', 'subgroup_hash': 48, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 71059902
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 18, 'counter': 153, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.18.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '72.48', 'subgroup_hash': 48, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 71059903
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 18, 'counter': 154, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.18.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '72.48', 'subgroup_hash': 48, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 71059904
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 6, 'counter': 155, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.18.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '72.48', 'subgroup_hash': 48, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 71059905
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 36, 'counter': 156, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.18.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '72.49', 'subgroup_hash': 49, 'subgroup_order': 72, 'subgroup_tex': 'C_6:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 71059906
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 36, 'counter': 157, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.18.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, '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': '72.29', 'subgroup_hash': 29, 'subgroup_order': 72, 'subgroup_tex': 'C_6:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 71059907
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 18, 'counter': 158, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.18.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '72.36', 'subgroup_hash': 36, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 71059908
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 36, 'counter': 159, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.18.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, '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': '72.29', 'subgroup_hash': 29, 'subgroup_order': 72, 'subgroup_tex': 'C_6:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 71059910
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 12, 'counter': 160, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.18.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '72.29', 'subgroup_hash': 29, 'subgroup_order': 72, 'subgroup_tex': 'C_6:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 71059911
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 36, 'counter': 161, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.18.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': '72.48', 'subgroup_hash': 48, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 71059912
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 36, 'counter': 162, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.18.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': '72.48', 'subgroup_hash': 48, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 71059913
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 12, 'counter': 163, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.18.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: 71059914
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 36, 'counter': 164, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.18.s1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '72.48', 'subgroup_hash': 48, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 71059915
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 36, 'counter': 165, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.18.t1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '72.46', 'subgroup_hash': 46, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 71059916
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 36, 'counter': 166, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.18.u1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '72.46', 'subgroup_hash': 46, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 71059917
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 12, 'counter': 167, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.18.v1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '72.46', 'subgroup_hash': 46, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 71059918
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 36, 'counter': 168, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.18.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': '72.27', 'subgroup_hash': 27, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 71059919
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 36, 'counter': 169, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.18.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': '72.27', 'subgroup_hash': 27, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 71059921
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 12, 'counter': 170, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.18.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': '72.27', 'subgroup_hash': 27, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 71059922
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 18, 'counter': 171, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.18.z1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '72.37', 'subgroup_hash': 37, 'subgroup_order': 72, 'subgroup_tex': 'D_4\\times C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 71059923
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 36, 'counter': 172, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.18.ba1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, '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': '72.30', 'subgroup_hash': 30, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 71059924
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 36, 'counter': 173, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.18.bb1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, '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': '72.30', 'subgroup_hash': 30, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 71059925
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 12, 'counter': 174, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.18.bc1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.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': 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: 71059926
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 18, 'counter': 175, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.18.bd1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.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': 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: 71059927
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 18, 'counter': 176, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.18.be1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.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': 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: 71059928
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 6, 'counter': 177, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.18.bf1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.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': 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: 71059929
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 36, 'counter': 178, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.18.bg1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.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': 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: 71059930
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 36, 'counter': 179, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.18.bh1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.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': 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: 71059932
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 36, 'counter': 180, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.18.bi1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.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': 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: 71059933
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 12, 'counter': 181, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.18.bj1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.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': 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: 71059934
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 36, 'counter': 182, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.18.bk1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.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': 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: 71059935
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 36, 'counter': 183, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.18.bl1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.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': 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: 71059936
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 36, 'counter': 184, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.18.bm1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.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': 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: 71059937
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 12, 'counter': 185, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.18.bn1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.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': 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: 71059938
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 18, 'counter': 186, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.18.bo1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.bo1.a1', 'outer_equivalence': False, 'perfect': False, '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: 71059939
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 36, 'counter': 187, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.18.bp1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.bp1.a1', 'outer_equivalence': False, 'perfect': False, '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: 71059940
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 18, 'counter': 188, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.18.bq1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.bq1.a1', 'outer_equivalence': False, 'perfect': False, '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: 71059941
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 18, 'counter': 189, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.18.br1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.br1.a1', 'outer_equivalence': False, 'perfect': False, '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: 71059943
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 36, 'counter': 190, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.18.bs1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.bs1.a1', 'outer_equivalence': False, 'perfect': False, '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: 71059944
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 36, 'counter': 191, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.18.bt1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.bt1.a1', 'outer_equivalence': False, 'perfect': False, '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: 71059945
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 18, 'counter': 192, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.18.bu1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.bu1.a1', 'outer_equivalence': False, 'perfect': False, '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: 71059946
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 18, 'counter': 193, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.18.bv1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.bv1.a1', 'outer_equivalence': False, 'perfect': False, '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: 71059947
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 6, 'counter': 194, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.18.bw1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.bw1.a1', 'outer_equivalence': False, 'perfect': False, '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: 71059948
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 36, 'counter': 195, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.18.bx1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.bx1.a1', 'outer_equivalence': False, 'perfect': False, '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: 71059949
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 36, 'counter': 196, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.18.by1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.by1.a1', 'outer_equivalence': False, 'perfect': False, '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: 71059950
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 12, 'counter': 197, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.18.bz1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.bz1.a1', 'outer_equivalence': False, 'perfect': False, '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: 71059951
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 36, 'counter': 198, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.18.ca1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.ca1.a1', 'outer_equivalence': False, 'perfect': False, '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: 71059952
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 36, 'counter': 199, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.18.cb1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.cb1.a1', 'outer_equivalence': False, 'perfect': False, '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': '72.33', 'subgroup_hash': 33, 'subgroup_order': 72, 'subgroup_tex': 'C_3:D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 71059955
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 324, 'characteristic': True, 'core_order': 54, 'counter': 200, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1296.3190.24.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '24.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '24.14', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 14, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '54.15', 'subgroup_hash': 15, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 71059956
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 324, 'characteristic': True, 'core_order': 54, 'counter': 201, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1296.3190.24.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '24.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '24.14', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 14, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '54.15', 'subgroup_hash': 15, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 71059957
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 324, 'characteristic': True, 'core_order': 54, 'counter': 202, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1296.3190.24.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '24.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '24.14', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 14, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '54.15', 'subgroup_hash': 15, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 71059958
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': True, 'core_order': 54, 'counter': 203, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1296.3190.24.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '24.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '24.15', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 15, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2\\times C_6', 'simple': False, 'solvable': True, 'special_labels': ['D', 'L1', 'D1'], 'split': False, '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: 71059959
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 54, 'counter': 204, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1296.3190.24.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '24.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '24.6', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 6, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_{12}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '54.12', 'subgroup_hash': 12, 'subgroup_order': 54, 'subgroup_tex': 'S_3\\times C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 71059960
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 54, 'counter': 205, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1296.3190.24.e1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '24.e1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '24.6', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 6, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_{12}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '54.12', 'subgroup_hash': 12, 'subgroup_order': 54, 'subgroup_tex': 'S_3\\times C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 71059961
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 54, 'counter': 206, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1296.3190.24.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '24.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '24.8', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 8, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3:D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '54.12', 'subgroup_hash': 12, 'subgroup_order': 54, 'subgroup_tex': 'S_3\\times C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 71059962
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 54, 'counter': 207, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1296.3190.24.f1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '24.f1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '24.8', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 8, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3:D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '54.12', 'subgroup_hash': 12, 'subgroup_order': 54, 'subgroup_tex': 'S_3\\times C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 71059963
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 54, 'counter': 208, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1296.3190.24.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '24.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '24.10', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 10, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3\\times D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '54.12', 'subgroup_hash': 12, 'subgroup_order': 54, 'subgroup_tex': 'S_3\\times C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 71059964
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 54, 'counter': 209, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1296.3190.24.g1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '24.g1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '24.10', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 10, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3\\times D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '54.12', 'subgroup_hash': 12, 'subgroup_order': 54, 'subgroup_tex': 'S_3\\times C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 71059966
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': False, 'core_order': 18, 'counter': 210, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.24.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '54.15', 'subgroup_hash': 15, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 71059967
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': False, 'core_order': 18, 'counter': 211, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.24.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '54.15', 'subgroup_hash': 15, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 71059968
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': False, 'core_order': 18, 'counter': 212, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.24.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '54.15', 'subgroup_hash': 15, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 71059969
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': False, 'core_order': 6, 'counter': 213, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.24.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '54.15', 'subgroup_hash': 15, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 71059970
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': False, 'core_order': 18, 'counter': 214, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.24.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '54.15', 'subgroup_hash': 15, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 71059971
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': False, 'core_order': 18, 'counter': 215, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.24.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '54.15', 'subgroup_hash': 15, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 71059972
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': False, 'core_order': 6, 'counter': 216, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.24.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '54.15', 'subgroup_hash': 15, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 71059973
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': False, 'core_order': 18, 'counter': 217, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.24.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.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': 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: 71059974
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': False, 'core_order': 6, 'counter': 218, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.24.p1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.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': 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: 71059975
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': False, 'core_order': 6, 'counter': 219, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.24.q1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.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': 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: 71059977
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': False, 'core_order': 2, 'counter': 220, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.24.r1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.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': 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: 71059978
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 27, 'counter': 221, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.24.s1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.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': 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: 71059979
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 27, 'counter': 222, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.24.s1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.s1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.15', 'subgroup_hash': 15, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 71059980
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 18, 'counter': 223, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.24.t1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.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': 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: 71059981
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 18, 'counter': 224, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.24.t1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.t1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.12', 'subgroup_hash': 12, 'subgroup_order': 54, 'subgroup_tex': 'S_3\\times C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 71059982
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 18, 'counter': 225, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.24.u1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.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': 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: 71059983
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 18, 'counter': 226, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.24.u1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.u1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.12', 'subgroup_hash': 12, 'subgroup_order': 54, 'subgroup_tex': 'S_3\\times C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 71059984
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 18, 'counter': 227, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.24.v1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.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': 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: 71059985
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 18, 'counter': 228, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.24.v1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.v1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.12', 'subgroup_hash': 12, 'subgroup_order': 54, 'subgroup_tex': 'S_3\\times C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 71059986
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 6, 'counter': 229, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.24.w1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.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': 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: 71059988
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 6, 'counter': 230, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.24.w1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.w1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.12', 'subgroup_hash': 12, 'subgroup_order': 54, 'subgroup_tex': 'S_3\\times C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 71059989
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 27, 'counter': 231, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.24.x1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.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': 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: 71059990
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 27, 'counter': 232, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.24.y1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.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': 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: 71059991
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 27, 'counter': 233, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.24.z1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.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': 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: 71059992
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 9, 'counter': 234, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.24.ba1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.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': 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: 71059993
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 27, 'counter': 235, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.24.bb1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.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': 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: 71059994
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 9, 'counter': 236, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.24.bc1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.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': 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: 71059995
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 9, 'counter': 237, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.24.bd1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.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': 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: 71059996
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 9, 'counter': 238, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.24.bd1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.bd1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.12', 'subgroup_hash': 12, 'subgroup_order': 54, 'subgroup_tex': 'S_3\\times C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 71059997
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 3, 'counter': 239, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.24.be1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.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': 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: 71059999
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 3, 'counter': 240, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.24.be1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.be1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.12', 'subgroup_hash': 12, 'subgroup_order': 54, 'subgroup_tex': 'S_3\\times C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 71060000
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 27, 'counter': 241, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.24.bf1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.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': 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: 71060001
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 27, 'counter': 242, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.24.bg1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.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': 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: 71060002
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 9, 'counter': 243, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.24.bh1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.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': 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: 71060003
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 27, 'counter': 244, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.24.bi1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.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': 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: 71060004
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 27, 'counter': 245, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.24.bj1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.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': 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: 71060005
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 9, 'counter': 246, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.24.bk1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.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': 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: 71060006
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 9, 'counter': 247, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.24.bk1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.bk1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.13', 'subgroup_hash': 13, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 71060007
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 27, 'counter': 248, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.24.bl1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.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': 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: 71060008
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 27, 'counter': 249, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.24.bm1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.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': 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: 71060010
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 9, 'counter': 250, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.24.bn1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.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': 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: 71060011
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 9, 'counter': 251, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.24.bn1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.bn1.a2', 'outer_equivalence': False, 'perfect': False, '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: 71060012
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 27, 'counter': 252, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.24.bo1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.bo1.a1', 'outer_equivalence': False, 'perfect': False, '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: 71060013
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 27, 'counter': 253, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.24.bp1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.bp1.a1', 'outer_equivalence': False, 'perfect': False, '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: 71060014
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 9, 'counter': 254, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.24.bq1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.bq1.a1', 'outer_equivalence': False, 'perfect': False, '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: 71060015
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 27, 'counter': 255, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.24.br1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.br1.a1', 'outer_equivalence': False, 'perfect': False, '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: 71060016
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 27, 'counter': 256, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.24.bs1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.bs1.a1', 'outer_equivalence': False, 'perfect': False, '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: 71060017
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 9, 'counter': 257, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.24.bt1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.bt1.a1', 'outer_equivalence': False, 'perfect': False, '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: 71060018
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 27, 'counter': 258, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.24.bu1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.bu1.a1', 'outer_equivalence': False, 'perfect': False, '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: 71060019
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 9, 'counter': 259, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.24.bv1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.bv1.a1', 'outer_equivalence': False, 'perfect': False, '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: 71060021
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 9, 'counter': 260, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.24.bw1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.bw1.a1', 'outer_equivalence': False, 'perfect': False, '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: 71060022
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 9, 'counter': 261, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.24.bw1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.bw1.a2', 'outer_equivalence': False, 'perfect': False, '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: 71060023
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 262, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.24.bx1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.bx1.a1', 'outer_equivalence': False, 'perfect': False, '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: 71060024
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 263, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.24.bx1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.bx1.a2', 'outer_equivalence': False, 'perfect': False, '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: 71060025
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 27, 'counter': 264, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.24.by1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.by1.a1', 'outer_equivalence': False, 'perfect': False, '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': '54.14', 'subgroup_hash': 14, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 71060026
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 6, 'counter': 265, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.27.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: 71060027
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 12, 'counter': 266, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.27.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: 71060028
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 12, 'counter': 267, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.27.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': '48.36', 'subgroup_hash': 36, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 71060029
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 12, 'counter': 268, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.27.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '27.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': 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: 71060030
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': True, 'centralizer_order': 216, 'characteristic': True, 'core_order': 36, 'counter': 269, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1296.3190.36.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '36.a1.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': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 71060032
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': True, 'core_order': 36, 'counter': 270, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1296.3190.36.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '36.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '36.12', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 12, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 36, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6\\times S_3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 71060033
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': True, 'core_order': 36, 'counter': 271, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1296.3190.36.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, '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': False, '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: 71060034
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': True, 'core_order': 36, 'counter': 272, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1296.3190.36.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '36.d1.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': True, '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: 71060035
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': True, 'core_order': 36, 'counter': 273, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1296.3190.36.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '36.e1.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': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 71060036
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': True, 'core_order': 36, 'counter': 274, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1296.3190.36.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '36.f1.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': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 71060037
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': True, 'core_order': 36, 'counter': 275, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1296.3190.36.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '36.g1.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': '36.13', 'subgroup_hash': 13, 'subgroup_order': 36, 'subgroup_tex': 'C_6:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 71060038
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': True, 'core_order': 36, 'counter': 276, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1296.3190.36.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '36.h1.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': '36.13', 'subgroup_hash': 13, 'subgroup_order': 36, 'subgroup_tex': 'C_6:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 71060039
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': True, 'core_order': 36, 'counter': 277, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1296.3190.36.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '36.i1.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': True, '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: 71060040
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': True, 'core_order': 36, 'counter': 278, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1296.3190.36.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '36.j1.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': ['C4'], 'split': True, '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: 71060041
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': True, 'core_order': 36, 'counter': 279, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1296.3190.36.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '36.k1.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': '36.6', 'subgroup_hash': 6, 'subgroup_order': 36, 'subgroup_tex': 'C_3:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 71060043
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': True, 'core_order': 36, 'counter': 280, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1296.3190.36.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '36.l1.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': '36.7', 'subgroup_hash': 7, 'subgroup_order': 36, 'subgroup_tex': 'C_3^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 71060044
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 216, 'characteristic': False, 'core_order': 18, 'counter': 281, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.36.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '36.14', 'subgroup_hash': 14, 'subgroup_order': 36, 'subgroup_tex': 'C_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 71060045
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 216, 'characteristic': False, 'core_order': 18, 'counter': 282, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.36.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '36.14', 'subgroup_hash': 14, 'subgroup_order': 36, 'subgroup_tex': 'C_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 71060046
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 6, 'counter': 283, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.36.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '36.14', 'subgroup_hash': 14, 'subgroup_order': 36, 'subgroup_tex': 'C_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 71060047
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 18, 'counter': 284, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.36.p1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '36.14', 'subgroup_hash': 14, 'subgroup_order': 36, 'subgroup_tex': 'C_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 71060048
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 6, 'counter': 285, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.36.q1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '36.14', 'subgroup_hash': 14, 'subgroup_order': 36, 'subgroup_tex': 'C_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 71060049
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 6, 'counter': 286, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.36.r1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '36.14', 'subgroup_hash': 14, 'subgroup_order': 36, 'subgroup_tex': 'C_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 71060050
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 2, 'counter': 287, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.36.s1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '36.14', 'subgroup_hash': 14, 'subgroup_order': 36, 'subgroup_tex': 'C_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 71060051
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 12, 'counter': 288, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.36.t1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, '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': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 71060052
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 12, 'counter': 289, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.36.u1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, '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': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 71060054
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 12, 'counter': 290, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.36.v1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, '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': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 71060055
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 12, 'counter': 291, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.36.w1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, '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': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 71060056
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 216, 'characteristic': False, 'core_order': 18, 'counter': 292, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.36.x1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '36.14', 'subgroup_hash': 14, 'subgroup_order': 36, 'subgroup_tex': 'C_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 71060057
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 18, 'counter': 293, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.36.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': '36.14', 'subgroup_hash': 14, 'subgroup_order': 36, 'subgroup_tex': 'C_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 71060058
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 6, 'counter': 294, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.36.z1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '36.14', 'subgroup_hash': 14, 'subgroup_order': 36, 'subgroup_tex': 'C_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 71060059
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 18, 'counter': 295, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.36.ba1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '36.14', 'subgroup_hash': 14, 'subgroup_order': 36, 'subgroup_tex': 'C_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 71060060
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 6, 'counter': 296, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.36.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: 71060061
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 6, 'counter': 297, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.36.bc1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '36.14', 'subgroup_hash': 14, 'subgroup_order': 36, 'subgroup_tex': 'C_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 71060062
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 2, 'counter': 298, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.36.bd1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '36.14', 'subgroup_hash': 14, 'subgroup_order': 36, 'subgroup_tex': 'C_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 71060063
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 12, 'counter': 299, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.36.be1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, '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': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 71060066
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 12, 'counter': 300, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.36.bf1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 71060067
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 12, 'counter': 301, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.36.bg1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 71060068
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 12, 'counter': 302, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.36.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: 71060069
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 18, 'counter': 303, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.36.bi1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '36.14', 'subgroup_hash': 14, 'subgroup_order': 36, 'subgroup_tex': 'C_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 71060070
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 18, 'counter': 304, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.36.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: 71060071
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 18, 'counter': 305, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.36.bk1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, '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': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 71060072
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 6, 'counter': 306, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.36.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: 71060073
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 18, 'counter': 307, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.36.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: 71060074
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 18, 'counter': 308, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.36.bn1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, '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': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 71060075
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 6, 'counter': 309, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.36.bo1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.bo1.a1', 'outer_equivalence': False, 'perfect': False, '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: 71060077
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 6, 'counter': 310, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.36.bp1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.bp1.a1', 'outer_equivalence': False, 'perfect': False, '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: 71060078
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 6, 'counter': 311, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.36.bq1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.bq1.a1', 'outer_equivalence': False, 'perfect': False, '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: 71060079
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 2, 'counter': 312, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.36.br1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.br1.a1', 'outer_equivalence': False, 'perfect': False, '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: 71060080
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 18, 'counter': 313, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.36.bs1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.bs1.a1', 'outer_equivalence': False, 'perfect': False, '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: 71060081
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 18, 'counter': 314, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.36.bt1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.bt1.a1', 'outer_equivalence': False, 'perfect': False, '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: 71060082
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 18, 'counter': 315, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.36.bu1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.bu1.a1', 'outer_equivalence': False, 'perfect': False, '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: 71060083
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 6, 'counter': 316, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.36.bv1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.bv1.a1', 'outer_equivalence': False, 'perfect': False, '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: 71060084
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 18, 'counter': 317, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.36.bw1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.bw1.a1', 'outer_equivalence': False, 'perfect': False, '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: 71060085
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 6, 'counter': 318, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.36.bx1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.bx1.a1', 'outer_equivalence': False, 'perfect': False, '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: 71060086
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 18, 'counter': 319, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.36.by1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.by1.a1', 'outer_equivalence': False, 'perfect': False, '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: 71060088
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 6, 'counter': 320, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.36.bz1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.bz1.a1', 'outer_equivalence': False, 'perfect': False, '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: 71060089
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 6, 'counter': 321, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.36.ca1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.ca1.a1', 'outer_equivalence': False, 'perfect': False, '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: 71060090
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 2, 'counter': 322, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.36.cb1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.cb1.a1', 'outer_equivalence': False, 'perfect': False, '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: 71060091
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 18, 'counter': 323, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.36.cc1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.cc1.a1', 'outer_equivalence': False, 'perfect': False, '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: 71060092
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 18, 'counter': 324, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.36.cd1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.cd1.a1', 'outer_equivalence': False, 'perfect': False, '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: 71060093
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 18, 'counter': 325, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.36.ce1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.ce1.a1', 'outer_equivalence': False, 'perfect': False, '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: 71060094
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 6, 'counter': 326, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.36.cf1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.cf1.a1', 'outer_equivalence': False, 'perfect': False, '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: 71060095
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 6, 'counter': 327, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.36.cg1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.cg1.a1', 'outer_equivalence': False, 'perfect': False, '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: 71060096
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 6, 'counter': 328, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.36.ch1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.ch1.a1', 'outer_equivalence': False, 'perfect': False, '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: 71060097
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 6, 'counter': 329, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.36.ci1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.ci1.a1', 'outer_equivalence': False, 'perfect': False, '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: 71060099
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 18, 'counter': 330, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.36.cj1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.cj1.a1', 'outer_equivalence': False, 'perfect': False, '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: 71060100
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 18, 'counter': 331, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.36.ck1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.ck1.a1', 'outer_equivalence': False, 'perfect': False, '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: 71060101
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 6, 'counter': 332, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.36.cl1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.cl1.a1', 'outer_equivalence': False, 'perfect': False, '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: 71060102
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 18, 'counter': 333, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.36.cm1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.cm1.a1', 'outer_equivalence': False, 'perfect': False, '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: 71060103
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 6, 'counter': 334, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.36.cn1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.cn1.a1', 'outer_equivalence': False, 'perfect': False, '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: 71060104
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 6, 'counter': 335, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.36.co1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.co1.a1', 'outer_equivalence': False, 'perfect': False, '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: 71060105
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 2, 'counter': 336, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.36.cp1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.cp1.a1', 'outer_equivalence': False, 'perfect': False, '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: 71060106
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 18, 'counter': 337, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.36.cq1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.cq1.a1', 'outer_equivalence': False, 'perfect': False, '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: 71060107
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 216, 'characteristic': False, 'core_order': 18, 'counter': 338, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.36.cr1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.cr1.a1', 'outer_equivalence': False, 'perfect': False, '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: 71060108
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 18, 'counter': 339, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.36.cs1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.cs1.a1', 'outer_equivalence': False, 'perfect': False, '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: 71060110
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 18, 'counter': 340, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.36.ct1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.ct1.a1', 'outer_equivalence': False, 'perfect': False, '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: 71060111
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 18, 'counter': 341, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.36.cu1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.cu1.a1', 'outer_equivalence': False, 'perfect': False, '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: 71060112
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 6, 'counter': 342, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.36.cv1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.cv1.a1', 'outer_equivalence': False, 'perfect': False, '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: 71060113
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 6, 'counter': 343, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.36.cw1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.cw1.a1', 'outer_equivalence': False, 'perfect': False, '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: 71060114
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 18, 'counter': 344, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.36.cx1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.cx1.a1', 'outer_equivalence': False, 'perfect': False, '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: 71060115
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 12, 'counter': 345, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.36.cy1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.cy1.a1', 'outer_equivalence': False, 'perfect': False, '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: 71060116
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 6, 'counter': 346, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.36.cz1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.cz1.a1', 'outer_equivalence': False, 'perfect': False, '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: 71060117
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 12, 'counter': 347, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.36.da1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.da1.a1', 'outer_equivalence': False, 'perfect': False, '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: 71060118
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 12, 'counter': 348, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.36.db1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.db1.a1', 'outer_equivalence': False, 'perfect': False, '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: 71060119
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 12, 'counter': 349, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.36.dc1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.dc1.a1', 'outer_equivalence': False, 'perfect': False, '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: 71060121
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 18, 'counter': 350, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.36.dd1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.dd1.a1', 'outer_equivalence': False, 'perfect': False, '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: 71060122
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 18, 'counter': 351, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.36.de1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.de1.a1', 'outer_equivalence': False, 'perfect': False, '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: 71060123
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 6, 'counter': 352, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.36.df1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.df1.a1', 'outer_equivalence': False, 'perfect': False, '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: 71060124
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 6, 'counter': 353, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.36.dg1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.dg1.a1', 'outer_equivalence': False, 'perfect': False, '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: 71060125
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 6, 'counter': 354, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.36.dh1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.dh1.a1', 'outer_equivalence': False, 'perfect': False, '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: 71060126
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 6, 'counter': 355, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.36.di1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.di1.a1', 'outer_equivalence': False, 'perfect': False, '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: 71060127
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 2, 'counter': 356, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.36.dj1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.dj1.a1', 'outer_equivalence': False, 'perfect': False, '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: 71060128
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 2, 'counter': 357, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.36.dk1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.dk1.a1', 'outer_equivalence': False, 'perfect': False, '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: 71060129
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 9, 'counter': 358, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.36.dl1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.dl1.a1', 'outer_equivalence': False, 'perfect': False, '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: 71060130
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 9, 'counter': 359, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.36.dl1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.dl1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.14', 'subgroup_hash': 14, 'subgroup_order': 36, 'subgroup_tex': 'C_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 71060132
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 9, 'counter': 360, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.36.dm1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.dm1.a1', 'outer_equivalence': False, 'perfect': False, '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: 71060133
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 9, 'counter': 361, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.36.dm1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.dm1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 71060134
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 9, 'counter': 362, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.36.dn1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.dn1.a1', 'outer_equivalence': False, 'perfect': False, '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: 71060135
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 9, 'counter': 363, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.36.dn1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.dn1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 71060136
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 3, 'counter': 364, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.36.do1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.do1.a1', 'outer_equivalence': False, 'perfect': False, '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: 71060137
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 3, 'counter': 365, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.36.do1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.do1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 71060138
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 3, 'counter': 366, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.36.do1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.do1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 71060139
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 3, 'counter': 367, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.36.do1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.do1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 71060140
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 9, 'counter': 368, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.36.dp1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.dp1.a1', 'outer_equivalence': False, 'perfect': False, '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: 71060141
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 9, 'counter': 369, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.36.dp1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.dp1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 71060143
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 9, 'counter': 370, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.36.dq1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.dq1.a1', 'outer_equivalence': False, 'perfect': False, '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: 71060144
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 9, 'counter': 371, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.36.dq1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.dq1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 71060145
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 372, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.36.dr1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.dr1.a1', 'outer_equivalence': False, 'perfect': False, '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: 71060146
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 373, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.36.dr1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.dr1.a2', 'outer_equivalence': False, 'perfect': False, '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: 71060147
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 374, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.36.dr1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.dr1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 71060148
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 375, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.36.dr1.b2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.dr1.b2', 'outer_equivalence': False, 'perfect': False, '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: 71060149
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 9, 'counter': 376, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.36.ds1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.ds1.a1', 'outer_equivalence': False, 'perfect': False, '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: 71060150
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 9, 'counter': 377, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.36.ds1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.ds1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.13', 'subgroup_hash': 13, 'subgroup_order': 36, 'subgroup_tex': 'C_6:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 71060151
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 18, 'counter': 378, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.36.dt1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.dt1.a1', 'outer_equivalence': False, 'perfect': False, '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: 71060152
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 18, 'counter': 379, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.36.dt1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.dt1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 71060154
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 18, 'counter': 380, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.36.du1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.du1.a1', 'outer_equivalence': False, 'perfect': False, '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: 71060155
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 18, 'counter': 381, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.36.du1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.du1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 71060156
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 6, 'counter': 382, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.36.dv1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.dv1.a1', 'outer_equivalence': False, 'perfect': False, '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: 71060157
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 6, 'counter': 383, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.36.dv1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.dv1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 71060158
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 6, 'counter': 384, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.36.dv1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.dv1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 71060159
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 6, 'counter': 385, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.36.dv1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.dv1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 71060160
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 18, 'counter': 386, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.36.dw1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.dw1.a1', 'outer_equivalence': False, 'perfect': False, '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: 71060161
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 18, 'counter': 387, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.36.dw1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.dw1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 71060162
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 18, 'counter': 388, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.36.dx1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.dx1.a1', 'outer_equivalence': False, 'perfect': False, '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: 71060163
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 18, 'counter': 389, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.36.dx1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.dx1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 71060165
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 18, 'counter': 390, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.36.dy1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.dy1.a1', 'outer_equivalence': False, 'perfect': False, '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: 71060166
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 18, 'counter': 391, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.36.dy1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.dy1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 71060167
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 18, 'counter': 392, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.36.dz1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.dz1.a1', 'outer_equivalence': False, 'perfect': False, '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: 71060168
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 18, 'counter': 393, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.36.dz1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.dz1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 71060169
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 6, 'counter': 394, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.36.ea1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.ea1.a1', 'outer_equivalence': False, 'perfect': False, '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: 71060170
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 6, 'counter': 395, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.36.ea1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.ea1.a2', 'outer_equivalence': False, 'perfect': False, '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: 71060171
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 6, 'counter': 396, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.36.ea1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.ea1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 71060172
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 6, 'counter': 397, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.36.ea1.b2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.ea1.b2', 'outer_equivalence': False, 'perfect': False, '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: 71060173
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 324, 'characteristic': True, 'core_order': 27, 'counter': 398, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1296.3190.48.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': '48.38', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 38, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 48, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3\\times D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 71060174
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 324, 'characteristic': True, 'core_order': 27, 'counter': 399, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1296.3190.48.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '48.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '48.36', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 36, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 48, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times D_{12}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 71060177
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 324, 'characteristic': True, 'core_order': 27, 'counter': 400, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1296.3190.48.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '48.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '48.43', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 43, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 48, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6:D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 71060178
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': True, 'core_order': 27, 'counter': 401, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1296.3190.48.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '48.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '48.45', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 45, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 48, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6\\times D_4', 'simple': False, 'solvable': True, 'special_labels': ['L2'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 71060179
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': False, 'core_order': 9, 'counter': 402, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.48.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 71060180
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': False, 'core_order': 9, 'counter': 403, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.48.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 71060181
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': False, 'core_order': 9, 'counter': 404, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.48.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 71060182
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': False, 'core_order': 3, 'counter': 405, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.48.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.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': 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': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 71060183
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': False, 'core_order': 9, 'counter': 406, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.48.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.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': 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': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 71060184
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': False, 'core_order': 9, 'counter': 407, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.48.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.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': 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': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 71060185
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': False, 'core_order': 3, 'counter': 408, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.48.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.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': 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': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 71060186
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': False, 'core_order': 9, 'counter': 409, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.48.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.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': 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': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 71060188
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': False, 'core_order': 3, 'counter': 410, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.48.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.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': 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': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 71060189
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': False, 'core_order': 3, 'counter': 411, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.48.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.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': 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': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 71060190
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': False, 'core_order': 1, 'counter': 412, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.48.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.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': 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': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 71060191
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 6, 'counter': 413, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.54.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '54.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': 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: 71060192
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 6, 'counter': 414, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.54.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: 71060193
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 2, 'counter': 415, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.54.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '54.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.15', 'subgroup_hash': 15, 'subgroup_order': 24, 'subgroup_tex': 'C_2^2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 71060194
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 12, 'counter': 416, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.54.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 71060195
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 6, 'counter': 417, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.54.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '24.15', 'subgroup_hash': 15, 'subgroup_order': 24, 'subgroup_tex': 'C_2^2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 71060196
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 6, 'counter': 418, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.54.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: 71060197
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 6, 'counter': 419, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.54.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 71060199
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 2, 'counter': 420, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.54.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 71060200
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 6, 'counter': 421, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.54.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '24.9', 'subgroup_hash': 9, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 71060201
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 12, 'counter': 422, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.54.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '24.7', 'subgroup_hash': 7, 'subgroup_order': 24, 'subgroup_tex': 'C_6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 71060202
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 6, 'counter': 423, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.54.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '24.9', 'subgroup_hash': 9, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 71060203
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 2, 'counter': 424, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.54.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '24.9', 'subgroup_hash': 9, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 71060204
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 12, 'counter': 425, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.54.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 71060205
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 12, 'counter': 426, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.54.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 71060206
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 12, 'counter': 427, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.54.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '24.5', 'subgroup_hash': 5, 'subgroup_order': 24, 'subgroup_tex': 'C_4\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 71060207
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 6, 'counter': 428, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.54.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: 71060208
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 6, 'counter': 429, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.54.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: 71060210
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 2, 'counter': 430, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.54.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: 71060211
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 12, 'counter': 431, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.54.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: 71060212
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 6, 'counter': 432, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.54.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: 71060213
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 6, 'counter': 433, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.54.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: 71060214
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 6, 'counter': 434, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.54.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: 71060215
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 2, 'counter': 435, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.54.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: 71060216
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 12, 'counter': 436, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.54.x1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.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': 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: 71060217
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 12, 'counter': 437, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.54.y1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.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': 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: 71060218
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 6, 'counter': 438, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.54.z1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '54.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': 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: 71060219
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 6, 'counter': 439, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.54.ba1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.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': 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: 71060221
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 6, 'counter': 440, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.54.bb1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '54.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': 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: 71060222
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 12, 'counter': 441, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.54.bc1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.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': 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: 71060223
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 6, 'counter': 442, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.54.bd1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.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': 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: 71060224
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 6, 'counter': 443, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.54.be1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.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': 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: 71060225
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 6, 'counter': 444, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.54.bf1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.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': 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: 71060226
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 6, 'counter': 445, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.54.bg1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.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': 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: 71060227
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 2, 'counter': 446, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.54.bh1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.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': 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: 71060228
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 648, 'characteristic': True, 'core_order': 18, 'counter': 447, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1296.3190.72.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '72.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '72.46', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 46, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 72, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3\\times D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 71060229
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 648, 'characteristic': True, 'core_order': 18, 'counter': 448, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1296.3190.72.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '72.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '72.46', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 46, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 72, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3\\times D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 71060230
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 648, 'characteristic': True, 'core_order': 18, 'counter': 449, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1296.3190.72.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '72.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '72.46', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 46, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 72, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3\\times D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 71060232
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 324, 'characteristic': True, 'core_order': 18, 'counter': 450, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1296.3190.72.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '72.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '72.48', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 48, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 72, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6\\times D_6', 'simple': False, 'solvable': True, 'special_labels': ['C5'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 71060233
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 324, 'characteristic': True, 'core_order': 18, 'counter': 451, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1296.3190.72.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '72.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '72.48', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 48, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 72, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6\\times D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 71060234
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 324, 'characteristic': True, 'core_order': 18, 'counter': 452, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1296.3190.72.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '72.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '72.48', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 48, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 72, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6\\times D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 71060235
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': True, 'centralizer_order': 216, 'characteristic': False, 'core_order': 18, 'counter': 453, 'cyclic': False, 'direct': True, 'hall': 0, 'label': '1296.3190.72.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '72.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '72.23', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 23, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 72, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3:D_{12}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 71060236
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': True, 'centralizer_order': 216, 'characteristic': False, 'core_order': 18, 'counter': 454, 'cyclic': False, 'direct': True, 'hall': 0, 'label': '1296.3190.72.g1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '72.g1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '72.23', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 23, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 72, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3:D_{12}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 71060237
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 18, 'counter': 455, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1296.3190.72.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '72.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '72.28', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 28, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 72, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3\\times D_{12}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 71060238
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 18, 'counter': 456, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1296.3190.72.h1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '72.h1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '72.28', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 28, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 72, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3\\times D_{12}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 71060239
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 18, 'counter': 457, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1296.3190.72.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '72.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '72.30', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 30, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 72, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6\\wr C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 71060240
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 18, 'counter': 458, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1296.3190.72.i1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '72.i1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '72.30', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 30, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 72, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6\\wr C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 71060241
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 324, 'characteristic': False, 'core_order': 6, 'counter': 459, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.72.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': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 71060243
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 324, 'characteristic': False, 'core_order': 6, 'counter': 460, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.72.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': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 71060244
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 324, 'characteristic': False, 'core_order': 6, 'counter': 461, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.72.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 71060245
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': False, 'core_order': 6, 'counter': 462, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.72.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: 71060246
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 324, 'characteristic': False, 'core_order': 6, 'counter': 463, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.72.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 71060247
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 324, 'characteristic': False, 'core_order': 6, 'counter': 464, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.72.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 71060248
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': False, 'core_order': 6, 'counter': 465, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.72.p1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 71060249
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': False, 'core_order': 6, 'counter': 466, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.72.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: 71060250
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 324, 'characteristic': False, 'core_order': 6, 'counter': 467, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.72.r1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 71060251
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 324, 'characteristic': False, 'core_order': 6, 'counter': 468, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.72.s1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 71060252
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': False, 'core_order': 6, 'counter': 469, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.72.t1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 71060254
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': False, 'core_order': 6, 'counter': 470, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.72.u1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 71060255
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 324, 'characteristic': False, 'core_order': 6, 'counter': 471, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.72.v1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 71060256
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 324, 'characteristic': False, 'core_order': 6, 'counter': 472, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.72.w1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 71060257
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': False, 'core_order': 6, 'counter': 473, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.72.x1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 71060258
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': False, 'core_order': 6, 'counter': 474, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.72.y1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 71060259
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 324, 'characteristic': False, 'core_order': 2, 'counter': 475, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.72.z1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 71060260
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 324, 'characteristic': False, 'core_order': 2, 'counter': 476, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.72.ba1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 71060261
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': False, 'core_order': 2, 'counter': 477, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.72.bb1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.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': 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: 71060262
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': False, 'core_order': 2, 'counter': 478, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.72.bc1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.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': 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: 71060263
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 324, 'characteristic': False, 'core_order': 2, 'counter': 479, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.72.bd1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.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': 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: 71060265
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': False, 'core_order': 2, 'counter': 480, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.72.be1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.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': 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: 71060266
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': False, 'core_order': 2, 'counter': 481, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.72.bf1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.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': 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: 71060267
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': False, 'core_order': 2, 'counter': 482, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.72.bg1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.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': 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: 71060268
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': False, 'core_order': 2, 'counter': 483, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.72.bh1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.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': 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: 71060269
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': False, 'core_order': 2, 'counter': 484, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.72.bi1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.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': 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: 71060270
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': False, 'core_order': 2, 'counter': 485, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.72.bj1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.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': 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: 71060271
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': False, 'core_order': 2, 'counter': 486, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.72.bk1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.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': 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: 71060272
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': False, 'core_order': 2, 'counter': 487, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.72.bl1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.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': 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: 71060273
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': False, 'core_order': 2, 'counter': 488, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.72.bm1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.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': 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: 71060274
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 216, 'characteristic': False, 'core_order': 9, 'counter': 489, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.72.bn1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.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': 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: 71060276
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 216, 'characteristic': False, 'core_order': 9, 'counter': 490, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.72.bn1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.bn1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 71060277
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 216, 'characteristic': False, 'core_order': 9, 'counter': 491, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.72.bo1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.bo1.a1', 'outer_equivalence': False, 'perfect': False, '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: 71060278
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 216, 'characteristic': False, 'core_order': 9, 'counter': 492, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.72.bo1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.bo1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 71060279
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 3, 'counter': 493, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.72.bp1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.bp1.a1', 'outer_equivalence': False, 'perfect': False, '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: 71060280
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 3, 'counter': 494, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.72.bp1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.bp1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 71060281
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 9, 'counter': 495, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.72.bq1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.bq1.a1', 'outer_equivalence': False, 'perfect': False, '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: 71060282
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 9, 'counter': 496, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.72.bq1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.bq1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 71060283
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 3, 'counter': 497, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.72.br1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.br1.a1', 'outer_equivalence': False, 'perfect': False, '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: 71060284
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 3, 'counter': 498, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.72.br1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.br1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 71060285
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 3, 'counter': 499, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.72.bs1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.bs1.a1', 'outer_equivalence': False, 'perfect': False, '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: 71060288
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 3, 'counter': 500, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.72.bs1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.bs1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 71060289
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 1, 'counter': 501, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.72.bt1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.bt1.a1', 'outer_equivalence': False, 'perfect': False, '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: 71060290
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 1, 'counter': 502, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.72.bt1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.bt1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 71060291
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 6, 'counter': 503, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.72.bu1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.bu1.a1', 'outer_equivalence': False, 'perfect': False, '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: 71060292
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 6, 'counter': 504, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.72.bu1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.bu1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 71060293
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 6, 'counter': 505, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.72.bv1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.bv1.a1', 'outer_equivalence': False, 'perfect': False, '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: 71060294
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 6, 'counter': 506, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.72.bv1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.bv1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 71060295
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 6, 'counter': 507, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.72.bw1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.bw1.a1', 'outer_equivalence': False, 'perfect': False, '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: 71060296
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 6, 'counter': 508, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.72.bw1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.bw1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 71060297
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 6, 'counter': 509, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.72.bx1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.bx1.a1', 'outer_equivalence': False, 'perfect': False, '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: 71060299
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 6, 'counter': 510, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.72.bx1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.bx1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 71060300
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 216, 'characteristic': False, 'core_order': 9, 'counter': 511, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.72.by1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.by1.a1', 'outer_equivalence': False, 'perfect': False, '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: 71060301
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 9, 'counter': 512, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.72.bz1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.bz1.a1', 'outer_equivalence': False, 'perfect': False, '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: 71060302
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 3, 'counter': 513, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.72.ca1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.ca1.a1', 'outer_equivalence': False, 'perfect': False, '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: 71060303
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 9, 'counter': 514, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.72.cb1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.cb1.a1', 'outer_equivalence': False, 'perfect': False, '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: 71060304
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 3, 'counter': 515, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.72.cc1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.cc1.a1', 'outer_equivalence': False, 'perfect': False, '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: 71060305
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 3, 'counter': 516, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.72.cd1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.cd1.a1', 'outer_equivalence': False, 'perfect': False, '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: 71060306
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 3, 'counter': 517, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.72.cd1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.cd1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 71060307
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 1, 'counter': 518, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.72.ce1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.ce1.a1', 'outer_equivalence': False, 'perfect': False, '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: 71060308
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 1, 'counter': 519, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.72.ce1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.ce1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 71060310
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 9, 'counter': 520, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.72.cf1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.cf1.a1', 'outer_equivalence': False, 'perfect': False, '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: 71060311
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 9, 'counter': 521, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.72.cg1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.cg1.a1', 'outer_equivalence': False, 'perfect': False, '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: 71060312
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 9, 'counter': 522, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.72.ch1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ch1.a1', 'outer_equivalence': False, 'perfect': False, '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: 71060313
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 3, 'counter': 523, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.72.ci1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ci1.a1', 'outer_equivalence': False, 'perfect': False, '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: 71060314
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 3, 'counter': 524, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.72.ci1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ci1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 71060315
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 3, 'counter': 525, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.72.cj1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.cj1.a1', 'outer_equivalence': False, 'perfect': False, '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: 71060316
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 3, 'counter': 526, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.72.ck1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ck1.a1', 'outer_equivalence': False, 'perfect': False, '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: 71060317
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 3, 'counter': 527, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.72.cl1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.cl1.a1', 'outer_equivalence': False, 'perfect': False, '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: 71060318
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 3, 'counter': 528, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.72.cl1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.cl1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 71060319
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 9, 'counter': 529, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.72.cm1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.cm1.a1', 'outer_equivalence': False, 'perfect': False, '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: 71060321
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 9, 'counter': 530, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.72.cn1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.cn1.a1', 'outer_equivalence': False, 'perfect': False, '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: 71060322
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 9, 'counter': 531, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.72.co1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.co1.a1', 'outer_equivalence': False, 'perfect': False, '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: 71060323
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 3, 'counter': 532, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.72.cp1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.cp1.a1', 'outer_equivalence': False, 'perfect': False, '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: 71060324
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 9, 'counter': 533, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.72.cq1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.cq1.a1', 'outer_equivalence': False, 'perfect': False, '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: 71060325
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 9, 'counter': 534, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.72.cr1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.cr1.a1', 'outer_equivalence': False, 'perfect': False, '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: 71060326
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 3, 'counter': 535, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.72.cs1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.cs1.a1', 'outer_equivalence': False, 'perfect': False, '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: 71060327
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 3, 'counter': 536, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.72.ct1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ct1.a1', 'outer_equivalence': False, 'perfect': False, '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: 71060328
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 3, 'counter': 537, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.72.ct1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ct1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 71060329
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 3, 'counter': 538, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.72.cu1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.cu1.a1', 'outer_equivalence': False, 'perfect': False, '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: 71060330
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 3, 'counter': 539, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.72.cu1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.cu1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 71060332
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 540, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.72.cv1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.cv1.a1', 'outer_equivalence': False, 'perfect': False, '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: 71060333
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 541, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.72.cv1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.cv1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 71060334
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 9, 'counter': 542, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.72.cw1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.cw1.a1', 'outer_equivalence': False, 'perfect': False, '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: 71060335
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 9, 'counter': 543, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.72.cx1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.cx1.a1', 'outer_equivalence': False, 'perfect': False, '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: 71060336
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 9, 'counter': 544, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.72.cy1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.cy1.a1', 'outer_equivalence': False, 'perfect': False, '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: 71060337
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 9, 'counter': 545, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.72.cz1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.cz1.a1', 'outer_equivalence': False, 'perfect': False, '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: 71060338
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 3, 'counter': 546, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.72.da1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.da1.a1', 'outer_equivalence': False, 'perfect': False, '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: 71060339
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 3, 'counter': 547, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.72.da1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.da1.a2', 'outer_equivalence': False, 'perfect': False, '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: 71060340
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 9, 'counter': 548, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.72.db1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.db1.a1', 'outer_equivalence': False, 'perfect': False, '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: 71060341
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 3, 'counter': 549, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.72.dc1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.dc1.a1', 'outer_equivalence': False, 'perfect': False, '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: 71060343
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 9, 'counter': 550, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.72.dd1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.dd1.a1', 'outer_equivalence': False, 'perfect': False, '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: 71060344
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 3, 'counter': 551, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.72.de1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.de1.a1', 'outer_equivalence': False, 'perfect': False, '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: 71060345
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 3, 'counter': 552, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.72.df1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.df1.a1', 'outer_equivalence': False, 'perfect': False, '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: 71060346
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 3, 'counter': 553, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.72.df1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.df1.a2', 'outer_equivalence': False, 'perfect': False, '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: 71060347
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 554, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.72.dg1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.dg1.a1', 'outer_equivalence': False, 'perfect': False, '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: 71060348
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 555, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.72.dg1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.dg1.a2', 'outer_equivalence': False, 'perfect': False, '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: 71060349
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 9, 'counter': 556, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.72.dh1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.dh1.a1', 'outer_equivalence': False, 'perfect': False, '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: 71060350
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 9, 'counter': 557, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.72.di1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.di1.a1', 'outer_equivalence': False, 'perfect': False, '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: 71060351
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 9, 'counter': 558, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.72.dj1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.dj1.a1', 'outer_equivalence': False, 'perfect': False, '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: 71060352
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 9, 'counter': 559, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.72.dk1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.dk1.a1', 'outer_equivalence': False, 'perfect': False, '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: 71060354
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 560, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.72.dl1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.dl1.a1', 'outer_equivalence': False, 'perfect': False, '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: 71060355
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 561, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.72.dl1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.dl1.a2', 'outer_equivalence': False, 'perfect': False, '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: 71060356
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 562, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.72.dm1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.dm1.a1', 'outer_equivalence': False, 'perfect': False, '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: 71060357
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 563, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.72.dn1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.dn1.a1', 'outer_equivalence': False, 'perfect': False, '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: 71060358
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 564, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.72.do1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.do1.a1', 'outer_equivalence': False, 'perfect': False, '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: 71060359
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 565, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.72.do1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.do1.a2', 'outer_equivalence': False, 'perfect': False, '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: 71060360
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 9, 'counter': 566, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.72.dp1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.dp1.a1', 'outer_equivalence': False, 'perfect': False, '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: 71060361
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 9, 'counter': 567, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.72.dq1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.dq1.a1', 'outer_equivalence': False, 'perfect': False, '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: 71060362
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 568, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.72.dr1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.dr1.a1', 'outer_equivalence': False, 'perfect': False, '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: 71060363
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 9, 'counter': 569, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.72.ds1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ds1.a1', 'outer_equivalence': False, 'perfect': False, '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: 71060365
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 570, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.72.dt1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.dt1.a1', 'outer_equivalence': False, 'perfect': False, '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: 71060366
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 571, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.72.du1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.du1.a1', 'outer_equivalence': False, 'perfect': False, '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: 71060367
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 572, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.72.du1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.du1.a2', 'outer_equivalence': False, 'perfect': False, '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: 71060368
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 573, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.72.dv1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.dv1.a1', 'outer_equivalence': False, 'perfect': False, '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: 71060369
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 574, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.72.dv1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.dv1.a2', 'outer_equivalence': False, 'perfect': False, '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: 71060370
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 2, 'counter': 575, 'cyclic': False, 'direct': None, 'hall': 2, 'label': '1296.3190.81.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: 71060371
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': True, 'centralizer_order': 216, 'characteristic': True, 'core_order': 12, 'counter': 576, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1296.3190.108.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 71060372
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': True, 'core_order': 12, 'counter': 577, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1296.3190.108.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '108.b1.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': True, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 71060373
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': True, 'core_order': 12, 'counter': 578, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1296.3190.108.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '108.c1.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': True, '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: 71060374
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 432, 'characteristic': False, 'core_order': 6, 'counter': 579, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.108.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: 71060376
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 216, 'characteristic': False, 'core_order': 6, 'counter': 580, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.108.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: 71060377
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 216, 'characteristic': False, 'core_order': 6, 'counter': 581, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.108.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 71060378
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 216, 'characteristic': False, 'core_order': 2, 'counter': 582, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.108.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: 71060379
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 216, 'characteristic': False, 'core_order': 2, 'counter': 583, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.108.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: 71060380
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 2, 'counter': 584, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.108.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: 71060381
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 2, 'counter': 585, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.108.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 71060382
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 216, 'characteristic': False, 'core_order': 6, 'counter': 586, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.108.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: 71060383
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 216, 'characteristic': False, 'core_order': 6, 'counter': 587, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.108.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: 71060384
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 6, 'counter': 588, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.108.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: 71060385
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 216, 'characteristic': False, 'core_order': 2, 'counter': 589, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.108.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 71060387
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 2, 'counter': 590, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.108.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: 71060388
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 2, 'counter': 591, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.108.p1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 71060389
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 2, 'counter': 592, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.108.q1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 71060390
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 6, 'counter': 593, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.108.r1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 71060391
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 6, 'counter': 594, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.108.s1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 71060392
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 2, 'counter': 595, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.108.t1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 71060393
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 6, 'counter': 596, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.108.u1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 71060394
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 6, 'counter': 597, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.108.v1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, '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': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 71060395
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 2, 'counter': 598, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.108.w1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 71060396
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 6, 'counter': 599, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.108.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': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 71060399
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 6, 'counter': 600, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.108.y1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 71060400
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 2, 'counter': 601, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.108.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': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 71060401
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 6, 'counter': 602, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.108.ba1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 71060402
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 6, 'counter': 603, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.108.bb1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 71060403
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 2, 'counter': 604, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.108.bc1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 71060404
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 6, 'counter': 605, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.108.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: 71060405
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 6, 'counter': 606, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.108.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: 71060406
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 6, 'counter': 607, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.108.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: 71060407
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 6, 'counter': 608, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.108.bg1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 71060408
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 2, 'counter': 609, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.108.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: 71060410
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 2, 'counter': 610, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.108.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: 71060411
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 2, 'counter': 611, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.108.bj1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.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': 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: 71060412
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 2, 'counter': 612, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.108.bk1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.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': 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: 71060413
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 216, 'characteristic': False, 'core_order': 6, 'counter': 613, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1296.3190.108.bl1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.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': 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: 71060414
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 6, 'counter': 614, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1296.3190.108.bm1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.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': 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: 71060415
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 6, 'counter': 615, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.108.bn1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.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': 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: 71060416
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 216, 'characteristic': False, 'core_order': 6, 'counter': 616, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1296.3190.108.bo1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.bo1.a1', 'outer_equivalence': False, 'perfect': False, '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: 71060417
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 6, 'counter': 617, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1296.3190.108.bp1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.bp1.a1', 'outer_equivalence': False, 'perfect': False, '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: 71060418
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 6, 'counter': 618, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1296.3190.108.bq1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.bq1.a1', 'outer_equivalence': False, 'perfect': False, '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: 71060419
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 6, 'counter': 619, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.108.br1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.br1.a1', 'outer_equivalence': False, 'perfect': False, '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: 71060421
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 216, 'characteristic': False, 'core_order': 2, 'counter': 620, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1296.3190.108.bs1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.bs1.a1', 'outer_equivalence': False, 'perfect': False, '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: 71060422
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 2, 'counter': 621, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1296.3190.108.bt1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.bt1.a1', 'outer_equivalence': False, 'perfect': False, '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: 71060423
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 2, 'counter': 622, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1296.3190.108.bu1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.bu1.a1', 'outer_equivalence': False, 'perfect': False, '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: 71060424
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 2, 'counter': 623, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.108.bv1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.bv1.a1', 'outer_equivalence': False, 'perfect': False, '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: 71060425
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 2, 'counter': 624, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1296.3190.108.bw1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.bw1.a1', 'outer_equivalence': False, 'perfect': False, '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: 71060426
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 2, 'counter': 625, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1296.3190.108.bx1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.bx1.a1', 'outer_equivalence': False, 'perfect': False, '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: 71060427
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 3, 'counter': 626, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.108.by1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.by1.a1', 'outer_equivalence': False, 'perfect': False, '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: 71060428
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 3, 'counter': 627, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.108.by1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.by1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 71060429
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 3, 'counter': 628, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.108.bz1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.bz1.a1', 'outer_equivalence': False, 'perfect': False, '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: 71060430
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 3, 'counter': 629, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.108.bz1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.bz1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 71060432
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 1, 'counter': 630, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.108.ca1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.ca1.a1', 'outer_equivalence': False, 'perfect': False, '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: 71060433
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 1, 'counter': 631, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.108.ca1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.ca1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 71060434
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 1, 'counter': 632, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.108.ca1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.ca1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 71060435
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 1, 'counter': 633, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.108.ca1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.ca1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 71060436
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 3, 'counter': 634, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.108.cb1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.cb1.a1', 'outer_equivalence': False, 'perfect': False, '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: 71060437
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 3, 'counter': 635, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.108.cb1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.cb1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 71060438
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 3, 'counter': 636, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.108.cc1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.cc1.a1', 'outer_equivalence': False, 'perfect': False, '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: 71060439
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 3, 'counter': 637, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.108.cc1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.cc1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 71060440
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 638, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.108.cd1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.cd1.a1', 'outer_equivalence': False, 'perfect': False, '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: 71060441
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 639, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.108.cd1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.cd1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 71060443
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 640, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.108.ce1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.ce1.a1', 'outer_equivalence': False, 'perfect': False, '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: 71060444
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 641, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.108.ce1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.ce1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 71060445
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 642, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.108.cf1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.cf1.a1', 'outer_equivalence': False, 'perfect': False, '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: 71060446
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 643, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.108.cf1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.cf1.a2', 'outer_equivalence': False, 'perfect': False, '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: 71060447
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 644, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.108.cf1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.cf1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 71060448
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 645, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.108.cf1.b2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.cf1.b2', 'outer_equivalence': False, 'perfect': False, '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: 71060449
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 6, 'counter': 646, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.108.cg1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.cg1.a1', 'outer_equivalence': False, 'perfect': False, '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: 71060450
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 6, 'counter': 647, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.108.cg1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.cg1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 71060451
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 6, 'counter': 648, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.108.ch1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.ch1.a1', 'outer_equivalence': False, 'perfect': False, '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: 71060452
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 6, 'counter': 649, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.108.ch1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.ch1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 71060454
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 648, 'characteristic': True, 'core_order': 9, 'counter': 650, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1296.3190.144.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': '144.144', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 144, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 144, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3\\times D_{12}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 71060455
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 648, 'characteristic': True, 'core_order': 9, 'counter': 651, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1296.3190.144.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': '144.153', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 153, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 144, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_6:D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 71060456
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 648, 'characteristic': True, 'core_order': 9, 'counter': 652, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1296.3190.144.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '144.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '144.151', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 151, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 144, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6:D_{12}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 71060457
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 324, 'characteristic': True, 'core_order': 9, 'counter': 653, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1296.3190.144.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '144.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '144.162', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 162, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 144, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{12}:D_6', 'simple': False, 'solvable': True, 'special_labels': ['C6'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 71060458
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 324, 'characteristic': True, 'core_order': 9, 'counter': 654, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1296.3190.144.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '144.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '144.160', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 160, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 144, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6\\times D_{12}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 71060459
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 324, 'characteristic': True, 'core_order': 9, 'counter': 655, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1296.3190.144.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '144.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '144.167', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 167, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 144, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6^2:C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 71060460
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 324, 'characteristic': False, 'core_order': 3, 'counter': 656, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.144.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': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 71060461
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 324, 'characteristic': False, 'core_order': 3, 'counter': 657, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.144.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: 71060462
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 324, 'characteristic': False, 'core_order': 3, 'counter': 658, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.144.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: 71060463
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': False, 'core_order': 3, 'counter': 659, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.144.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 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: 71060465
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 324, 'characteristic': False, 'core_order': 3, 'counter': 660, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.144.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 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: 71060466
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 324, 'characteristic': False, 'core_order': 3, 'counter': 661, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.144.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 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: 71060467
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': False, 'core_order': 3, 'counter': 662, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.144.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 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: 71060468
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': False, 'core_order': 3, 'counter': 663, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.144.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 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: 71060469
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 324, 'characteristic': False, 'core_order': 3, 'counter': 664, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.144.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 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: 71060470
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 324, 'characteristic': False, 'core_order': 3, 'counter': 665, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.144.p1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 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: 71060471
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': False, 'core_order': 3, 'counter': 666, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.144.q1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 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: 71060472
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': False, 'core_order': 3, 'counter': 667, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.144.r1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 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: 71060473
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 324, 'characteristic': False, 'core_order': 3, 'counter': 668, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.144.s1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 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: 71060474
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 324, 'characteristic': False, 'core_order': 3, 'counter': 669, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.144.t1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 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: 71060476
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': False, 'core_order': 3, 'counter': 670, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.144.u1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 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: 71060477
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': False, 'core_order': 3, 'counter': 671, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.144.v1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 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: 71060478
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 324, 'characteristic': False, 'core_order': 1, 'counter': 672, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.144.w1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 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: 71060479
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 324, 'characteristic': False, 'core_order': 1, 'counter': 673, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.144.x1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 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: 71060480
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': False, 'core_order': 1, 'counter': 674, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.144.y1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 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: 71060481
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': False, 'core_order': 1, 'counter': 675, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.144.z1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 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: 71060482
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 324, 'characteristic': False, 'core_order': 1, 'counter': 676, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.144.ba1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 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: 71060483
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': False, 'core_order': 1, 'counter': 677, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.144.bb1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 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: 71060484
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': False, 'core_order': 1, 'counter': 678, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.144.bc1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 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: 71060485
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': False, 'core_order': 1, 'counter': 679, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.144.bd1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 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: 71060487
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': False, 'core_order': 1, 'counter': 680, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.144.be1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 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: 71060488
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': False, 'core_order': 1, 'counter': 681, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.144.bf1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 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: 71060489
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': False, 'core_order': 1, 'counter': 682, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.144.bg1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 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: 71060490
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': False, 'core_order': 1, 'counter': 683, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.144.bh1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 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: 71060491
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': False, 'core_order': 1, 'counter': 684, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.144.bi1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 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: 71060492
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': False, 'core_order': 1, 'counter': 685, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.144.bj1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 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: 71060493
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 2, 'counter': 686, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.162.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: 71060494
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 2, 'counter': 687, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.162.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 71060495
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 2, 'counter': 688, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.162.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': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 71060496
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 2, 'counter': 689, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.162.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: 71060498
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 2, 'counter': 690, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.162.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 71060499
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 2, 'counter': 691, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.162.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: 71060500
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 2, 'counter': 692, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.162.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: 71060501
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': True, 'central_factor': False, 'centralizer_order': 1296, 'characteristic': True, 'core_order': 6, 'counter': 693, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '1296.3190.216.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '216.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '216.162', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 162, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 216, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3^3', 'simple': False, 'solvable': True, 'special_labels': ['Z', 'U0'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 71060502
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 648, 'characteristic': True, 'core_order': 6, 'counter': 694, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '1296.3190.216.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '216.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '216.170', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 170, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 216, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6\\times S_3^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 71060503
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 648, 'characteristic': True, 'core_order': 6, 'counter': 695, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '1296.3190.216.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '216.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '216.170', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 170, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 216, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6\\times S_3^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 71060504
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 648, 'characteristic': True, 'core_order': 6, 'counter': 696, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '1296.3190.216.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '216.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '216.170', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 170, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 216, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6\\times S_3^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 71060505
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': True, 'centralizer_order': 216, 'characteristic': False, 'core_order': 6, 'counter': 697, 'cyclic': False, 'direct': True, 'hall': 0, 'label': '1296.3190.216.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '216.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '216.122', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 122, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 216, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3^2:D_{12}', '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: 71060506
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': True, 'centralizer_order': 216, 'characteristic': False, 'core_order': 6, 'counter': 698, 'cyclic': False, 'direct': True, 'hall': 0, 'label': '1296.3190.216.e1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '216.e1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '216.122', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 122, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 216, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3^2:D_{12}', '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: 71060507
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 648, 'characteristic': False, 'core_order': 2, 'counter': 699, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1296.3190.216.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: 71060510
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 648, 'characteristic': False, 'core_order': 2, 'counter': 700, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1296.3190.216.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: 71060511
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 648, 'characteristic': False, 'core_order': 2, 'counter': 701, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1296.3190.216.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: 71060512
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 324, 'characteristic': False, 'core_order': 2, 'counter': 702, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1296.3190.216.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: 71060513
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 324, 'characteristic': False, 'core_order': 2, 'counter': 703, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1296.3190.216.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: 71060514
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 324, 'characteristic': False, 'core_order': 2, 'counter': 704, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1296.3190.216.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: 71060515
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 324, 'characteristic': False, 'core_order': 2, 'counter': 705, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1296.3190.216.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: 71060516
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 324, 'characteristic': False, 'core_order': 2, 'counter': 706, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1296.3190.216.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: 71060517
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 324, 'characteristic': False, 'core_order': 2, 'counter': 707, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1296.3190.216.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 71060518
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': False, 'core_order': 2, 'counter': 708, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1296.3190.216.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: 71060519
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': False, 'core_order': 2, 'counter': 709, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1296.3190.216.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: 71060521
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 432, 'characteristic': False, 'core_order': 3, 'counter': 710, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1296.3190.216.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: 71060522
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 432, 'characteristic': False, 'core_order': 3, 'counter': 711, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1296.3190.216.q1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.q1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 71060523
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 216, 'characteristic': False, 'core_order': 3, 'counter': 712, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1296.3190.216.r1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 71060524
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 216, 'characteristic': False, 'core_order': 3, 'counter': 713, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1296.3190.216.r1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.r1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 71060525
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 216, 'characteristic': False, 'core_order': 3, 'counter': 714, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1296.3190.216.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: 71060526
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 216, 'characteristic': False, 'core_order': 3, 'counter': 715, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1296.3190.216.s1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.s1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 71060527
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 216, 'characteristic': False, 'core_order': 1, 'counter': 716, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1296.3190.216.t1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 71060528
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 216, 'characteristic': False, 'core_order': 1, 'counter': 717, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1296.3190.216.t1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.t1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 71060529
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 216, 'characteristic': False, 'core_order': 1, 'counter': 718, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1296.3190.216.u1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 71060530
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 216, 'characteristic': False, 'core_order': 1, 'counter': 719, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1296.3190.216.u1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.u1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 71060532
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 1, 'counter': 720, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1296.3190.216.v1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 71060533
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 1, 'counter': 721, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1296.3190.216.v1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.v1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 71060534
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 1, 'counter': 722, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1296.3190.216.w1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.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': 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: 71060535
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 1, 'counter': 723, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1296.3190.216.w1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.w1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 71060536
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 216, 'characteristic': False, 'core_order': 3, 'counter': 724, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1296.3190.216.x1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.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': 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: 71060537
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 216, 'characteristic': False, 'core_order': 3, 'counter': 725, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1296.3190.216.y1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.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': 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: 71060538
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 3, 'counter': 726, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1296.3190.216.z1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.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': 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: 71060539
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 216, 'characteristic': False, 'core_order': 1, 'counter': 727, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1296.3190.216.ba1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.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': 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: 71060540
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 216, 'characteristic': False, 'core_order': 1, 'counter': 728, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1296.3190.216.ba1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.ba1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 71060541
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 1, 'counter': 729, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1296.3190.216.bb1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.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': 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: 71060543
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 1, 'counter': 730, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1296.3190.216.bc1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.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': 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: 71060544
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 1, 'counter': 731, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1296.3190.216.bd1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.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': 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: 71060545
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 1, 'counter': 732, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1296.3190.216.bd1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.bd1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 71060546
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 3, 'counter': 733, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.216.be1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.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': 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: 71060547
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 3, 'counter': 734, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1296.3190.216.bf1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.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': 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: 71060548
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 3, 'counter': 735, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1296.3190.216.bg1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.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': 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: 71060549
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 1, 'counter': 736, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1296.3190.216.bh1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.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': 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: 71060550
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 1, 'counter': 737, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1296.3190.216.bh1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.bh1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 71060551
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 3, 'counter': 738, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.216.bi1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.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': 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: 71060552
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 3, 'counter': 739, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.216.bj1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.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': 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: 71060554
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 740, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.216.bk1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.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': 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: 71060555
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 3, 'counter': 741, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1296.3190.216.bl1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.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': 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: 71060556
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 3, 'counter': 742, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1296.3190.216.bm1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.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': 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: 71060557
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1, 'counter': 743, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1296.3190.216.bn1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.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': 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: 71060558
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 3, 'counter': 744, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.216.bo1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.bo1.a1', 'outer_equivalence': False, 'perfect': False, '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: 71060559
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 3, 'counter': 745, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.216.bp1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.bp1.a1', 'outer_equivalence': False, 'perfect': False, '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: 71060560
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1, 'counter': 746, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.216.bq1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.bq1.a1', 'outer_equivalence': False, 'perfect': False, '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: 71060561
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1, 'counter': 747, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.216.bq1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.bq1.a2', 'outer_equivalence': False, 'perfect': False, '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: 71060562
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 3, 'counter': 748, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1296.3190.216.br1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.br1.a1', 'outer_equivalence': False, 'perfect': False, '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: 71060563
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 749, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.216.bs1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.bs1.a1', 'outer_equivalence': False, 'perfect': False, '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: 71060565
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 750, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.216.bt1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.bt1.a1', 'outer_equivalence': False, 'perfect': False, '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: 71060566
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 751, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.216.bu1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.bu1.a1', 'outer_equivalence': False, 'perfect': False, '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: 71060567
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 752, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.216.bv1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.bv1.a1', 'outer_equivalence': False, 'perfect': False, '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: 71060568
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 753, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.216.bv1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.bv1.a2', 'outer_equivalence': False, 'perfect': False, '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: 71060569
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 754, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.216.bw1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.bw1.a1', 'outer_equivalence': False, 'perfect': False, '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: 71060570
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 755, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.216.bx1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.bx1.a1', 'outer_equivalence': False, 'perfect': False, '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: 71060571
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 756, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.216.by1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.by1.a1', 'outer_equivalence': False, 'perfect': False, '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: 71060572
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 757, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.216.by1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '216.by1.a2', 'outer_equivalence': False, 'perfect': False, '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: 71060573
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 432, 'characteristic': False, 'core_order': 2, 'counter': 758, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.324.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '324.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': 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: 71060574
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 216, 'characteristic': False, 'core_order': 2, 'counter': 759, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.324.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: 71060576
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 2, 'counter': 760, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.324.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: 71060577
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 2, 'counter': 761, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.324.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: 71060578
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 2, 'counter': 762, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.324.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: 71060579
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 216, 'characteristic': False, 'core_order': 2, 'counter': 763, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1296.3190.324.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: 71060580
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 2, 'counter': 764, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1296.3190.324.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: 71060581
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 1, 'counter': 765, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.324.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: 71060582
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 1, 'counter': 766, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.324.h1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '324.h1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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: 71060583
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 767, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.324.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: 71060584
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 768, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1296.3190.324.i1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '324.i1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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: 71060585
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': True, 'central_factor': False, 'centralizer_order': 1296, 'characteristic': True, 'core_order': 3, 'counter': 769, 'cyclic': True, 'direct': True, 'hall': 0, 'label': '1296.3190.432.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': '432.598', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 598, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 432, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_6:S_3^2', 'simple': True, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '3.1', 'subgroup_hash': 1, 'subgroup_order': 3, 'subgroup_tex': 'C_3', 'supersolvable': True, 'sylow': 0}
  • id: 71060587
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 648, 'characteristic': True, 'core_order': 3, 'counter': 770, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '1296.3190.432.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': '432.649', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 649, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 432, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{12}:S_3^2', 'simple': True, 'solvable': True, 'special_labels': ['C7'], '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: 71060588
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 648, 'characteristic': True, 'core_order': 3, 'counter': 771, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '1296.3190.432.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '432.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '432.658', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 658, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 432, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6^2:D_6', 'simple': True, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '3.1', 'subgroup_hash': 1, 'subgroup_order': 3, 'subgroup_tex': 'C_3', 'supersolvable': True, 'sylow': 0}
  • id: 71060589
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 648, 'characteristic': True, 'core_order': 3, 'counter': 772, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '1296.3190.432.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '432.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '432.656', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 656, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 432, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6^2.D_6', 'simple': True, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '3.1', 'subgroup_hash': 1, 'subgroup_order': 3, 'subgroup_tex': 'C_3', 'supersolvable': True, 'sylow': 0}
  • id: 71060590
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 648, 'characteristic': False, 'core_order': 1, 'counter': 773, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1296.3190.432.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: 71060591
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 648, 'characteristic': False, 'core_order': 1, 'counter': 774, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1296.3190.432.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.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': 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: 71060592
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 648, 'characteristic': False, 'core_order': 1, 'counter': 775, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1296.3190.432.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.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': 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: 71060593
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 324, 'characteristic': False, 'core_order': 1, 'counter': 776, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1296.3190.432.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.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': 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: 71060594
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 324, 'characteristic': False, 'core_order': 1, 'counter': 777, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1296.3190.432.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.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': 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: 71060595
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 324, 'characteristic': False, 'core_order': 1, 'counter': 778, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1296.3190.432.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.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': 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: 71060596
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 324, 'characteristic': False, 'core_order': 1, 'counter': 779, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1296.3190.432.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.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': 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: 71060598
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 324, 'characteristic': False, 'core_order': 1, 'counter': 780, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1296.3190.432.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.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': 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: 71060599
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 324, 'characteristic': False, 'core_order': 1, 'counter': 781, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1296.3190.432.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.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': 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: 71060600
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': False, 'core_order': 1, 'counter': 782, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1296.3190.432.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.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': 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: 71060601
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': False, 'core_order': 1, 'counter': 783, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1296.3190.432.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.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': 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: 71060602
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': True, 'central_factor': False, 'centralizer_order': 1296, 'characteristic': True, 'core_order': 2, 'counter': 784, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '1296.3190.648.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '648.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '648.731', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 731, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 648, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3\\times S_3^3', 'simple': True, 'solvable': True, 'special_labels': ['Phi'], 'split': False, 'standard_generators': False, 'stem': True, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
  • id: 71060603
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 432, 'characteristic': False, 'core_order': 1, 'counter': 785, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1296.3190.648.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: 71060604
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 432, 'characteristic': False, 'core_order': 1, 'counter': 786, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1296.3190.648.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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: 71060605
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 216, 'characteristic': False, 'core_order': 1, 'counter': 787, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1296.3190.648.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: 71060606
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 1, 'counter': 788, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1296.3190.648.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: 71060607
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 1, 'counter': 789, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1296.3190.648.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: 71060609
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 790, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1296.3190.648.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.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': 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: 71060610
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1296.3190', 'ambient_counter': 3190, 'ambient_order': 1296, 'ambient_tex': 'C_6.S_3^3', 'central': True, 'central_factor': False, 'centralizer_order': 1296, 'characteristic': True, 'core_order': 1, 'counter': 791, 'cyclic': True, 'direct': True, 'hall': 1, 'label': '1296.3190.1296.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': '1296.3190', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3190, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 1296, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6.S_3^3', 'simple': False, 'solvable': True, 'special_labels': ['PC', 'U1', 'D2', 'C8'], '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: 71059842
    {'ambient': '1296.3190', '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': '216.a1.a1', 'complements': ['1296.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': [], 'contains': ['2.a1.a1', '2.b1.a1', '2.c1.a1', '2.d1.a1', '2.e1.a1', '2.f1.a1', '2.g1.a1', '3.a1.a1', '3.b1.a1', '3.c1.a1', '3.d1.a1'], 'core': '1.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4324, 5324, 6852, 4876, 4574, 5659, 6466, 5157], 'generators': [3, 216, 12, 18, 2, 432, 144, 108], 'label': '1296.3190.1.a1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '1.a1.a1', 'normal_contained_in': [], 'normal_contains': ['2.a1.a1', '2.b1.a1', '2.c1.a1', '2.d1.a1', '2.e1.a1', '2.f1.a1', '2.g1.a1', '3.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '1.a1.a1', 'projective_image': '216.162', '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': '216.162'}
  • id: 71059843
    {'ambient': '1296.3190', 'aut_centralizer_order': 2, 'aut_label': '3.b1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '576.8675', 'aut_weyl_index': 6, 'centralizer': '108.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['6.f1.a1', '6.k1.a1', '6.l1.a1', '6.m1.a1', '6.y1.a1', '6.bc1.a1', '6.bd1.a1', '9.a1.a1', '9.b1.a1', '9.c1.a1'], 'core': '6.f1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3707, -1, 7969, -1, 4504, -1, 6785, -1], 'generators': [3, 144, 216, 18, 432, 108, 2], 'label': '1296.3190.3.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': '216.162', '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': '36.10'}
  • id: 71059844
    {'ambient': '1296.3190', 'aut_centralizer_order': 12, 'aut_label': '12.bd1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '144.192', 'aut_weyl_index': 24, 'centralizer': '72.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.c1.a1', '6.o1.a1'], 'contains': ['24.o1.a1', '24.bk1.a1', '24.bk1.b1', '36.g1.a1', '36.bp1.a1', '36.bq1.a1', '36.br1.a1'], 'core': '36.g1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [4933, -1, 3552, -1, 6658, -1, 1384, -1], 'generators': [9, 144, 216, 434, 12], 'label': '1296.3190.12.bd1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '12.bd1.a1', 'projective_image': '648.731', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bd1.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 71059845
    {'ambient': '1296.3190', 'aut_centralizer_order': 24, 'aut_label': '12.be1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '48.51', 'aut_weyl_index': 72, 'centralizer': '72.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.d1.a1', '6.p1.a1', '6.u1.a1', '6.bb1.a1'], 'contains': ['24.b1.a1', '24.bl1.a1', '36.bs1.a1', '36.bt1.a1', '36.bw1.a1', '36.bx1.a1'], 'core': '24.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7029, -1, 5547, -1, 6588, -1, 5680, -1], 'generators': [54, 432, 216, 2, 12], 'label': '1296.3190.12.be1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1.a1', 'old_label': '12.be1.a1', 'projective_image': '216.162', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.be1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 71059846
    {'ambient': '1296.3190', 'aut_centralizer_order': 24, 'aut_label': '12.bf1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '48.51', 'aut_weyl_index': 72, 'centralizer': '72.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.d1.a1', '6.q1.a1', '6.w1.a1', '6.bg1.a1'], 'contains': ['24.c1.a1', '24.bm1.a1', '36.bs1.a1', '36.bu1.a1', '36.by1.a1', '36.bz1.a1'], 'core': '24.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6970, -1, 5758, -1, 6173, -1, 5857, -1], 'generators': [54, 144, 216, 2, 12], 'label': '1296.3190.12.bf1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.d1.a1', 'old_label': '12.bf1.a1', 'projective_image': '216.162', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bf1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 71059847
    {'ambient': '1296.3190', 'aut_centralizer_order': 12, 'aut_label': '12.bg1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '48.51', 'aut_weyl_index': 72, 'centralizer': '72.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.d1.a1', '6.r1.a1'], 'contains': ['24.j1.a1', '24.bn1.a1', '24.bn1.a2', '36.bs1.a1', '36.bv1.a1', '36.ca1.a1', '36.cb1.a1'], 'core': '72.c1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [7187, -1, 4718, -1, 7822, -1, 5562, -1], 'generators': [54, 576, 216, 2, 12], 'label': '1296.3190.12.bg1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.r1.a1', 'old_label': '12.bg1.a1', 'projective_image': '216.162', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bg1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 71059848
    {'ambient': '1296.3190', 'aut_centralizer_order': 12, 'aut_label': '12.bh1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '144.192', 'aut_weyl_index': 24, 'centralizer': '72.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.d1.a1', '6.x1.a1'], 'contains': ['24.l1.a1', '24.bq1.a1', '36.h1.a1', '36.bx1.a1', '36.bz1.a1', '36.cb1.a1'], 'core': '36.h1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [6874, -1, 6358, -1, 5726, -1, 6034, -1], 'generators': [54, 432, 216, 14, 144], 'label': '1296.3190.12.bh1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.a1', 'old_label': '12.bh1.a1', 'projective_image': '648.731', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bh1.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 71059849
    {'ambient': '1296.3190', 'aut_centralizer_order': 8, 'aut_label': '12.bi1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '144.192', 'aut_weyl_index': 24, 'centralizer': '108.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.e1.a1', '6.l1.a1', '6.y1.a1', '6.bd1.a1'], 'contains': ['24.a1.a1', '24.br1.a1', '36.cc1.a1', '36.cd1.a1', '36.cf1.a1', '36.cj1.a1'], 'core': '24.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4107, -1, 8573, -1, 3854, -1, 6777, -1], 'generators': [45, 432, 216, 2, 144], 'label': '1296.3190.12.bi1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '12.bi1.a1', 'projective_image': '216.162', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bi1.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 71059850
    {'ambient': '1296.3190', 'aut_centralizer_order': 8, 'aut_label': '12.bj1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '144.192', 'aut_weyl_index': 24, 'centralizer': '216.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.e1.a1', '6.p1.a1', '6.v1.a1', '6.be1.a1'], 'contains': ['24.b1.a1', '24.bs1.a1', '36.cc1.a1', '36.ce1.a1', '36.cg1.a1', '36.ck1.a1'], 'core': '24.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4464, -1, 7103, -1, 3958, -1, 6460, -1], 'generators': [45, 432, 216, 2, 12], 'label': '1296.3190.12.bj1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1.a1', 'old_label': '12.bj1.a1', 'projective_image': '216.162', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bj1.a1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 71059851
    {'ambient': '1296.3190', 'aut_centralizer_order': 4, 'aut_label': '12.bk1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '144.192', 'aut_weyl_index': 24, 'centralizer': '216.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.e1.a1', '6.bf1.a1'], 'contains': ['24.h1.a1', '24.bt1.a1', '36.cc1.a1', '36.ch1.a1', '36.ci1.a1', '36.cl1.a1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [3175, -1, 9282, -1, 2488, -1, 8426, -1], 'generators': [45, 432, 216, 2, 156], 'label': '1296.3190.12.bk1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.bf1.a1', 'old_label': '12.bk1.a1', 'projective_image': '216.162', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bk1.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 71059852
    {'ambient': '1296.3190', 'aut_centralizer_order': 8, 'aut_label': '12.bl1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '144.192', 'aut_weyl_index': 24, 'centralizer': '216.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.e1.a1', '6.q1.a1', '6.z1.a1', '6.bh1.a1'], 'contains': ['24.c1.a1', '24.bu1.a1', '36.cd1.a1', '36.ce1.a1', '36.ch1.a1', '36.cm1.a1'], 'core': '24.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3834, -1, 7966, -1, 3792, -1, 6408, -1], 'generators': [45, 144, 216, 2, 12], 'label': '1296.3190.12.bl1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.d1.a1', 'old_label': '12.bl1.a1', 'projective_image': '216.162', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bl1.a1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 71059853
    {'ambient': '1296.3190', 'aut_centralizer_order': 4, 'aut_label': '12.bm1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '144.192', 'aut_weyl_index': 24, 'centralizer': '216.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.e1.a1', '6.ba1.a1'], 'contains': ['24.i1.a1', '24.bv1.a1', '36.cd1.a1', '36.cg1.a1', '36.ci1.a1', '36.cn1.a1'], 'core': '72.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2300, -1, 8363, -1, 2612, -1, 7988, -1], 'generators': [45, 144, 216, 2, 444], 'label': '1296.3190.12.bm1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.ba1.a1', 'old_label': '12.bm1.a1', 'projective_image': '216.162', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bm1.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 71059854
    {'ambient': '1296.3190', 'aut_centralizer_order': 2, 'aut_label': '3.c1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '576.8675', 'aut_weyl_index': 6, 'centralizer': '216.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['6.d1.a1', '6.n1.a1', '6.p1.a1', '6.u1.a1', '6.v1.a1', '6.bb1.a1', '6.be1.a1', '9.a1.a1', '9.d1.a1', '9.e1.a1'], 'core': '6.d1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4902, -1, 6015, -1, 4744, -1, 6466, -1], 'generators': [3, 12, 216, 18, 432, 108, 2], 'label': '1296.3190.3.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': '216.162', '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: 71059855
    {'ambient': '1296.3190', 'aut_centralizer_order': 4, 'aut_label': '12.bn1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '144.192', 'aut_weyl_index': 24, 'centralizer': '216.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.e1.a1', '6.r1.a1'], 'contains': ['24.j1.a1', '24.bw1.a1', '24.bw1.a2', '36.ce1.a1', '36.cf1.a1', '36.ci1.a1', '36.co1.a1'], 'core': '72.c1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [5253, -1, 6298, -1, 4876, -1, 6512, -1], 'generators': [45, 576, 216, 2, 12], 'label': '1296.3190.12.bn1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.r1.a1', 'old_label': '12.bn1.a1', 'projective_image': '216.162', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bn1.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 71059856
    {'ambient': '1296.3190', 'aut_centralizer_order': 4, 'aut_label': '12.bo1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '72.49', 'aut_weyl_index': 48, 'centralizer': '216.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.e1.a1'], 'contains': ['24.k1.a1', '24.bx1.a1', '24.bx1.a2', '36.cf1.a1', '36.cg1.a1', '36.ch1.a1', '36.ci1.a1', '36.cp1.a1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [3089, -1, 8928, -1, 2550, -1, 8321, -1], 'generators': [45, 576, 216, 2, 444], 'label': '1296.3190.12.bo1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bo1.a1', 'old_label': '12.bo1.a1', 'projective_image': '216.162', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bo1.a1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 71059857
    {'ambient': '1296.3190', 'aut_centralizer_order': 24, 'aut_label': '12.bp1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '48.51', 'aut_weyl_index': 72, 'centralizer': '36.n1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.g1.a1', '6.m1.a1', '6.y1.a1', '6.bc1.a1'], 'contains': ['24.a1.a1', '36.cq1.a1', '36.cs1.a1', '36.cx1.a1', '36.cz1.a1'], 'core': '24.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [1572, -1, 9024, -1, 1691, -1, 8103, -1], 'generators': [111, 432, 2, 144, 216], 'label': '1296.3190.12.bp1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '12.bp1.a1', 'projective_image': '216.162', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bp1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 71059858
    {'ambient': '1296.3190', 'aut_centralizer_order': 36, 'aut_label': '12.bq1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '48.51', 'aut_weyl_index': 72, 'centralizer': '24.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.f1.a1', '6.bf1.a1'], 'contains': ['24.h1.a1', '36.i1.a1', '36.cw1.a1', '36.db1.a1', '36.dc1.a1'], 'core': '36.i1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1003, -1, 9809, -1, 637, -1, 9562, -1], 'generators': [108, 432, 2, 156, 216], 'label': '1296.3190.12.bq1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.g1.a1', 'old_label': '12.bq1.a1', 'projective_image': '216.162', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bq1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 71059859
    {'ambient': '1296.3190', 'aut_centralizer_order': 72, 'aut_label': '12.br1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '16.14', 'aut_weyl_index': 216, 'centralizer': '12.br1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.f1.a1', '6.s1.a1', '6.w1.a1', '6.bh1.a1'], 'contains': ['24.c1.a1', '36.cr1.a1', '36.ct1.a1', '36.cw1.a1', '36.dd1.a1', '36.df1.a1', '36.dh1.a1', '36.dj1.a1'], 'core': '24.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [551, -1, 8436, -1, 971, -1, 8937, -1], 'generators': [108, 216, 2, 12, 144], 'label': '1296.3190.12.br1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.d1.a1', 'old_label': '12.br1.a1', 'projective_image': '216.162', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.br1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 71059860
    {'ambient': '1296.3190', 'aut_centralizer_order': 24, 'aut_label': '12.bs1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '48.51', 'aut_weyl_index': 72, 'centralizer': '36.cr1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.g1.a1', '6.s1.a1', '6.z1.a1', '6.bg1.a1'], 'contains': ['24.c1.a1', '36.cs1.a1', '36.cu1.a1', '36.de1.a1', '36.di1.a1'], 'core': '24.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [2080, -1, 8223, -1, 1832, -1, 7252, -1], 'generators': [111, 12, 2, 144, 216], 'label': '1296.3190.12.bs1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.d1.a1', 'old_label': '12.bs1.a1', 'projective_image': '216.162', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bs1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 71059861
    {'ambient': '1296.3190', 'aut_centralizer_order': 12, 'aut_label': '12.bt1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '48.51', 'aut_weyl_index': 72, 'centralizer': '72.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.g1.a1', '6.ba1.a1'], 'contains': ['24.i1.a1', '36.cs1.a1', '36.cv1.a1', '36.dg1.a1', '36.dk1.a1'], 'core': '72.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [312, -1, 8967, -1, 1621, -1, 8680, -1], 'generators': [111, 444, 2, 144, 216], 'label': '1296.3190.12.bt1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.ba1.a1', 'old_label': '12.bt1.a1', 'projective_image': '216.162', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bt1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 71059862
    {'ambient': '1296.3190', 'aut_centralizer_order': 36, 'aut_label': '12.bu1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '48.51', 'aut_weyl_index': 72, 'centralizer': '24.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.f1.a1', '6.x1.a1'], 'contains': ['24.l1.a1', '36.j1.a1', '36.da1.a1', '36.dc1.a1', '36.df1.a1'], 'core': '36.j1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [500, -1, 8477, -1, 901, -1, 9016, -1], 'generators': [108, 432, 14, 144, 216], 'label': '1296.3190.12.bu1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.a1', 'old_label': '12.bu1.a1', 'projective_image': '648.731', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bu1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 71059863
    {'ambient': '1296.3190', 'aut_centralizer_order': 36, 'aut_label': '12.bv1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '48.51', 'aut_weyl_index': 72, 'centralizer': '24.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.f1.a1', '6.t1.a1'], 'contains': ['24.m1.a1', '36.k1.a1', '36.cy1.a1', '36.dc1.a1', '36.dh1.a1'], 'core': '36.k1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [951, -1, 9894, -1, 567, -1, 9075, -1], 'generators': [108, 432, 146, 12, 216], 'label': '1296.3190.12.bv1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '12.bv1.a1', 'projective_image': '648.731', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bv1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 71059864
    {'ambient': '1296.3190', 'aut_centralizer_order': 12, 'aut_label': '12.bw1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '144.192', 'aut_weyl_index': 24, 'centralizer': '72.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.g1.a1', '6.t1.a1'], 'contains': ['24.m1.a1', '36.l1.a1', '36.cz1.a1', '36.di1.a1', '36.dk1.a1'], 'core': '36.l1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1664, -1, 9704, -1, 831, -1, 8266, -1], 'generators': [111, 432, 146, 216, 12], 'label': '1296.3190.12.bw1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '12.bw1.a1', 'projective_image': '648.731', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bw1.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 71059865
    {'ambient': '1296.3190', 'aut_centralizer_order': 2, 'aut_label': '3.d1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '576.8675', 'aut_weyl_index': 6, 'centralizer': '216.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['6.a1.a1', '6.q1.a1', '6.s1.a1', '6.w1.a1', '6.z1.a1', '6.bg1.a1', '6.bh1.a1', '9.b1.a1', '9.d1.a1', '9.f1.a1'], 'core': '6.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4324, -1, 6280, -1, 4654, -1, 6391, -1], 'generators': [3, 12, 216, 18, 144, 108, 2], 'label': '1296.3190.3.d1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.d1.a1', 'old_label': '3.d1.a1', 'projective_image': '216.162', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3.d1.a1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 71059866
    {'ambient': '1296.3190', 'aut_centralizer_order': 36, 'aut_label': '12.bx1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '24.14', 'aut_weyl_index': 144, 'centralizer': '24.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.f1.a1'], 'contains': ['24.n1.a1', '36.cy1.a1', '36.da1.a1', '36.db1.a1', '36.dc1.a1', '36.dj1.a1'], 'core': '108.c1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [658, -1, 9768, -1, 275, -1, 9769, -1], 'generators': [108, 432, 146, 156, 216], 'label': '1296.3190.12.bx1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.f1.a1', 'old_label': '12.bx1.a1', 'projective_image': '648.731', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bx1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 71059867
    {'ambient': '1296.3190', 'aut_centralizer_order': 12, 'aut_label': '12.by1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '24.14', 'aut_weyl_index': 144, 'centralizer': '36.m1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.h1.a1', '6.k1.a1'], 'contains': ['24.s1.a1', '24.y1.a1', '24.bf1.a1', '36.dl1.a1', '36.dm1.a1', '36.dn1.a1', '36.do1.a1', '36.do1.b1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [8786, -1, 1569, -1, 8465, -1, 1037, -1], 'generators': [3, 144, 18, 2, 432], 'label': '1296.3190.12.by1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.k1.a1', 'old_label': '12.by1.a1', 'projective_image': '432.598', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.by1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 71059868
    {'ambient': '1296.3190', 'aut_centralizer_order': 12, 'aut_label': '12.by1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '24.14', 'aut_weyl_index': 144, 'centralizer': '36.m1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.h1.b1', '6.k1.a1'], 'contains': ['24.s1.b1', '24.y1.a1', '24.bf1.a1', '36.dl1.b1', '36.dm1.b1', '36.dn1.b1', '36.do1.c1', '36.do1.d1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [8786, -1, 2402, -1, 8465, -1, 1168, -1], 'generators': [219, 144, 18, 2, 432], 'label': '1296.3190.12.by1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.k1.a1', 'old_label': '12.by1.b1', 'projective_image': '432.598', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.by1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 71059869
    {'ambient': '1296.3190', 'aut_centralizer_order': 4, 'aut_label': '12.bz1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '72.46', 'aut_weyl_index': 48, 'centralizer': '108.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.i1.a1', '6.l1.a1'], 'contains': ['24.s1.a1', '24.bo1.a1', '24.br1.a1', '36.dp1.a1', '36.dq1.a1', '36.dr1.a1', '36.dr1.a2', '36.ds1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [9186, -1, 4873, -1, 9021, -1, 3849, -1], 'generators': [3, 432, 54, 2, 144], 'label': '1296.3190.12.bz1.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': '12.bz1.a1', 'projective_image': '432.598', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bz1.a1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 71059870
    {'ambient': '1296.3190', 'aut_centralizer_order': 4, 'aut_label': '12.bz1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '72.46', 'aut_weyl_index': 48, 'centralizer': '108.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.i1.b1', '6.l1.a1'], 'contains': ['24.s1.b1', '24.bo1.a1', '24.br1.a1', '36.dp1.b1', '36.dq1.b1', '36.dr1.b1', '36.dr1.b2', '36.ds1.b1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [9186, -1, 5010, -1, 9021, -1, 4052, -1], 'generators': [219, 432, 54, 2, 144], 'label': '1296.3190.12.bz1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.l1.a1', 'old_label': '12.bz1.b1', 'projective_image': '432.598', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bz1.b1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 71059871
    {'ambient': '1296.3190', 'aut_centralizer_order': 12, 'aut_label': '12.ca1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '24.14', 'aut_weyl_index': 144, 'centralizer': '36.x1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.h1.a1', '6.n1.a1'], 'contains': ['24.e1.a1', '24.x1.a1', '24.bg1.a1', '36.dl1.a1', '36.dt1.a1', '36.du1.a1', '36.dv1.a1', '36.dv1.b1'], 'core': '24.e1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [9104, -1, 980, -1, 8660, -1, 971, -1], 'generators': [3, 12, 18, 2, 432], 'label': '1296.3190.12.ca1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.n1.a1', 'old_label': '12.ca1.a1', 'projective_image': '432.598', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.ca1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 71059872
    {'ambient': '1296.3190', 'aut_centralizer_order': 12, 'aut_label': '12.ca1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '24.14', 'aut_weyl_index': 144, 'centralizer': '36.x1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.h1.b1', '6.n1.a1'], 'contains': ['24.e1.b1', '24.x1.a1', '24.bg1.a1', '36.dl1.b1', '36.dt1.b1', '36.du1.b1', '36.dv1.c1', '36.dv1.d1'], 'core': '24.e1.b1', 'coset_action_label': None, 'count': 6, 'diagramx': [9104, -1, 1033, -1, 8660, -1, 1103, -1], 'generators': [219, 12, 18, 2, 432], 'label': '1296.3190.12.ca1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.n1.a1', 'old_label': '12.ca1.b1', 'projective_image': '432.598', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.ca1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 71059873
    {'ambient': '1296.3190', 'aut_centralizer_order': 12, 'aut_label': '12.cb1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '72.46', 'aut_weyl_index': 48, 'centralizer': '72.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.h1.a1', '6.a1.a1'], 'contains': ['24.f1.a1', '24.z1.a1', '24.bi1.a1', '36.dm1.a1', '36.dt1.a1', '36.dw1.a1'], 'core': '24.f1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8928, -1, 1247, -1, 8592, -1, 1435, -1], 'generators': [3, 144, 18, 2, 12], 'label': '1296.3190.12.cb1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '12.cb1.a1', 'projective_image': '432.598', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.cb1.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 71059874
    {'ambient': '1296.3190', 'aut_centralizer_order': 12, 'aut_label': '12.cb1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '72.46', 'aut_weyl_index': 48, 'centralizer': '72.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.h1.b1', '6.a1.a1'], 'contains': ['24.f1.b1', '24.z1.a1', '24.bi1.a1', '36.dm1.b1', '36.dt1.b1', '36.dw1.b1'], 'core': '24.f1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [8928, -1, 1431, -1, 8592, -1, 1484, -1], 'generators': [219, 144, 18, 2, 12], 'label': '1296.3190.12.cb1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '12.cb1.b1', 'projective_image': '432.598', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.cb1.b1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 71059875
    {'ambient': '1296.3190', 'aut_centralizer_order': 12, 'aut_label': '12.cc1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '72.46', 'aut_weyl_index': 48, 'centralizer': '72.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.h1.a1', '6.b1.a1'], 'contains': ['24.g1.a1', '24.bb1.a1', '24.bj1.a1', '36.dn1.a1', '36.du1.a1', '36.dw1.a1'], 'core': '24.g1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8987, -1, 1381, -1, 8534, -1, 1285, -1], 'generators': [3, 144, 18, 432, 12], 'label': '1296.3190.12.cc1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '12.cc1.a1', 'projective_image': '1296.3190', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.cc1.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 71059876
    {'ambient': '1296.3190', 'aut_centralizer_order': 36, 'aut_label': '4.a1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '96.230', 'aut_weyl_index': 36, 'centralizer': '24.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '2.b1.a1', '2.c1.a1'], 'contains': ['8.a1.a1', '8.b1.a1', '8.b1.b1', '12.a1.a1', '12.b1.a1', '12.c1.a1', '12.q1.a1', '12.r1.a1', '12.s1.a1', '12.t1.a1', '12.u1.a1'], 'core': '4.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6019, 8297, 3660, 2142, 7351, 1530, 2753, 1327], 'generators': [3, 12, 432, 216, 2, 144], 'label': '1296.3190.4.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': ['8.a1.a1', '8.b1.a1', '8.b1.b1', '12.b1.a1', '12.a1.a1', '12.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.a1.a1', 'projective_image': '216.162', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.a1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 71059877
    {'ambient': '1296.3190', 'aut_centralizer_order': 12, 'aut_label': '12.cc1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '72.46', 'aut_weyl_index': 48, 'centralizer': '72.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.h1.b1', '6.b1.a1'], 'contains': ['24.g1.b1', '24.bb1.a1', '24.bj1.a1', '36.dn1.b1', '36.du1.b1', '36.dw1.b1'], 'core': '24.g1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [8987, -1, 1500, -1, 8534, -1, 1334, -1], 'generators': [219, 144, 18, 432, 12], 'label': '1296.3190.12.cc1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '12.cc1.b1', 'projective_image': '1296.3190', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.cc1.b1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 71059878
    {'ambient': '1296.3190', 'aut_centralizer_order': 6, 'aut_label': '12.cd1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '72.46', 'aut_weyl_index': 48, 'centralizer': '72.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.h1.a1', '6.o1.a1'], 'contains': ['24.v1.a1', '24.bd1.a1', '24.bk1.b1', '36.do1.a1', '36.dv1.a1', '36.dw1.a1'], 'core': '72.i1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8533, -1, 594, -1, 8729, -1, 570, -1], 'generators': [3, 144, 18, 434, 12], 'label': '1296.3190.12.cd1.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': '12.cd1.a1', 'projective_image': '1296.3190', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.cd1.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 71059879
    {'ambient': '1296.3190', 'aut_centralizer_order': 6, 'aut_label': '12.cd1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '72.46', 'aut_weyl_index': 48, 'centralizer': '72.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.h1.a1', '6.o1.a1'], 'contains': ['24.v1.a1', '24.bd1.b1', '24.bk1.a1', '36.do1.b1', '36.dv1.b1', '36.dw1.a1'], 'core': '72.i1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8533, -1, 658, -1, 8729, -1, 653, -1], 'generators': [3, 144, 18, 866, 12], 'label': '1296.3190.12.cd1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '12.cd1.b1', 'projective_image': '1296.3190', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.cd1.b1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 71059880
    {'ambient': '1296.3190', 'aut_centralizer_order': 6, 'aut_label': '12.cd1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '72.46', 'aut_weyl_index': 48, 'centralizer': '72.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.h1.b1', '6.o1.a1'], 'contains': ['24.v1.b1', '24.bd1.a1', '24.bk1.a1', '36.do1.c1', '36.dv1.c1', '36.dw1.b1'], 'core': '72.i1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [8533, -1, 757, -1, 8729, -1, 773, -1], 'generators': [219, 144, 18, 434, 12], 'label': '1296.3190.12.cd1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '12.cd1.c1', 'projective_image': '1296.3190', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.cd1.c1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 71059881
    {'ambient': '1296.3190', 'aut_centralizer_order': 6, 'aut_label': '12.cd1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '72.46', 'aut_weyl_index': 48, 'centralizer': '72.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.h1.b1', '6.o1.a1'], 'contains': ['24.v1.b1', '24.bd1.b1', '24.bk1.b1', '36.do1.d1', '36.dv1.d1', '36.dw1.b1'], 'core': '72.i1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [8533, -1, 715, -1, 8729, -1, 719, -1], 'generators': [219, 144, 18, 866, 12], 'label': '1296.3190.12.cd1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '12.cd1.d1', 'projective_image': '1296.3190', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.cd1.d1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 71059882
    {'ambient': '1296.3190', 'aut_centralizer_order': 4, 'aut_label': '12.ce1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '72.46', 'aut_weyl_index': 48, 'centralizer': '216.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.i1.a1', '6.p1.a1'], 'contains': ['24.e1.a1', '24.bl1.a1', '24.bs1.a1', '36.dp1.a1', '36.dx1.a1', '36.dy1.a1'], 'core': '24.e1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [9614, -1, 3179, -1, 9311, -1, 3569, -1], 'generators': [3, 432, 54, 2, 12], 'label': '1296.3190.12.ce1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.p1.a1', 'old_label': '12.ce1.a1', 'projective_image': '432.598', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.ce1.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 71059883
    {'ambient': '1296.3190', 'aut_centralizer_order': 4, 'aut_label': '12.ce1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '72.46', 'aut_weyl_index': 48, 'centralizer': '216.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.i1.b1', '6.p1.a1'], 'contains': ['24.e1.b1', '24.bl1.a1', '24.bs1.a1', '36.dp1.b1', '36.dx1.b1', '36.dy1.b1'], 'core': '24.e1.b1', 'coset_action_label': None, 'count': 6, 'diagramx': [9614, -1, 3442, -1, 9311, -1, 3742, -1], 'generators': [219, 432, 54, 2, 12], 'label': '1296.3190.12.ce1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.p1.a1', 'old_label': '12.ce1.b1', 'projective_image': '432.598', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.ce1.b1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 71059884
    {'ambient': '1296.3190', 'aut_centralizer_order': 4, 'aut_label': '12.cf1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '72.46', 'aut_weyl_index': 48, 'centralizer': '216.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.i1.a1', '6.q1.a1'], 'contains': ['24.f1.a1', '24.bm1.a1', '24.bu1.a1', '36.dq1.a1', '36.dx1.a1', '36.dz1.a1'], 'core': '24.f1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [9043, -1, 3476, -1, 9252, -1, 3466, -1], 'generators': [3, 144, 54, 2, 12], 'label': '1296.3190.12.cf1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.q1.a1', 'old_label': '12.cf1.a1', 'projective_image': '432.598', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.cf1.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 71059885
    {'ambient': '1296.3190', 'aut_centralizer_order': 4, 'aut_label': '12.cf1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '72.46', 'aut_weyl_index': 48, 'centralizer': '216.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.i1.b1', '6.q1.a1'], 'contains': ['24.f1.b1', '24.bm1.a1', '24.bu1.a1', '36.dq1.b1', '36.dx1.b1', '36.dz1.b1'], 'core': '24.f1.b1', 'coset_action_label': None, 'count': 6, 'diagramx': [9043, -1, 3614, -1, 9252, -1, 3651, -1], 'generators': [219, 144, 54, 2, 12], 'label': '1296.3190.12.cf1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.q1.a1', 'old_label': '12.cf1.b1', 'projective_image': '432.598', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.cf1.b1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 71059886
    {'ambient': '1296.3190', 'aut_centralizer_order': 2, 'aut_label': '12.cg1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '72.46', 'aut_weyl_index': 48, 'centralizer': '216.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.i1.a1', '6.r1.a1'], 'contains': ['24.t1.a1', '24.bn1.a1', '24.bw1.a1', '36.dr1.a1', '36.dx1.a1', '36.ea1.a1'], 'core': '72.g1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [9751, -1, 3107, -1, 9745, -1, 3952, -1], 'generators': [3, 576, 54, 2, 12], 'label': '1296.3190.12.cg1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.r1.a1', 'old_label': '12.cg1.a1', 'projective_image': '432.598', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.cg1.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 71059887
    {'ambient': '1296.3190', 'aut_centralizer_order': 36, 'aut_label': '4.b1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '96.230', 'aut_weyl_index': 36, 'centralizer': '24.b1.a1', 'complements': ['324.i1.a1', '324.i1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '2.d1.a1', '2.e1.a1'], 'contains': ['8.a1.a1', '8.c1.a1', '12.d1.a1', '12.e1.a1', '12.f1.a1', '12.v1.a1', '12.w1.a1', '12.x1.a1', '12.y1.a1', '12.z1.a1'], 'core': '4.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3483, 4991, 6826, 6453, 4107, 5392, 5298, 4817], 'generators': [18, 144, 432, 216, 2, 12], 'label': '1296.3190.4.b1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.b1.a1', 'normal_contained_in': ['2.a1.a1', '2.d1.a1', '2.e1.a1'], 'normal_contains': ['8.a1.a1', '12.d1.a1', '12.e1.a1', '12.f1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.b1.a1', 'projective_image': '216.162', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.b1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 71059888
    {'ambient': '1296.3190', 'aut_centralizer_order': 2, 'aut_label': '12.cg1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '72.46', 'aut_weyl_index': 48, 'centralizer': '216.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.i1.a1', '6.r1.a1'], 'contains': ['24.t1.a1', '24.bn1.a2', '24.bw1.a2', '36.dr1.a2', '36.dx1.a1', '36.ea1.a2'], 'core': '72.g1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [9751, -1, 3224, -1, 9745, -1, 4001, -1], 'generators': [3, 1008, 54, 2, 12], 'label': '1296.3190.12.cg1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.r1.a1', 'old_label': '12.cg1.a2', 'projective_image': '432.598', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.cg1.a2', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 71059889
    {'ambient': '1296.3190', 'aut_centralizer_order': 2, 'aut_label': '12.cg1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '72.46', 'aut_weyl_index': 48, 'centralizer': '216.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.i1.b1', '6.r1.a1'], 'contains': ['24.t1.b1', '24.bn1.a1', '24.bw1.a2', '36.dr1.b1', '36.dx1.b1', '36.ea1.b1'], 'core': '72.g1.b1', 'coset_action_label': None, 'count': 6, 'diagramx': [9751, -1, 3375, -1, 9745, -1, 4154, -1], 'generators': [219, 576, 54, 2, 12], 'label': '1296.3190.12.cg1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.r1.a1', 'old_label': '12.cg1.b1', 'projective_image': '432.598', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.cg1.b1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 71059890
    {'ambient': '1296.3190', 'aut_centralizer_order': 2, 'aut_label': '12.cg1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '72.46', 'aut_weyl_index': 48, 'centralizer': '216.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.i1.b1', '6.r1.a1'], 'contains': ['24.t1.b1', '24.bn1.a2', '24.bw1.a1', '36.dr1.b2', '36.dx1.b1', '36.ea1.b2'], 'core': '72.g1.b1', 'coset_action_label': None, 'count': 6, 'diagramx': [9751, -1, 3408, -1, 9745, -1, 4203, -1], 'generators': [219, 1008, 54, 2, 12], 'label': '1296.3190.12.cg1.b2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.r1.a1', 'old_label': '12.cg1.b2', 'projective_image': '432.598', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.cg1.b2', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 71059891
    {'ambient': '1296.3190', 'aut_centralizer_order': 4, 'aut_label': '12.ch1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '216.162', 'aut_weyl_index': 16, 'centralizer': '216.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.i1.a1', '6.c1.a1'], 'contains': ['24.g1.a1', '24.bp1.a1', '24.by1.a1', '36.ds1.a1', '36.dy1.a1', '36.dz1.a1', '36.ea1.a1', '36.ea1.a2'], 'core': '24.g1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [9411, -1, 3740, -1, 9441, -1, 3901, -1], 'generators': [3, 432, 54, 12, 144], 'label': '1296.3190.12.ch1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '12.ch1.a1', 'projective_image': '1296.3190', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.ch1.a1', 'subgroup_fusion': None, 'weyl_group': '108.39'}
  • id: 71059892
    {'ambient': '1296.3190', 'aut_centralizer_order': 4, 'aut_label': '12.ch1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '216.162', 'aut_weyl_index': 16, 'centralizer': '216.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.i1.b1', '6.c1.a1'], 'contains': ['24.g1.b1', '24.bp1.a1', '24.by1.a1', '36.ds1.b1', '36.dy1.b1', '36.dz1.b1', '36.ea1.b1', '36.ea1.b2'], 'core': '24.g1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [9411, -1, 4025, -1, 9441, -1, 4104, -1], 'generators': [219, 432, 54, 12, 144], 'label': '1296.3190.12.ch1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '12.ch1.b1', 'projective_image': '1296.3190', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.ch1.b1', 'subgroup_fusion': None, 'weyl_group': '108.39'}
  • id: 71059893
    {'ambient': '1296.3190', 'aut_centralizer_order': 216, 'aut_label': '16.a1', 'aut_quo_index': 8, 'aut_stab_index': 1, 'aut_weyl_group': '16.14', 'aut_weyl_index': 216, 'centralizer': '8.a1.a1', 'complements': ['81.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '8.b1.a1', '8.b1.b1', '8.c1.a1', '8.d1.a1', '8.e1.a1', '8.f1.a1'], 'contains': ['48.a1.a1', '48.b1.a1', '48.c1.a1', '48.d1.a1', '48.e1.a1', '48.f1.a1', '48.g1.a1', '48.h1.a1', '48.i1.a1', '48.j1.a1', '48.k1.a1', '48.l1.a1', '48.m1.a1', '48.n1.a1', '48.o1.a1'], 'core': '16.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7327, 6242, 2144, 2812, 7521, 3468, 4870, 3492], 'generators': [2, 12, 144, 432], 'label': '1296.3190.16.a1.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '16.a1.a1', 'normal_contained_in': ['8.a1.a1', '8.b1.a1', '8.b1.b1'], 'normal_contains': ['48.a1.a1', '48.c1.a1', '48.b1.a1', '48.d1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.a1.a1', 'projective_image': '432.598', 'quotient_action_image': '8.5', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '16.a1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 71059894
    {'ambient': '1296.3190', 'aut_centralizer_order': 24, 'aut_label': '18.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '144.192', 'aut_weyl_index': 24, 'centralizer': '72.a1.a1', 'complements': ['72.cy1.a1', '72.da1.a1', '72.da1.a2', '72.dc1.a1', '72.dg1.a1', '72.dg1.a2', '72.di1.a1', '72.dl1.a1', '72.dl1.a2', '72.dm1.a1', '72.do1.a1', '72.do1.a2'], 'conjugacy_class_count': 1, 'contained_in': ['6.a1.a1', '6.b1.a1', '6.o1.a1', '9.f1.a1'], 'contains': ['36.c1.a1', '36.f1.a1', '36.g1.a1', '36.dw1.a1', '36.dw1.b1', '54.d1.a1', '54.m1.a1'], 'core': '18.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5793, 7662, 4625, 3316, 6379, 2144, 1832, 2566], 'generators': [3, 144, 18, 216, 12], 'label': '1296.3190.18.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.c1.a1', '36.f1.a1', '36.g1.a1'], 'normalizer': '1.a1.a1', 'old_label': '18.a1.a1', 'projective_image': '648.731', 'quotient_action_image': '2.1', 'quotient_action_kernel': '9.2', 'quotient_action_kernel_order': 9, 'quotient_fusion': None, 'short_label': '18.a1.a1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 71059895
    {'ambient': '1296.3190', 'aut_centralizer_order': 24, 'aut_label': '18.b1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '144.192', 'aut_weyl_index': 24, 'centralizer': '72.b1.a1', 'complements': ['72.cf1.a1', '72.ci1.a1', '72.ci1.b1', '72.cz1.a1', '72.da1.a1', '72.da1.a2', '72.cj1.a1', '72.cl1.a1', '72.cl1.b1', '72.de1.a1', '72.dg1.a1', '72.dg1.a2', '72.cn1.a1', '72.ct1.b1', '72.ct1.a1', '72.dj1.a1', '72.dl1.a1', '72.dl1.a2', '72.cp1.a1', '72.cv1.b1', '72.cv1.a1', '72.dn1.a1', '72.do1.a1', '72.do1.a2'], 'conjugacy_class_count': 1, 'contained_in': ['6.d1.a1', '6.e1.a1', '6.t1.a1', '9.e1.a1'], 'contains': ['36.b1.a1', '36.k1.a1', '36.l1.a1', '54.j1.a1', '54.o1.a1'], 'core': '18.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1919, 3776, 9128, 6791, 1433, 3124, 7884, 6716], 'generators': [3, 432, 108, 216, 12], 'label': '1296.3190.18.b1.a1', 'mobius_quo': 0, 'mobius_sub': -3, 'normal_closure': '18.b1.a1', 'normal_contained_in': ['6.d1.a1', '6.e1.a1'], 'normal_contains': ['36.b1.a1', '36.k1.a1', '36.l1.a1'], 'normalizer': '1.a1.a1', 'old_label': '18.b1.a1', 'projective_image': '648.731', 'quotient_action_image': '2.1', 'quotient_action_kernel': '9.2', 'quotient_action_kernel_order': 9, 'quotient_fusion': None, 'short_label': '18.b1.a1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 71059911
    {'ambient': '1296.3190', 'aut_centralizer_order': 24, 'aut_label': '18.p1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '48.51', 'aut_weyl_index': 72, 'centralizer': '36.x1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.a1.a1', '6.n1.a1', '9.d1.a1'], 'contains': ['36.a1.a1', '36.y1.a1', '36.bk1.a1', '36.dt1.a1', '36.dt1.b1', '54.a1.a1', '54.m1.a1'], 'core': '36.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5744, -1, 3939, -1, 6447, -1, 2235, -1], 'generators': [3, 12, 18, 216, 2], 'label': '1296.3190.18.p1.a1', 'mobius_quo': None, 'mobius_sub': -3, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1.a1', 'old_label': '18.p1.a1', 'projective_image': '216.162', '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': '12.4'}
  • id: 71059896
    {'ambient': '1296.3190', 'aut_centralizer_order': 24, 'aut_label': '18.c1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '144.192', 'aut_weyl_index': 24, 'centralizer': '36.a1.a1', 'complements': ['72.g1.a1', '72.bu1.a1', '72.bv1.a1', '72.bx1.a1', '72.g1.b1', '72.bu1.b1', '72.bv1.b1', '72.bx1.b1', '72.co1.a1', '72.cu1.b1', '72.cu1.a1', '72.cp1.a1', '72.cv1.b1', '72.cv1.a1', '72.dk1.a1', '72.dm1.a1', '72.dn1.a1', '72.do1.a1', '72.do1.a2'], 'conjugacy_class_count': 1, 'contained_in': ['6.f1.a1', '6.g1.a1', '6.x1.a1', '9.c1.a1'], 'contains': ['36.e1.a1', '36.h1.a1', '36.j1.a1', '54.s1.a1', '54.x1.a1'], 'core': '18.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1722, 908, 8255, 8449, 3906, 9874, 7154, 9401], 'generators': [18, 432, 108, 216, 144], 'label': '1296.3190.18.c1.a1', 'mobius_quo': 0, 'mobius_sub': -3, 'normal_closure': '18.c1.a1', 'normal_contained_in': ['6.f1.a1', '6.g1.a1'], 'normal_contains': ['36.e1.a1', '36.h1.a1', '36.j1.a1'], 'normalizer': '1.a1.a1', 'old_label': '18.c1.a1', 'projective_image': '648.731', 'quotient_action_image': '1.1', 'quotient_action_kernel': '18.3', 'quotient_action_kernel_order': 18, 'quotient_fusion': None, 'short_label': '18.c1.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 71059897
    {'ambient': '1296.3190', 'aut_centralizer_order': 24, 'aut_label': '18.d1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '16.14', 'aut_weyl_index': 216, 'centralizer': '18.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.k1.a1', '6.n1.a1', '9.a1.a1'], 'contains': ['36.m1.a1', '36.x1.a1', '36.bi1.a1', '36.dl1.a1', '36.dl1.b1', '54.a1.a1', '54.b1.a1', '54.c1.a1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [5500, -1, 5286, -1, 6242, -1, 1882, -1], 'generators': [3, 432, 18, 216, 2], 'label': '1296.3190.18.d1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '18.d1.a1', 'projective_image': '216.162', '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': '2.1'}
  • id: 71059898
    {'ambient': '1296.3190', 'aut_centralizer_order': 12, 'aut_label': '4.c1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '288.1040', 'aut_weyl_index': 12, 'centralizer': '72.a1.a1', 'complements': ['324.i1.a1', '324.i1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '2.f1.a1', '2.g1.a1'], 'contains': ['8.a1.a1', '8.d1.a1', '12.g1.a1', '12.h1.a1', '12.ba1.a1', '12.bb1.a1', '12.bc1.a1', '12.bd1.a1'], 'core': '4.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4815, 7170, 6310, 3369, 5797, 2791, 4980, 2721], 'generators': [9, 144, 12, 216, 2, 432], 'label': '1296.3190.4.c1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.c1.a1', 'normal_contained_in': ['2.a1.a1', '2.f1.a1', '2.g1.a1'], 'normal_contains': ['8.a1.a1', '12.g1.a1', '12.h1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.c1.a1', 'projective_image': '216.162', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.c1.a1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 71059899
    {'ambient': '1296.3190', 'aut_centralizer_order': 24, 'aut_label': '18.e1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '48.51', 'aut_weyl_index': 72, 'centralizer': '36.m1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.a1.a1', '6.k1.a1', '9.b1.a1'], 'contains': ['36.d1.a1', '36.n1.a1', '36.bj1.a1', '36.dm1.a1', '36.dm1.b1', '54.a1.a1', '54.d1.a1'], 'core': '36.d1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5429, -1, 5499, -1, 6094, -1, 2301, -1], 'generators': [3, 144, 18, 216, 2], 'label': '1296.3190.18.e1.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.e1.a1', 'projective_image': '216.162', '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: 71059900
    {'ambient': '1296.3190', 'aut_centralizer_order': 24, 'aut_label': '18.f1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '48.51', 'aut_weyl_index': 72, 'centralizer': '36.m1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1.a1', '6.k1.a1', '9.c1.a1'], 'contains': ['36.e1.a1', '36.p1.a1', '36.bm1.a1', '36.dn1.a1', '36.dn1.b1', '54.b1.a1', '54.d1.a1'], 'core': '36.e1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5551, -1, 5343, -1, 6016, -1, 2005, -1], 'generators': [3, 144, 18, 216, 432], 'label': '1296.3190.18.f1.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.f1.a1', 'projective_image': '648.731', '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': '12.4'}
  • id: 71059901
    {'ambient': '1296.3190', 'aut_centralizer_order': 12, 'aut_label': '18.g1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '48.51', 'aut_weyl_index': 72, 'centralizer': '36.m1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.k1.a1', '6.o1.a1'], 'contains': ['36.r1.a1', '36.be1.a1', '36.bp1.a1', '36.do1.a1', '36.do1.b1', '36.do1.c1', '36.do1.d1', '54.c1.a1', '54.d1.a1'], 'core': '108.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [5608, -1, 2327, -1, 6869, -1, 905, -1], 'generators': [3, 144, 18, 216, 434], 'label': '1296.3190.18.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.k1.a1', 'old_label': '18.g1.a1', 'projective_image': '648.731', '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': '6.1'}
  • id: 71059902
    {'ambient': '1296.3190', 'aut_centralizer_order': 8, 'aut_label': '18.h1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '48.51', 'aut_weyl_index': 72, 'centralizer': '108.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.l1.a1', '6.p1.a1', '9.a1.a1'], 'contains': ['36.m1.a1', '36.bt1.a1', '36.cc1.a1', '36.dp1.a1', '36.dp1.b1', '54.e1.a1', '54.f1.a1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [6600, -1, 6003, -1, 7018, -1, 4681, -1], 'generators': [3, 432, 54, 216, 2], 'label': '1296.3190.18.h1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '18.h1.a1', 'projective_image': '216.162', '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: 71059903
    {'ambient': '1296.3190', 'aut_centralizer_order': 8, 'aut_label': '18.i1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '48.51', 'aut_weyl_index': 72, 'centralizer': '108.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.l1.a1', '6.q1.a1', '9.b1.a1'], 'contains': ['36.n1.a1', '36.bu1.a1', '36.cd1.a1', '36.dq1.a1', '36.dq1.b1', '54.e1.a1', '54.g1.a1'], 'core': '72.b1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [6542, -1, 5810, -1, 6791, -1, 4615, -1], 'generators': [3, 144, 54, 216, 2], 'label': '1296.3190.18.i1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1.a1', 'old_label': '18.i1.a1', 'projective_image': '216.162', '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: 71059904
    {'ambient': '1296.3190', 'aut_centralizer_order': 4, 'aut_label': '18.j1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '48.51', 'aut_weyl_index': 72, 'centralizer': '108.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.l1.a1', '6.r1.a1'], 'contains': ['36.o1.a1', '36.bv1.a1', '36.cf1.a1', '36.dr1.a1', '36.dr1.a2', '36.dr1.b1', '36.dr1.b2', '54.e1.a1', '54.h1.a1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [6852, -1, 5230, -1, 7979, -1, 4747, -1], 'generators': [3, 576, 54, 216, 2], 'label': '1296.3190.18.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.j1.a1', 'old_label': '18.j1.a1', 'projective_image': '216.162', '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': '6.1'}
  • id: 71059905
    {'ambient': '1296.3190', 'aut_centralizer_order': 8, 'aut_label': '18.k1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '144.192', 'aut_weyl_index': 24, 'centralizer': '108.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.c1.a1', '6.l1.a1', '9.c1.a1'], 'contains': ['36.h1.a1', '36.p1.a1', '36.cj1.a1', '36.ds1.a1', '36.ds1.b1', '54.f1.a1', '54.g1.a1', '54.h1.a1'], 'core': '36.h1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6655, -1, 6072, -1, 6944, -1, 4859, -1], 'generators': [3, 432, 54, 216, 144], 'label': '1296.3190.18.k1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '6.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '18.k1.a1', 'projective_image': '648.731', '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': '36.10'}
  • id: 71059906
    {'ambient': '1296.3190', 'aut_centralizer_order': 24, 'aut_label': '18.l1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '48.51', 'aut_weyl_index': 72, 'centralizer': '36.n1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.d1.a1', '6.m1.a1', '9.a1.a1'], 'contains': ['36.i1.a1', '36.m1.a1', '36.cq1.a1', '54.i1.a1', '54.j1.a1'], 'core': '36.i1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [1559, -1, 8132, -1, 1371, -1, 8625, -1], 'generators': [3, 432, 108, 2, 216], 'label': '1296.3190.18.l1.a1', 'mobius_quo': None, 'mobius_sub': -3, 'normal_closure': '6.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '18.l1.a1', 'projective_image': '216.162', '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': '12.4'}
  • id: 71059907
    {'ambient': '1296.3190', 'aut_centralizer_order': 24, 'aut_label': '18.m1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '16.14', 'aut_weyl_index': 216, 'centralizer': '18.m1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.m1.a1', '6.s1.a1', '9.b1.a1'], 'contains': ['36.n1.a1', '36.cr1.a1', '36.cs1.a1', '54.i1.a1', '54.k1.a1', '54.l1.a1'], 'core': '72.b1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [644, -1, 8944, -1, 1247, -1, 8513, -1], 'generators': [3, 216, 108, 2, 144], 'label': '1296.3190.18.m1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1.a1', 'old_label': '18.m1.a1', 'projective_image': '216.162', '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': '2.1'}
  • id: 71059908
    {'ambient': '1296.3190', 'aut_centralizer_order': 24, 'aut_label': '18.n1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '48.51', 'aut_weyl_index': 72, 'centralizer': '36.n1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.e1.a1', '6.m1.a1', '9.c1.a1'], 'contains': ['36.j1.a1', '36.p1.a1', '36.cx1.a1', '54.j1.a1', '54.k1.a1'], 'core': '36.j1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [1376, -1, 9555, -1, 1308, -1, 8159, -1], 'generators': [3, 432, 108, 144, 216], 'label': '1296.3190.18.n1.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.n1.a1', 'projective_image': '648.731', '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': '12.4'}
  • id: 71059909
    {'ambient': '1296.3190', 'aut_centralizer_order': 12, 'aut_label': '4.d1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '288.1040', 'aut_weyl_index': 12, 'centralizer': '72.c1.a1', 'complements': ['324.h1.a1', '324.h1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '2.d1.a1', '2.f1.a1'], 'contains': ['8.a1.a1', '8.e1.a1', '12.i1.a1', '12.j1.a1', '12.be1.a1', '12.bf1.a1', '12.bg1.a1', '12.bh1.a1'], 'core': '4.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6883, 3537, 6198, 7070, 6518, 8537, 5739, 7972], 'generators': [54, 432, 144, 216, 2, 12], 'label': '1296.3190.4.d1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.d1.a1', 'normal_contained_in': ['2.b1.a1', '2.d1.a1', '2.f1.a1'], 'normal_contains': ['8.a1.a1', '12.i1.a1', '12.j1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.d1.a1', 'projective_image': '216.162', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.d1.a1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 71059910
    {'ambient': '1296.3190', 'aut_centralizer_order': 12, 'aut_label': '18.o1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '48.51', 'aut_weyl_index': 72, 'centralizer': '36.n1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.m1.a1', '6.t1.a1'], 'contains': ['36.q1.a1', '36.cy1.a1', '36.cz1.a1', '54.j1.a1', '54.l1.a1'], 'core': '108.c1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [1234, -1, 9941, -1, 704, -1, 8736, -1], 'generators': [3, 432, 108, 146, 216], 'label': '1296.3190.18.o1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.m1.a1', 'old_label': '18.o1.a1', 'projective_image': '648.731', '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: 71060284
    {'ambient': '1296.3190', 'aut_centralizer_order': 72, 'aut_label': '72.br1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '4.2', 'aut_weyl_index': 864, 'centralizer': '12.q1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.s1.b1', '24.u1.b1', '36.q1.a1'], 'contains': ['144.k1.a1', '216.r1.b1', '216.u1.b1', '216.w1.b1'], 'core': '432.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [8330, -1, 4092, -1, 8165, -1, 2550, -1], 'generators': [219, 146, 432], 'label': '1296.3190.72.br1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.m1.a1', 'old_label': '72.br1.b1', 'projective_image': '1296.3190', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.br1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 71059912
    {'ambient': '1296.3190', 'aut_centralizer_order': 24, 'aut_label': '18.q1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '48.51', 'aut_weyl_index': 72, 'centralizer': '36.x1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1.a1', '6.n1.a1', '9.e1.a1'], 'contains': ['36.b1.a1', '36.ba1.a1', '36.bn1.a1', '36.du1.a1', '36.du1.b1', '54.b1.a1', '54.m1.a1'], 'core': '36.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5666, -1, 4763, -1, 6310, -1, 1939, -1], 'generators': [3, 12, 18, 216, 432], 'label': '1296.3190.18.q1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '6.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1.a1', 'old_label': '18.q1.a1', 'projective_image': '648.731', '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': '12.4'}
  • id: 71059913
    {'ambient': '1296.3190', 'aut_centralizer_order': 12, 'aut_label': '18.r1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '48.51', 'aut_weyl_index': 72, 'centralizer': '36.x1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.n1.a1', '6.o1.a1'], 'contains': ['36.t1.a1', '36.bc1.a1', '36.bq1.a1', '36.dv1.a1', '36.dv1.b1', '36.dv1.c1', '36.dv1.d1', '54.c1.a1', '54.m1.a1'], 'core': '108.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [5875, -1, 924, -1, 7430, -1, 839, -1], 'generators': [3, 12, 18, 216, 434], 'label': '1296.3190.18.r1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.n1.a1', 'old_label': '18.r1.a1', 'projective_image': '648.731', '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': '6.1'}
  • id: 71059914
    {'ambient': '1296.3190', 'aut_centralizer_order': 8, 'aut_label': '18.s1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '48.51', 'aut_weyl_index': 72, 'centralizer': '108.x1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.p1.a1', '6.q1.a1', '6.r1.a1', '9.d1.a1'], 'contains': ['36.a1.a1', '36.bs1.a1', '36.ce1.a1', '36.dx1.a1', '36.dx1.b1', '54.e1.a1', '54.n1.a1'], 'core': '36.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [6794, -1, 4568, -1, 7665, -1, 4418, -1], 'generators': [3, 12, 54, 216, 2], 'label': '1296.3190.18.s1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.d1.a1', 'old_label': '18.s1.a1', 'projective_image': '216.162', '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': '12.4'}
  • id: 71059915
    {'ambient': '1296.3190', 'aut_centralizer_order': 8, 'aut_label': '18.t1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '144.192', 'aut_weyl_index': 24, 'centralizer': '216.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.c1.a1', '6.p1.a1', '9.e1.a1'], 'contains': ['36.b1.a1', '36.bw1.a1', '36.ck1.a1', '36.dy1.a1', '36.dy1.b1', '54.f1.a1', '54.n1.a1'], 'core': '36.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6702, -1, 5181, -1, 7145, -1, 4360, -1], 'generators': [3, 432, 54, 216, 12], 'label': '1296.3190.18.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': '648.731', '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': '72.46'}
  • id: 71059916
    {'ambient': '1296.3190', 'aut_centralizer_order': 8, 'aut_label': '18.u1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '144.192', 'aut_weyl_index': 24, 'centralizer': '216.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.c1.a1', '6.q1.a1', '9.f1.a1'], 'contains': ['36.c1.a1', '36.by1.a1', '36.cm1.a1', '36.dz1.a1', '36.dz1.b1', '54.g1.a1', '54.n1.a1'], 'core': '36.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6744, -1, 5115, -1, 7087, -1, 4311, -1], 'generators': [3, 144, 54, 216, 12], 'label': '1296.3190.18.u1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '6.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.d1.a1', 'old_label': '18.u1.a1', 'projective_image': '648.731', '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': '72.46'}
  • id: 71059917
    {'ambient': '1296.3190', 'aut_centralizer_order': 4, 'aut_label': '18.v1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '144.192', 'aut_weyl_index': 24, 'centralizer': '216.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.c1.a1', '6.r1.a1'], 'contains': ['36.v1.a1', '36.ca1.a1', '36.co1.a1', '36.ea1.a1', '36.ea1.a2', '36.ea1.b1', '36.ea1.b2', '54.h1.a1', '54.n1.a1'], 'core': '108.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [6902, -1, 4084, -1, 8126, -1, 4805, -1], 'generators': [3, 576, 54, 216, 12], 'label': '1296.3190.18.v1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.r1.a1', 'old_label': '18.v1.a1', 'projective_image': '648.731', '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': '36.10'}
  • id: 71059918
    {'ambient': '1296.3190', 'aut_centralizer_order': 24, 'aut_label': '18.w1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '48.51', 'aut_weyl_index': 72, 'centralizer': '36.cr1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.d1.a1', '6.s1.a1', '9.d1.a1'], 'contains': ['36.a1.a1', '36.ct1.a1', '36.cu1.a1', '54.i1.a1', '54.o1.a1'], 'core': '36.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [2052, -1, 8037, -1, 1555, -1, 7773, -1], 'generators': [3, 12, 108, 2, 216], 'label': '1296.3190.18.w1.a1', 'mobius_quo': None, 'mobius_sub': -3, 'normal_closure': '6.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.d1.a1', 'old_label': '18.w1.a1', 'projective_image': '216.162', '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: 71059919
    {'ambient': '1296.3190', 'aut_centralizer_order': 24, 'aut_label': '18.x1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '48.51', 'aut_weyl_index': 72, 'centralizer': '36.cr1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.e1.a1', '6.s1.a1', '9.f1.a1'], 'contains': ['36.c1.a1', '36.dd1.a1', '36.de1.a1', '54.k1.a1', '54.o1.a1'], 'core': '36.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [1997, -1, 8809, -1, 1495, -1, 7197, -1], 'generators': [3, 12, 108, 144, 216], 'label': '1296.3190.18.x1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '6.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.d1.a1', 'old_label': '18.x1.a1', 'projective_image': '648.731', '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': '12.4'}
  • id: 71059920
    {'ambient': '1296.3190', 'aut_centralizer_order': 4, 'aut_label': '4.e1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '864.4704', 'aut_weyl_index': 4, 'centralizer': '216.a1.a1', 'complements': ['324.h1.a1', '324.h1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '2.e1.a1', '2.g1.a1'], 'contains': ['8.a1.a1', '8.f1.a1', '12.k1.a1', '12.bi1.a1', '12.bj1.a1', '12.bk1.a1', '12.bl1.a1', '12.bm1.a1', '12.bn1.a1', '12.bo1.a1'], 'core': '4.e1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3868, 6315, 7895, 4177, 3725, 6838, 6802, 3876], 'generators': [45, 432, 144, 216, 2, 12], 'label': '1296.3190.4.e1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.e1.a1', 'normal_contained_in': ['2.b1.a1', '2.e1.a1', '2.g1.a1'], 'normal_contains': ['8.a1.a1', '12.k1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.e1.a1', 'projective_image': '216.162', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.e1.a1', 'subgroup_fusion': None, 'weyl_group': '216.162'}
  • id: 71059921
    {'ambient': '1296.3190', 'aut_centralizer_order': 12, 'aut_label': '18.y1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '48.51', 'aut_weyl_index': 72, 'centralizer': '36.cr1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.s1.a1', '6.t1.a1'], 'contains': ['36.u1.a1', '36.dh1.a1', '36.di1.a1', '54.l1.a1', '54.o1.a1'], 'core': '108.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [1801, -1, 9495, -1, 765, -1, 8211, -1], 'generators': [3, 12, 108, 146, 216], 'label': '1296.3190.18.y1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.s1.a1', 'old_label': '18.y1.a1', 'projective_image': '648.731', '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': '6.1'}
  • id: 71059922
    {'ambient': '1296.3190', 'aut_centralizer_order': 24, 'aut_label': '18.z1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '16.14', 'aut_weyl_index': 216, 'centralizer': '72.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.u1.a1', '6.w1.a1', '9.d1.a1'], 'contains': ['36.y1.a1', '36.bs1.a1', '36.ct1.a1', '54.p1.a1', '54.q1.a1', '54.r1.a1'], 'core': '72.c1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [3300, -1, 5720, -1, 4562, -1, 6988, -1], 'generators': [18, 216, 108, 2, 12], 'label': '1296.3190.18.z1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.d1.a1', 'old_label': '18.z1.a1', 'projective_image': '216.162', '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': '8.5'}
  • id: 71059923
    {'ambient': '1296.3190', 'aut_centralizer_order': 24, 'aut_label': '18.ba1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '48.51', 'aut_weyl_index': 72, 'centralizer': '36.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.f1.a1', '6.u1.a1', '9.a1.a1'], 'contains': ['36.i1.a1', '36.x1.a1', '36.bt1.a1', '54.p1.a1', '54.s1.a1'], 'core': '36.i1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [2931, -1, 7393, -1, 4376, -1, 7669, -1], 'generators': [18, 432, 108, 2, 216], 'label': '1296.3190.18.ba1.a1', 'mobius_quo': None, 'mobius_sub': -3, 'normal_closure': '6.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1.a1', 'old_label': '18.ba1.a1', 'projective_image': '216.162', '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': '12.4'}
  • id: 71059924
    {'ambient': '1296.3190', 'aut_centralizer_order': 24, 'aut_label': '18.bb1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '48.51', 'aut_weyl_index': 72, 'centralizer': '72.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.g1.a1', '6.u1.a1', '9.e1.a1'], 'contains': ['36.k1.a1', '36.ba1.a1', '36.bw1.a1', '54.q1.a1', '54.s1.a1'], 'core': '36.k1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4129, -1, 5929, -1, 4501, -1, 6216, -1], 'generators': [18, 432, 108, 12, 216], 'label': '1296.3190.18.bb1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '6.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1.a1', 'old_label': '18.bb1.a1', 'projective_image': '648.731', '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': '24.14'}
  • id: 71059925
    {'ambient': '1296.3190', 'aut_centralizer_order': 12, 'aut_label': '18.bc1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '48.51', 'aut_weyl_index': 72, 'centralizer': '72.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.u1.a1', '6.x1.a1'], 'contains': ['36.bb1.a1', '36.bx1.a1', '36.da1.a1', '54.r1.a1', '54.s1.a1'], 'core': '108.c1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [254, -1, 6286, -1, 2972, -1, 7721, -1], 'generators': [18, 432, 108, 14, 216], 'label': '1296.3190.18.bc1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.u1.a1', 'old_label': '18.bc1.a1', 'projective_image': '648.731', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.bc1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 71059926
    {'ambient': '1296.3190', 'aut_centralizer_order': 8, 'aut_label': '18.bd1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '48.51', 'aut_weyl_index': 72, 'centralizer': '108.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.v1.a1', '6.y1.a1', '9.a1.a1'], 'contains': ['36.x1.a1', '36.cc1.a1', '36.cq1.a1', '54.t1.a1', '54.u1.a1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [3893, -1, 7463, -1, 3349, -1, 7351, -1], 'generators': [111, 432, 18, 2, 216], 'label': '1296.3190.18.bd1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '18.bd1.a1', 'projective_image': '216.162', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.bd1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 71059927
    {'ambient': '1296.3190', 'aut_centralizer_order': 8, 'aut_label': '18.be1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '48.51', 'aut_weyl_index': 72, 'centralizer': '216.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.v1.a1', '6.z1.a1', '9.d1.a1'], 'contains': ['36.y1.a1', '36.ce1.a1', '36.cu1.a1', '54.t1.a1', '54.v1.a1'], 'core': '72.c1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [5033, -1, 6371, -1, 3659, -1, 6268, -1], 'generators': [111, 12, 18, 2, 216], 'label': '1296.3190.18.be1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.d1.a1', 'old_label': '18.be1.a1', 'projective_image': '216.162', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.be1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 71059928
    {'ambient': '1296.3190', 'aut_centralizer_order': 4, 'aut_label': '18.bf1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '48.51', 'aut_weyl_index': 72, 'centralizer': '216.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.v1.a1', '6.ba1.a1'], 'contains': ['36.z1.a1', '36.cg1.a1', '36.cv1.a1', '54.t1.a1', '54.w1.a1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [125, -1, 7557, -1, 2426, -1, 8374, -1], 'generators': [111, 444, 18, 2, 216], 'label': '1296.3190.18.bf1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bf1.a1', 'old_label': '18.bf1.a1', 'projective_image': '216.162', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.bf1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 71059929
    {'ambient': '1296.3190', 'aut_centralizer_order': 8, 'aut_label': '18.bg1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '144.192', 'aut_weyl_index': 24, 'centralizer': '216.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.h1.a1', '6.v1.a1', '9.e1.a1'], 'contains': ['36.l1.a1', '36.ba1.a1', '36.ck1.a1', '54.u1.a1', '54.v1.a1', '54.w1.a1'], 'core': '36.l1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4322, -1, 6401, -1, 3401, -1, 6695, -1], 'generators': [111, 432, 18, 216, 12], 'label': '1296.3190.18.bg1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '6.h1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1.a1', 'old_label': '18.bg1.a1', 'projective_image': '648.731', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.bg1.a1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 71059930
    {'ambient': '1296.3190', 'aut_centralizer_order': 24, 'aut_label': '18.bh1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '48.51', 'aut_weyl_index': 72, 'centralizer': '36.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.f1.a1', '6.w1.a1', '9.b1.a1'], 'contains': ['36.d1.a1', '36.bu1.a1', '36.cr1.a1', '54.p1.a1', '54.x1.a1'], 'core': '36.d1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [2886, -1, 7953, -1, 4256, -1, 7455, -1], 'generators': [18, 144, 108, 2, 216], 'label': '1296.3190.18.bh1.a1', 'mobius_quo': None, 'mobius_sub': -3, 'normal_closure': '6.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.d1.a1', 'old_label': '18.bh1.a1', 'projective_image': '216.162', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.bh1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 71059931
    {'ambient': '1296.3190', 'aut_centralizer_order': 36, 'aut_label': '4.f1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '96.230', 'aut_weyl_index': 36, 'centralizer': '24.c1.a1', 'complements': ['324.h1.a1', '324.h1.b1', '324.i1.a1', '324.i1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1', '2.d1.a1', '2.g1.a1'], 'contains': ['8.a1.a1', '12.l1.a1', '12.m1.a1', '12.o1.a1', '12.bq1.a1', '12.br1.a1', '12.bu1.a1', '12.bv1.a1', '12.bx1.a1'], 'core': '4.f1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1272, 2410, 8563, 7931, 1075, 7969, 8724, 8995], 'generators': [108, 432, 216, 2, 12, 144], 'label': '1296.3190.4.f1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.f1.a1', 'normal_contained_in': ['2.c1.a1', '2.d1.a1', '2.g1.a1'], 'normal_contains': ['8.a1.a1', '12.l1.a1', '12.m1.a1', '12.o1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.f1.a1', 'projective_image': '216.162', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.f1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 71059932
    {'ambient': '1296.3190', 'aut_centralizer_order': 24, 'aut_label': '18.bi1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '48.51', 'aut_weyl_index': 72, 'centralizer': '72.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.g1.a1', '6.w1.a1', '9.f1.a1'], 'contains': ['36.f1.a1', '36.by1.a1', '36.dd1.a1', '54.q1.a1', '54.x1.a1'], 'core': '36.f1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4074, -1, 6200, -1, 4439, -1, 6128, -1], 'generators': [18, 144, 108, 12, 216], 'label': '1296.3190.18.bi1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '6.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.d1.a1', 'old_label': '18.bi1.a1', 'projective_image': '648.731', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.bi1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 71059933
    {'ambient': '1296.3190', 'aut_centralizer_order': 12, 'aut_label': '18.bj1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '48.51', 'aut_weyl_index': 72, 'centralizer': '72.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.w1.a1', '6.x1.a1'], 'contains': ['36.bf1.a1', '36.bz1.a1', '36.df1.a1', '54.r1.a1', '54.x1.a1'], 'core': '108.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [1311, -1, 6604, -1, 2910, -1, 7506, -1], 'generators': [18, 144, 108, 14, 216], 'label': '1296.3190.18.bj1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.w1.a1', 'old_label': '18.bj1.a1', 'projective_image': '648.731', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.bj1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 71059934
    {'ambient': '1296.3190', 'aut_centralizer_order': 8, 'aut_label': '18.bk1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '48.51', 'aut_weyl_index': 72, 'centralizer': '108.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.y1.a1', '6.z1.a1', '6.ba1.a1', '9.b1.a1'], 'contains': ['36.d1.a1', '36.cd1.a1', '36.cs1.a1', '54.t1.a1', '54.y1.a1'], 'core': '36.d1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [3365, -1, 8175, -1, 3245, -1, 7617, -1], 'generators': [111, 144, 18, 2, 216], 'label': '1296.3190.18.bk1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1.a1', 'old_label': '18.bk1.a1', 'projective_image': '216.162', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.bk1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 71059935
    {'ambient': '1296.3190', 'aut_centralizer_order': 8, 'aut_label': '18.bl1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '144.192', 'aut_weyl_index': 24, 'centralizer': '108.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.h1.a1', '6.y1.a1', '9.c1.a1'], 'contains': ['36.e1.a1', '36.cj1.a1', '36.cx1.a1', '54.u1.a1', '54.y1.a1'], 'core': '36.e1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3760, -1, 8998, -1, 3297, -1, 7030, -1], 'generators': [111, 432, 18, 216, 144], 'label': '1296.3190.18.bl1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '6.h1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '18.bl1.a1', 'projective_image': '648.731', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.bl1.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 71059936
    {'ambient': '1296.3190', 'aut_centralizer_order': 8, 'aut_label': '18.bm1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '144.192', 'aut_weyl_index': 24, 'centralizer': '216.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.h1.a1', '6.z1.a1', '9.f1.a1'], 'contains': ['36.f1.a1', '36.cm1.a1', '36.de1.a1', '54.v1.a1', '54.y1.a1'], 'core': '36.f1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4250, -1, 7526, -1, 3606, -1, 6172, -1], 'generators': [111, 144, 18, 216, 12], 'label': '1296.3190.18.bm1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '6.h1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.d1.a1', 'old_label': '18.bm1.a1', 'projective_image': '648.731', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.bm1.a1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 71059937
    {'ambient': '1296.3190', 'aut_centralizer_order': 4, 'aut_label': '18.bn1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '144.192', 'aut_weyl_index': 24, 'centralizer': '216.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.h1.a1', '6.ba1.a1'], 'contains': ['36.bg1.a1', '36.cn1.a1', '36.dg1.a1', '54.w1.a1', '54.y1.a1'], 'core': '108.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [456, -1, 8905, -1, 2373, -1, 8470, -1], 'generators': [111, 144, 18, 216, 444], 'label': '1296.3190.18.bn1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.h1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.ba1.a1', 'old_label': '18.bn1.a1', 'projective_image': '648.731', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.bn1.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 71059938
    {'ambient': '1296.3190', 'aut_centralizer_order': 8, 'aut_label': '18.bo1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '48.51', 'aut_weyl_index': 72, 'centralizer': '108.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.bb1.a1', '6.bc1.a1', '9.a1.a1'], 'contains': ['36.bi1.a1', '36.bt1.a1', '36.cq1.a1', '54.z1.a1', '54.ba1.a1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [4417, -1, 7279, -1, 5392, -1, 6652, -1], 'generators': [111, 432, 54, 2, 216], 'label': '1296.3190.18.bo1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '18.bo1.a1', 'projective_image': '216.162', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.bo1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 71059939
    {'ambient': '1296.3190', 'aut_centralizer_order': 8, 'aut_label': '18.bp1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '48.51', 'aut_weyl_index': 72, 'centralizer': '108.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.bd1.a1', '6.be1.a1', '6.bf1.a1', '9.a1.a1'], 'contains': ['36.i1.a1', '36.bi1.a1', '36.cc1.a1', '54.bb1.a1', '54.bc1.a1'], 'core': '36.i1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [3680, -1, 8722, -1, 3034, -1, 7936, -1], 'generators': [9, 432, 108, 2, 216], 'label': '1296.3190.18.bp1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '18.bp1.a1', 'projective_image': '216.162', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.bp1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 71059940
    {'ambient': '1296.3190', 'aut_centralizer_order': 8, 'aut_label': '18.bq1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '48.51', 'aut_weyl_index': 72, 'centralizer': '216.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.bb1.a1', '6.bg1.a1', '9.d1.a1'], 'contains': ['36.bk1.a1', '36.bs1.a1', '36.cu1.a1', '54.z1.a1', '54.bd1.a1'], 'core': '72.c1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [5378, -1, 5450, -1, 5602, -1, 5981, -1], 'generators': [111, 12, 54, 2, 216], 'label': '1296.3190.18.bq1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.d1.a1', 'old_label': '18.bq1.a1', 'projective_image': '216.162', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.bq1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 71059941
    {'ambient': '1296.3190', 'aut_centralizer_order': 8, 'aut_label': '18.br1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '48.51', 'aut_weyl_index': 72, 'centralizer': '108.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.bc1.a1', '6.bg1.a1', '9.b1.a1'], 'contains': ['36.bj1.a1', '36.bu1.a1', '36.cs1.a1', '54.z1.a1', '54.be1.a1'], 'core': '72.b1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [4372, -1, 7885, -1, 5329, -1, 6599, -1], 'generators': [111, 144, 54, 2, 216], 'label': '1296.3190.18.br1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1.a1', 'old_label': '18.br1.a1', 'projective_image': '216.162', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.br1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 71059942
    {'ambient': '1296.3190', 'aut_centralizer_order': 12, 'aut_label': '4.g1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '288.1040', 'aut_weyl_index': 12, 'centralizer': '72.b1.a1', 'complements': ['324.h1.a1', '324.h1.b1', '324.i1.a1', '324.i1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1', '2.e1.a1', '2.f1.a1'], 'contains': ['8.a1.a1', '12.n1.a1', '12.p1.a1', '12.bp1.a1', '12.bs1.a1', '12.bt1.a1', '12.bw1.a1'], 'core': '4.g1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1735, 4164, 8415, 5675, 1797, 4438, 7738, 6178], 'generators': [111, 432, 12, 2, 144, 216], 'label': '1296.3190.4.g1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.g1.a1', 'normal_contained_in': ['2.c1.a1', '2.e1.a1', '2.f1.a1'], 'normal_contains': ['8.a1.a1', '12.n1.a1', '12.p1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.g1.a1', 'projective_image': '216.162', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.g1.a1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 71059943
    {'ambient': '1296.3190', 'aut_centralizer_order': 8, 'aut_label': '18.bs1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '144.192', 'aut_weyl_index': 24, 'centralizer': '216.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.i1.a1', '6.bb1.a1', '9.e1.a1'], 'contains': ['36.l1.a1', '36.bn1.a1', '36.bw1.a1', '54.ba1.a1', '54.bd1.a1'], 'core': '36.l1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5155, -1, 5852, -1, 5553, -1, 5940, -1], 'generators': [111, 432, 54, 216, 12], 'label': '1296.3190.18.bs1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '6.i1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1.a1', 'old_label': '18.bs1.a1', 'projective_image': '648.731', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.bs1.a1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 71059944
    {'ambient': '1296.3190', 'aut_centralizer_order': 8, 'aut_label': '18.bt1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '144.192', 'aut_weyl_index': 24, 'centralizer': '108.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.i1.a1', '6.bc1.a1', '9.c1.a1'], 'contains': ['36.h1.a1', '36.bm1.a1', '36.cx1.a1', '54.ba1.a1', '54.be1.a1'], 'core': '36.h1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4611, -1, 8085, -1, 5199, -1, 6556, -1], 'generators': [111, 432, 54, 216, 144], 'label': '1296.3190.18.bt1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '6.i1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '18.bt1.a1', 'projective_image': '648.731', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.bt1.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 71059945
    {'ambient': '1296.3190', 'aut_centralizer_order': 8, 'aut_label': '18.bu1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '48.51', 'aut_weyl_index': 72, 'centralizer': '108.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.bd1.a1', '6.bh1.a1', '9.b1.a1'], 'contains': ['36.bj1.a1', '36.cd1.a1', '36.cr1.a1', '54.bb1.a1', '54.bf1.a1'], 'core': '72.b1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [3441, -1, 8562, -1, 3139, -1, 7403, -1], 'generators': [9, 144, 108, 2, 216], 'label': '1296.3190.18.bu1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1.a1', 'old_label': '18.bu1.a1', 'projective_image': '216.162', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.bu1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 71059946
    {'ambient': '1296.3190', 'aut_centralizer_order': 8, 'aut_label': '18.bv1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '48.51', 'aut_weyl_index': 72, 'centralizer': '216.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.be1.a1', '6.bh1.a1', '9.d1.a1'], 'contains': ['36.bk1.a1', '36.ce1.a1', '36.ct1.a1', '54.bb1.a1', '54.bg1.a1'], 'core': '72.c1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [5100, -1, 7634, -1, 3554, -1, 6356, -1], 'generators': [9, 12, 108, 2, 216], 'label': '1296.3190.18.bv1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.d1.a1', 'old_label': '18.bv1.a1', 'projective_image': '216.162', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.bv1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 71059947
    {'ambient': '1296.3190', 'aut_centralizer_order': 4, 'aut_label': '18.bw1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '48.51', 'aut_weyl_index': 72, 'centralizer': '216.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.bf1.a1', '6.bh1.a1'], 'contains': ['36.bl1.a1', '36.ch1.a1', '36.cw1.a1', '54.bb1.a1', '54.bh1.a1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [3194, -1, 9418, -1, 2321, -1, 8824, -1], 'generators': [9, 156, 108, 2, 216], 'label': '1296.3190.18.bw1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bw1.a1', 'old_label': '18.bw1.a1', 'projective_image': '216.162', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.bw1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 71059948
    {'ambient': '1296.3190', 'aut_centralizer_order': 8, 'aut_label': '18.bx1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '144.192', 'aut_weyl_index': 24, 'centralizer': '108.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.j1.a1', '6.bd1.a1', '9.c1.a1'], 'contains': ['36.j1.a1', '36.bm1.a1', '36.cj1.a1', '54.bc1.a1', '54.bf1.a1'], 'core': '36.j1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3479, -1, 9257, -1, 3087, -1, 7118, -1], 'generators': [9, 432, 108, 216, 144], 'label': '1296.3190.18.bx1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '6.j1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '18.bx1.a1', 'projective_image': '648.731', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.bx1.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 71059949
    {'ambient': '1296.3190', 'aut_centralizer_order': 8, 'aut_label': '18.by1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '144.192', 'aut_weyl_index': 24, 'centralizer': '216.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.j1.a1', '6.be1.a1', '9.e1.a1'], 'contains': ['36.k1.a1', '36.bn1.a1', '36.ck1.a1', '54.bc1.a1', '54.bg1.a1'], 'core': '36.k1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4850, -1, 7837, -1, 3502, -1, 6312, -1], 'generators': [9, 432, 108, 216, 12], 'label': '1296.3190.18.by1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '6.j1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1.a1', 'old_label': '18.by1.a1', 'projective_image': '648.731', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.by1.a1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 71059950
    {'ambient': '1296.3190', 'aut_centralizer_order': 4, 'aut_label': '18.bz1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '144.192', 'aut_weyl_index': 24, 'centralizer': '216.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.j1.a1', '6.bf1.a1'], 'contains': ['36.bo1.a1', '36.cl1.a1', '36.db1.a1', '54.bc1.a1', '54.bh1.a1'], 'core': '108.c1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [3135, -1, 9803, -1, 2269, -1, 8780, -1], 'generators': [9, 432, 108, 216, 156], 'label': '1296.3190.18.bz1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.j1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.bf1.a1', 'old_label': '18.bz1.a1', 'projective_image': '648.731', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.bz1.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 71059951
    {'ambient': '1296.3190', 'aut_centralizer_order': 8, 'aut_label': '18.ca1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '144.192', 'aut_weyl_index': 24, 'centralizer': '216.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.i1.a1', '6.bg1.a1', '9.f1.a1'], 'contains': ['36.g1.a1', '36.by1.a1', '36.de1.a1', '54.bd1.a1', '54.be1.a1'], 'core': '36.g1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4975, -1, 6170, -1, 5514, -1, 5908, -1], 'generators': [111, 144, 54, 216, 12], 'label': '1296.3190.18.ca1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '6.i1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.d1.a1', 'old_label': '18.ca1.a1', 'projective_image': '648.731', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.ca1.a1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 71059952
    {'ambient': '1296.3190', 'aut_centralizer_order': 8, 'aut_label': '18.cb1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '144.192', 'aut_weyl_index': 24, 'centralizer': '216.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.j1.a1', '6.bh1.a1', '9.f1.a1'], 'contains': ['36.g1.a1', '36.cm1.a1', '36.dd1.a1', '54.bf1.a1', '54.bg1.a1', '54.bh1.a1'], 'core': '36.g1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3802, -1, 8314, -1, 3192, -1, 6732, -1], 'generators': [9, 144, 108, 216, 12], 'label': '1296.3190.18.cb1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '6.j1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.d1.a1', 'old_label': '18.cb1.a1', 'projective_image': '648.731', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.cb1.a1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 71059953
    {'ambient': '1296.3190', 'aut_centralizer_order': 6, 'aut_label': '2.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '576.8675', 'aut_weyl_index': 6, 'centralizer': '72.a1.a1', 'complements': ['648.e1.a1', '648.f1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1', '4.b1.a1', '4.c1.a1', '4.h1.a1', '4.h1.b1', '6.a1.a1', '6.b1.a1', '6.k1.a1', '6.n1.a1', '6.o1.a1'], 'core': '2.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5464, 7509, 4712, 2998, 6208, 3055, 2252, 2470], 'generators': [3, 12, 432, 18, 144, 216, 2], 'label': '1296.3190.2.a1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.a1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.a1.a1', '4.b1.a1', '4.c1.a1', '6.a1.a1', '6.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.a1.a1', 'projective_image': '216.162', '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': '72.46'}
  • id: 71059954
    {'ambient': '1296.3190', 'aut_centralizer_order': 6, 'aut_label': '4.h1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '144.192', 'aut_weyl_index': 24, 'centralizer': '72.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1'], 'contains': ['8.b1.a1', '8.c1.a1', '8.d1.a1', '12.by1.a1', '12.ca1.a1', '12.cb1.a1', '12.cc1.a1', '12.cd1.a1', '12.cd1.b1'], 'core': '8.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8752, -1, 1048, -1, 8534, -1, 1243, -1], 'generators': [3, 144, 12, 18, 2, 432], 'label': '1296.3190.4.h1.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': '4.h1.a1', 'projective_image': '432.598', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.h1.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 71059955
    {'ambient': '1296.3190', 'aut_centralizer_order': 432, 'aut_label': '24.a1', 'aut_quo_index': 24, 'aut_stab_index': 1, 'aut_weyl_group': '8.5', 'aut_weyl_index': 432, 'centralizer': '4.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '12.d1.a1', '12.i1.a1', '12.l1.a1', '12.q1.a1', '12.ba1.a1', '12.bi1.a1', '12.bp1.a1'], 'contains': ['48.a1.a1', '72.a1.a1', '72.b1.a1', '72.d1.a1', '72.j1.a1', '72.n1.a1', '72.r1.a1', '72.z1.a1'], 'core': '24.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3686, 2352, 7717, 7447, 3723, 6507, 6423, 6810], 'generators': [216, 2, 144, 432], 'label': '1296.3190.24.a1.a1', 'mobius_quo': 1, 'mobius_sub': 24, 'normal_closure': '24.a1.a1', 'normal_contained_in': ['8.a1.a1', '12.d1.a1', '12.i1.a1', '12.l1.a1'], 'normal_contains': ['48.a1.a1', '72.b1.a1', '72.a1.a1', '72.d1.a1'], 'normalizer': '1.a1.a1', 'old_label': '24.a1.a1', 'projective_image': '216.162', 'quotient_action_image': '4.2', 'quotient_action_kernel': '6.1', 'quotient_action_kernel_order': 6, 'quotient_fusion': None, 'short_label': '24.a1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 71059956
    {'ambient': '1296.3190', 'aut_centralizer_order': 432, 'aut_label': '24.b1', 'aut_quo_index': 24, 'aut_stab_index': 1, 'aut_weyl_group': '8.5', 'aut_weyl_index': 432, 'centralizer': '4.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '12.a1.a1', '12.m1.a1', '12.n1.a1', '12.v1.a1', '12.bb1.a1', '12.be1.a1', '12.bj1.a1'], 'contains': ['48.b1.a1', '72.a1.a1', '72.c1.a1', '72.e1.a1', '72.k1.a1', '72.o1.a1', '72.v1.a1', '72.ba1.a1'], 'core': '24.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4188, 4812, 6717, 5029, 3866, 4879, 6321, 5358], 'generators': [216, 2, 12, 432], 'label': '1296.3190.24.b1.a1', 'mobius_quo': 1, 'mobius_sub': 24, 'normal_closure': '24.b1.a1', 'normal_contained_in': ['8.a1.a1', '12.a1.a1', '12.m1.a1', '12.n1.a1'], 'normal_contains': ['48.b1.a1', '72.a1.a1', '72.c1.a1', '72.e1.a1'], 'normalizer': '1.a1.a1', 'old_label': '24.b1.a1', 'projective_image': '216.162', 'quotient_action_image': '4.2', 'quotient_action_kernel': '6.1', 'quotient_action_kernel_order': 6, 'quotient_fusion': None, 'short_label': '24.b1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 71059957
    {'ambient': '1296.3190', 'aut_centralizer_order': 432, 'aut_label': '24.c1', 'aut_quo_index': 24, 'aut_stab_index': 1, 'aut_weyl_group': '8.5', 'aut_weyl_index': 432, 'centralizer': '4.f1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '12.b1.a1', '12.e1.a1', '12.g1.a1', '12.bf1.a1', '12.bl1.a1', '12.br1.a1', '12.bs1.a1'], 'contains': ['48.c1.a1', '72.b1.a1', '72.c1.a1', '72.f1.a1', '72.l1.a1', '72.s1.a1', '72.w1.a1', '72.bd1.a1'], 'core': '24.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3771, 6716, 6776, 4105, 3330, 3151, 6829, 4218], 'generators': [216, 2, 12, 144], 'label': '1296.3190.24.c1.a1', 'mobius_quo': 1, 'mobius_sub': 24, 'normal_closure': '24.c1.a1', 'normal_contained_in': ['8.a1.a1', '12.b1.a1', '12.e1.a1', '12.g1.a1'], 'normal_contains': ['48.c1.a1', '72.b1.a1', '72.c1.a1', '72.f1.a1'], 'normalizer': '1.a1.a1', 'old_label': '24.c1.a1', 'projective_image': '216.162', 'quotient_action_image': '4.2', 'quotient_action_kernel': '6.1', 'quotient_action_kernel_order': 6, 'quotient_fusion': None, 'short_label': '24.c1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 71059958
    {'ambient': '1296.3190', 'aut_centralizer_order': 432, 'aut_label': '24.d1', 'aut_quo_index': 168, 'aut_stab_index': 1, 'aut_weyl_group': '8.5', 'aut_weyl_index': 432, 'centralizer': '8.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '12.c1.a1', '12.f1.a1', '12.h1.a1', '12.j1.a1', '12.k1.a1', '12.o1.a1', '12.p1.a1'], 'contains': ['48.d1.a1', '72.d1.a1', '72.e1.a1', '72.f1.a1', '72.p1.a1', '72.t1.a1', '72.x1.a1', '72.bi1.a1'], 'core': '24.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4253, 5658, 7649, 4618, 3489, 5294, 6935, 4959], 'generators': [216, 12, 144, 432], 'label': '1296.3190.24.d1.a1', 'mobius_quo': 1, 'mobius_sub': 8, 'normal_closure': '24.d1.a1', 'normal_contained_in': ['8.a1.a1', '12.c1.a1', '12.f1.a1', '12.j1.a1', '12.h1.a1', '12.k1.a1', '12.o1.a1', '12.p1.a1'], 'normal_contains': ['48.d1.a1', '72.d1.a1', '72.e1.a1', '72.f1.a1'], 'normalizer': '1.a1.a1', 'old_label': '24.d1.a1', 'projective_image': '648.731', 'quotient_action_image': '8.5', 'quotient_action_kernel': '3.1', 'quotient_action_kernel_order': 3, 'quotient_fusion': None, 'short_label': '24.d1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 71059959
    {'ambient': '1296.3190', 'aut_centralizer_order': 72, 'aut_label': '24.e1', 'aut_quo_index': 2, 'aut_stab_index': 2, 'aut_weyl_group': '24.14', 'aut_weyl_index': 144, 'centralizer': '12.d1.a1', 'complements': ['54.x1.a1', '54.bf1.a1', '54.bh1.a1', '54.y1.a1', '54.be1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['8.b1.a1', '12.a1.a1', '12.ca1.a1', '12.ce1.a1'], 'contains': ['48.b1.a1', '72.g1.a1', '72.h1.a1', '72.bn1.a1', '72.bu1.a1'], 'core': '24.e1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [9242, 8185, 1250, 2919, 9369, 1607, 1803, 2845], 'generators': [3, 2, 432, 12], 'label': '1296.3190.24.e1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '24.e1.a1', 'normal_contained_in': ['8.b1.a1', '12.a1.a1'], 'normal_contains': ['48.b1.a1', '72.g1.a1', '72.h1.a1'], 'normalizer': '1.a1.a1', 'old_label': '24.e1.a1', 'projective_image': '432.598', 'quotient_action_image': '2.1', 'quotient_action_kernel': '12.4', 'quotient_action_kernel_order': 12, 'quotient_fusion': None, 'short_label': '24.e1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 71059960
    {'ambient': '1296.3190', 'aut_centralizer_order': 72, 'aut_label': '24.e1', 'aut_quo_index': 2, 'aut_stab_index': 2, 'aut_weyl_group': '24.14', 'aut_weyl_index': 144, 'centralizer': '12.d1.a1', 'complements': ['54.x1.a1', '54.bf1.a1', '54.bh1.a1', '54.y1.a1', '54.be1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['8.b1.b1', '12.a1.a1', '12.ca1.b1', '12.ce1.b1'], 'contains': ['48.b1.a1', '72.g1.b1', '72.h1.b1', '72.bn1.b1', '72.bu1.b1'], 'core': '24.e1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [9242, 8185, 1292, 1395, 9369, 1607, 2431, 2104], 'generators': [219, 2, 432, 12], 'label': '1296.3190.24.e1.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '24.e1.b1', 'normal_contained_in': ['8.b1.b1', '12.a1.a1'], 'normal_contains': ['48.b1.a1', '72.g1.b1', '72.h1.b1'], 'normalizer': '1.a1.a1', 'old_label': '24.e1.b1', 'projective_image': '432.598', 'quotient_action_image': '2.1', 'quotient_action_kernel': '12.4', 'quotient_action_kernel_order': 12, 'quotient_fusion': None, 'short_label': '24.e1.b1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 71059961
    {'ambient': '1296.3190', 'aut_centralizer_order': 72, 'aut_label': '24.f1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '24.14', 'aut_weyl_index': 144, 'centralizer': '12.l1.a1', 'complements': ['54.s1.a1', '54.bc1.a1', '54.u1.a1', '54.w1.a1', '54.ba1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['8.b1.a1', '12.b1.a1', '12.cb1.a1', '12.cf1.a1'], 'contains': ['48.c1.a1', '72.g1.a1', '72.i1.a1', '72.bo1.a1', '72.bv1.a1'], 'core': '24.f1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8926, 9265, 1582, 2411, 9252, 835, 1852, 571], 'generators': [3, 2, 144, 12], 'label': '1296.3190.24.f1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '24.f1.a1', 'normal_contained_in': ['8.b1.a1', '12.b1.a1'], 'normal_contains': ['48.c1.a1', '72.g1.a1', '72.i1.a1'], 'normalizer': '1.a1.a1', 'old_label': '24.f1.a1', 'projective_image': '432.598', 'quotient_action_image': '2.1', 'quotient_action_kernel': '12.1', 'quotient_action_kernel_order': 12, 'quotient_fusion': None, 'short_label': '24.f1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 71059962
    {'ambient': '1296.3190', 'aut_centralizer_order': 72, 'aut_label': '24.f1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '24.14', 'aut_weyl_index': 144, 'centralizer': '12.l1.a1', 'complements': ['54.s1.a1', '54.bc1.a1', '54.u1.a1', '54.w1.a1', '54.ba1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['8.b1.b1', '12.b1.a1', '12.cb1.b1', '12.cf1.b1'], 'contains': ['48.c1.a1', '72.g1.b1', '72.i1.b1', '72.bo1.b1', '72.bv1.b1'], 'core': '24.f1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [8926, 9265, 2349, 689, 9252, 835, 2480, 175], 'generators': [219, 2, 144, 12], 'label': '1296.3190.24.f1.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '24.f1.b1', 'normal_contained_in': ['8.b1.b1', '12.b1.a1'], 'normal_contains': ['48.c1.a1', '72.g1.b1', '72.i1.b1'], 'normalizer': '1.a1.a1', 'old_label': '24.f1.b1', 'projective_image': '432.598', 'quotient_action_image': '2.1', 'quotient_action_kernel': '12.1', 'quotient_action_kernel_order': 12, 'quotient_fusion': None, 'short_label': '24.f1.b1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 71059963
    {'ambient': '1296.3190', 'aut_centralizer_order': 72, 'aut_label': '24.g1', 'aut_quo_index': 2, 'aut_stab_index': 2, 'aut_weyl_group': '24.14', 'aut_weyl_index': 144, 'centralizer': '24.a1.a1', 'complements': ['54.p1.a1', '54.r1.a1', '54.bb1.a1', '54.t1.a1', '54.z1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['8.b1.a1', '12.c1.a1', '12.cc1.a1', '12.ch1.a1'], 'contains': ['48.d1.a1', '72.h1.a1', '72.i1.a1', '72.bq1.a1', '72.bw1.a1'], 'core': '24.g1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [9153, 8725, 2041, 1803, 9311, 2379, 2049, 1708], 'generators': [3, 144, 432, 12], 'label': '1296.3190.24.g1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '24.g1.a1', 'normal_contained_in': ['8.b1.a1', '12.c1.a1'], 'normal_contains': ['48.d1.a1', '72.h1.a1', '72.i1.a1'], 'normalizer': '1.a1.a1', 'old_label': '24.g1.a1', 'projective_image': '1296.3190', 'quotient_action_image': '4.2', 'quotient_action_kernel': '6.2', 'quotient_action_kernel_order': 6, 'quotient_fusion': None, 'short_label': '24.g1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 71059964
    {'ambient': '1296.3190', 'aut_centralizer_order': 72, 'aut_label': '24.g1', 'aut_quo_index': 2, 'aut_stab_index': 2, 'aut_weyl_group': '24.14', 'aut_weyl_index': 144, 'centralizer': '24.a1.a1', 'complements': ['54.p1.a1', '54.r1.a1', '54.bb1.a1', '54.t1.a1', '54.z1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['8.b1.b1', '12.c1.a1', '12.cc1.b1', '12.ch1.b1'], 'contains': ['48.d1.a1', '72.h1.b1', '72.i1.b1', '72.bq1.b1', '72.bw1.b1'], 'core': '24.g1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [9153, 8725, 3035, 181, 9311, 2379, 2578, 967], 'generators': [219, 144, 432, 12], 'label': '1296.3190.24.g1.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '24.g1.b1', 'normal_contained_in': ['8.b1.b1', '12.c1.a1'], 'normal_contains': ['48.d1.a1', '72.h1.b1', '72.i1.b1'], 'normalizer': '1.a1.a1', 'old_label': '24.g1.b1', 'projective_image': '1296.3190', 'quotient_action_image': '4.2', 'quotient_action_kernel': '6.2', 'quotient_action_kernel_order': 6, 'quotient_fusion': None, 'short_label': '24.g1.b1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 71059965
    {'ambient': '1296.3190', 'aut_centralizer_order': 6, 'aut_label': '4.h1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '144.192', 'aut_weyl_index': 24, 'centralizer': '72.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1'], 'contains': ['8.b1.b1', '8.c1.a1', '8.d1.a1', '12.by1.b1', '12.ca1.b1', '12.cb1.b1', '12.cc1.b1', '12.cd1.c1', '12.cd1.d1'], 'core': '8.b1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [8752, -1, 1372, -1, 8534, -1, 1310, -1], 'generators': [219, 144, 12, 18, 2, 432], 'label': '1296.3190.4.h1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '4.h1.b1', 'projective_image': '432.598', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.h1.b1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 71059966
    {'ambient': '1296.3190', 'aut_centralizer_order': 216, 'aut_label': '24.h1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '8.5', 'aut_weyl_index': 432, 'centralizer': '8.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '12.bc1.a1', '12.bk1.a1', '12.bq1.a1'], 'contains': ['48.e1.a1', '72.a1.a1', '72.l1.a1', '72.m1.a1', '72.p1.a1', '72.q1.a1', '72.bb1.a1', '72.bc1.a1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2322, -1, 9485, -1, 2119, -1, 8541, -1], 'generators': [216, 2, 156, 432], 'label': '1296.3190.24.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.g1.a1', 'old_label': '24.h1.a1', 'projective_image': '216.162', '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': '4.2'}
  • id: 71059967
    {'ambient': '1296.3190', 'aut_centralizer_order': 216, 'aut_label': '24.i1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '8.5', 'aut_weyl_index': 432, 'centralizer': '8.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '12.w1.a1', '12.bm1.a1', '12.bt1.a1'], 'contains': ['48.f1.a1', '72.b1.a1', '72.k1.a1', '72.m1.a1', '72.t1.a1', '72.u1.a1', '72.be1.a1', '72.bf1.a1'], 'core': '72.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [945, -1, 8552, -1, 2178, -1, 8184, -1], 'generators': [216, 2, 444, 144], 'label': '1296.3190.24.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.e1.a1', 'old_label': '24.i1.a1', 'projective_image': '216.162', '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': '4.2'}
  • id: 71059968
    {'ambient': '1296.3190', 'aut_centralizer_order': 216, 'aut_label': '24.j1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '8.5', 'aut_weyl_index': 432, 'centralizer': '8.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '12.r1.a1', '12.bg1.a1', '12.bn1.a1'], 'contains': ['48.g1.a1', '72.c1.a1', '72.j1.a1', '72.m1.a1', '72.x1.a1', '72.y1.a1', '72.bg1.a1', '72.bh1.a1'], 'core': '72.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [4814, -1, 5849, -1, 4794, -1, 6737, -1], 'generators': [216, 2, 12, 576], 'label': '1296.3190.24.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '24.j1.a1', 'projective_image': '216.162', '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': '4.2'}
  • id: 71059969
    {'ambient': '1296.3190', 'aut_centralizer_order': 216, 'aut_label': '24.k1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '4.2', 'aut_weyl_index': 864, 'centralizer': '8.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '12.bo1.a1'], 'contains': ['48.h1.a1', '72.j1.a1', '72.k1.a1', '72.l1.a1', '72.m1.a1', '72.bi1.a1', '72.bj1.a1', '72.bk1.a1', '72.bl1.a1', '72.bm1.a1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [1177, -1, 8314, -1, 2027, -1, 8590, -1], 'generators': [216, 2, 444, 576], 'label': '1296.3190.24.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.e1.a1', 'old_label': '24.k1.a1', 'projective_image': '216.162', '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': '2.1'}
  • id: 71059970
    {'ambient': '1296.3190', 'aut_centralizer_order': 216, 'aut_label': '24.l1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '8.5', 'aut_weyl_index': 432, 'centralizer': '8.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '12.x1.a1', '12.bh1.a1', '12.bu1.a1'], 'contains': ['48.i1.a1', '72.d1.a1', '72.o1.a1', '72.q1.a1', '72.s1.a1', '72.u1.a1', '72.bg1.a1', '72.bj1.a1'], 'core': '72.d1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1938, -1, 6944, -1, 2443, -1, 7269, -1], 'generators': [216, 14, 144, 432], 'label': '1296.3190.24.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.a1', 'old_label': '24.l1.a1', 'projective_image': '648.731', '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': '4.2'}
  • id: 71059971
    {'ambient': '1296.3190', 'aut_centralizer_order': 216, 'aut_label': '24.m1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '8.5', 'aut_weyl_index': 432, 'centralizer': '8.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '12.s1.a1', '12.bv1.a1', '12.bw1.a1'], 'contains': ['48.j1.a1', '72.e1.a1', '72.n1.a1', '72.q1.a1', '72.w1.a1', '72.y1.a1', '72.be1.a1', '72.bk1.a1'], 'core': '72.e1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2365, -1, 9154, -1, 1910, -1, 7371, -1], 'generators': [216, 146, 12, 432], 'label': '1296.3190.24.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '24.m1.a1', 'projective_image': '648.731', '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': '4.2'}
  • id: 71059972
    {'ambient': '1296.3190', 'aut_centralizer_order': 216, 'aut_label': '24.n1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '4.2', 'aut_weyl_index': 864, 'centralizer': '8.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '12.bx1.a1'], 'contains': ['48.k1.a1', '72.n1.a1', '72.o1.a1', '72.p1.a1', '72.q1.a1', '72.bd1.a1', '72.bf1.a1', '72.bh1.a1', '72.bl1.a1', '72.bm1.a1'], 'core': '216.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [1449, -1, 8353, -1, 1851, -1, 8492, -1], 'generators': [216, 146, 156, 432], 'label': '1296.3190.24.n1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.f1.a1', 'old_label': '24.n1.a1', 'projective_image': '648.731', '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': '2.1'}
  • id: 71059973
    {'ambient': '1296.3190', 'aut_centralizer_order': 216, 'aut_label': '24.o1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '8.5', 'aut_weyl_index': 432, 'centralizer': '8.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '12.t1.a1', '12.y1.a1', '12.bd1.a1'], 'contains': ['48.l1.a1', '72.f1.a1', '72.r1.a1', '72.u1.a1', '72.v1.a1', '72.y1.a1', '72.bb1.a1', '72.bl1.a1'], 'core': '72.f1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3559, -1, 3657, -1, 4602, -1, 5611, -1], 'generators': [216, 434, 12, 144], 'label': '1296.3190.24.o1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '24.o1.a1', 'projective_image': '648.731', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.o1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 71059974
    {'ambient': '1296.3190', 'aut_centralizer_order': 216, 'aut_label': '24.p1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '4.2', 'aut_weyl_index': 864, 'centralizer': '8.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '12.z1.a1'], 'contains': ['48.m1.a1', '72.r1.a1', '72.s1.a1', '72.t1.a1', '72.u1.a1', '72.ba1.a1', '72.bc1.a1', '72.bh1.a1', '72.bk1.a1', '72.bm1.a1'], 'core': '216.c1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [602, -1, 6910, -1, 2237, -1, 7953, -1], 'generators': [216, 434, 444, 144], 'label': '1296.3190.24.p1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.a1', 'old_label': '24.p1.a1', 'projective_image': '648.731', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.p1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 71059975
    {'ambient': '1296.3190', 'aut_centralizer_order': 216, 'aut_label': '24.q1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '4.2', 'aut_weyl_index': 864, 'centralizer': '8.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '12.u1.a1'], 'contains': ['48.n1.a1', '72.v1.a1', '72.w1.a1', '72.x1.a1', '72.y1.a1', '72.z1.a1', '72.bc1.a1', '72.bf1.a1', '72.bj1.a1', '72.bm1.a1'], 'core': '216.d1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [3220, -1, 4663, -1, 4021, -1, 6515, -1], 'generators': [216, 434, 12, 576], 'label': '1296.3190.24.q1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '24.q1.a1', 'projective_image': '648.731', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.q1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 71059976
    {'ambient': '1296.3190', 'aut_centralizer_order': 2, 'aut_label': '4.i1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '432.759', 'aut_weyl_index': 8, 'centralizer': '216.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1'], 'contains': ['8.b1.a1', '8.e1.a1', '8.f1.a1', '12.bz1.a1', '12.ce1.a1', '12.cf1.a1', '12.cg1.a1', '12.cg1.a2', '12.ch1.a1'], 'core': '8.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [9172, -1, 3360, -1, 9252, -1, 3927, -1], 'generators': [3, 432, 144, 54, 2, 12], 'label': '1296.3190.4.i1.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': '4.i1.a1', 'projective_image': '432.598', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.i1.a1', 'subgroup_fusion': None, 'weyl_group': '108.39'}
  • id: 71059977
    {'ambient': '1296.3190', 'aut_centralizer_order': 216, 'aut_label': '24.r1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1728, 'centralizer': '8.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1'], 'contains': ['48.o1.a1', '72.z1.a1', '72.ba1.a1', '72.bb1.a1', '72.bc1.a1', '72.bd1.a1', '72.be1.a1', '72.bf1.a1', '72.bg1.a1', '72.bh1.a1', '72.bi1.a1', '72.bj1.a1', '72.bk1.a1', '72.bl1.a1'], 'core': '648.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [1278, -1, 7027, -1, 1969, -1, 8400, -1], 'generators': [216, 434, 444, 576], 'label': '1296.3190.24.r1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.a1.a1', 'old_label': '24.r1.a1', 'projective_image': '648.731', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.r1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 71059978
    {'ambient': '1296.3190', 'aut_centralizer_order': 72, 'aut_label': '24.s1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '8.5', 'aut_weyl_index': 432, 'centralizer': '12.q1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.b1.a1', '12.q1.a1', '12.by1.a1', '12.bz1.a1'], 'contains': ['48.a1.a1', '72.bn1.a1', '72.bo1.a1', '72.bp1.a1', '72.bq1.a1', '72.br1.a1', '72.bs1.a1', '72.bt1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8785, -1, 3523, -1, 8910, -1, 1901, -1], 'generators': [3, 2, 144, 432], 'label': '1296.3190.24.s1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '24.s1.a1', 'projective_image': '432.598', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.s1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 71059979
    {'ambient': '1296.3190', 'aut_centralizer_order': 72, 'aut_label': '24.s1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '8.5', 'aut_weyl_index': 432, 'centralizer': '12.q1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.b1.b1', '12.q1.a1', '12.by1.b1', '12.bz1.b1'], 'contains': ['48.a1.a1', '72.bn1.b1', '72.bo1.b1', '72.bp1.b1', '72.bq1.b1', '72.br1.b1', '72.bs1.b1', '72.bt1.b1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8785, -1, 4211, -1, 8910, -1, 2529, -1], 'generators': [219, 2, 144, 432], 'label': '1296.3190.24.s1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '24.s1.b1', 'projective_image': '432.598', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.s1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 71059980
    {'ambient': '1296.3190', 'aut_centralizer_order': 36, 'aut_label': '24.t1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '24.14', 'aut_weyl_index': 144, 'centralizer': '24.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.b1.a1', '12.r1.a1', '12.cg1.a1', '12.cg1.a2'], 'contains': ['48.g1.a1', '72.g1.a1', '72.bp1.a1', '72.bw1.a1', '72.bx1.a1'], 'core': '72.g1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [9326, -1, 1683, -1, 9772, -1, 2855, -1], 'generators': [3, 2, 576, 12], 'label': '1296.3190.24.t1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '24.t1.a1', 'projective_image': '432.598', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.t1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 71059981
    {'ambient': '1296.3190', 'aut_centralizer_order': 36, 'aut_label': '24.t1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '24.14', 'aut_weyl_index': 144, 'centralizer': '24.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.b1.b1', '12.r1.a1', '12.cg1.b1', '12.cg1.b2'], 'contains': ['48.g1.a1', '72.g1.b1', '72.bp1.b1', '72.bw1.b1', '72.bx1.b1'], 'core': '72.g1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [9326, -1, 2182, -1, 9772, -1, 2973, -1], 'generators': [219, 2, 576, 12], 'label': '1296.3190.24.t1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '24.t1.b1', 'projective_image': '432.598', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.t1.b1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 71059982
    {'ambient': '1296.3190', 'aut_centralizer_order': 36, 'aut_label': '24.u1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '24.14', 'aut_weyl_index': 144, 'centralizer': '24.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.b1.a1', '12.s1.a1'], 'contains': ['48.j1.a1', '72.h1.a1', '72.br1.a1', '72.bv1.a1', '72.bx1.a1'], 'core': '72.h1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8441, -1, 2993, -1, 9194, -1, 1754, -1], 'generators': [3, 146, 432, 12], 'label': '1296.3190.24.u1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '24.u1.a1', 'projective_image': '1296.3190', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.u1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 71059983
    {'ambient': '1296.3190', 'aut_centralizer_order': 36, 'aut_label': '24.u1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '24.14', 'aut_weyl_index': 144, 'centralizer': '24.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.b1.b1', '12.s1.a1'], 'contains': ['48.j1.a1', '72.h1.b1', '72.br1.b1', '72.bv1.b1', '72.bx1.b1'], 'core': '72.h1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [8441, -1, 3557, -1, 9194, -1, 2382, -1], 'generators': [219, 146, 432, 12], 'label': '1296.3190.24.u1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '24.u1.b1', 'projective_image': '1296.3190', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.u1.b1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 71059984
    {'ambient': '1296.3190', 'aut_centralizer_order': 36, 'aut_label': '24.v1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '24.14', 'aut_weyl_index': 144, 'centralizer': '24.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.b1.a1', '12.t1.a1', '12.cd1.a1', '12.cd1.b1'], 'contains': ['48.l1.a1', '72.i1.a1', '72.bs1.a1', '72.bu1.a1', '72.bx1.a1'], 'core': '72.i1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8561, -1, 425, -1, 9427, -1, 715, -1], 'generators': [3, 434, 144, 12], 'label': '1296.3190.24.v1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '24.v1.a1', 'projective_image': '1296.3190', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.v1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 71059985
    {'ambient': '1296.3190', 'aut_centralizer_order': 36, 'aut_label': '24.v1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '24.14', 'aut_weyl_index': 144, 'centralizer': '24.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.b1.b1', '12.t1.a1', '12.cd1.c1', '12.cd1.d1'], 'contains': ['48.l1.a1', '72.i1.b1', '72.bs1.b1', '72.bu1.b1', '72.bx1.b1'], 'core': '72.i1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [8561, -1, 546, -1, 9427, -1, 1032, -1], 'generators': [219, 434, 144, 12], 'label': '1296.3190.24.v1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '24.v1.b1', 'projective_image': '1296.3190', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.v1.b1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 71059986
    {'ambient': '1296.3190', 'aut_centralizer_order': 36, 'aut_label': '24.w1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '12.4', 'aut_weyl_index': 288, 'centralizer': '24.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.b1.a1', '12.u1.a1'], 'contains': ['48.n1.a1', '72.bt1.a1', '72.bu1.a1', '72.bv1.a1', '72.bw1.a1', '72.bx1.a1'], 'core': '216.e1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [8498, -1, 1119, -1, 9486, -1, 1705, -1], 'generators': [3, 434, 576, 12], 'label': '1296.3190.24.w1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '24.w1.a1', 'projective_image': '1296.3190', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.w1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 71059987
    {'ambient': '1296.3190', 'aut_centralizer_order': 2, 'aut_label': '4.i1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '432.759', 'aut_weyl_index': 8, 'centralizer': '216.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1'], 'contains': ['8.b1.b1', '8.e1.a1', '8.f1.a1', '12.bz1.b1', '12.ce1.b1', '12.cf1.b1', '12.cg1.b1', '12.cg1.b2', '12.ch1.b1'], 'core': '8.b1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [9172, -1, 3719, -1, 9252, -1, 4129, -1], 'generators': [219, 432, 144, 54, 2, 12], 'label': '1296.3190.4.i1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '4.i1.b1', 'projective_image': '432.598', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.i1.b1', 'subgroup_fusion': None, 'weyl_group': '108.39'}
  • id: 71059988
    {'ambient': '1296.3190', 'aut_centralizer_order': 36, 'aut_label': '24.w1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '12.4', 'aut_weyl_index': 288, 'centralizer': '24.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.b1.b1', '12.u1.a1'], 'contains': ['48.n1.a1', '72.bt1.b1', '72.bu1.b1', '72.bv1.b1', '72.bw1.b1', '72.bx1.b1'], 'core': '216.e1.b1', 'coset_action_label': None, 'count': 4, 'diagramx': [8498, -1, 1162, -1, 9486, -1, 2264, -1], 'generators': [219, 434, 576, 12], 'label': '1296.3190.24.w1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '24.w1.b1', 'projective_image': '1296.3190', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.w1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 71059989
    {'ambient': '1296.3190', 'aut_centralizer_order': 72, 'aut_label': '24.x1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '8.5', 'aut_weyl_index': 432, 'centralizer': '12.v1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.c1.a1', '12.v1.a1', '12.ca1.a1', '12.ca1.b1'], 'contains': ['48.b1.a1', '72.by1.a1', '72.bz1.a1', '72.ca1.a1', '72.cb1.a1', '72.cc1.a1', '72.cd1.a1', '72.cd1.b1', '72.ce1.a1', '72.ce1.b1'], 'core': '48.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [7402, -1, 1014, -1, 5101, -1, 1950, -1], 'generators': [18, 2, 12, 432], 'label': '1296.3190.24.x1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.n1.a1', 'old_label': '24.x1.a1', 'projective_image': '432.598', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.x1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 71059990
    {'ambient': '1296.3190', 'aut_centralizer_order': 72, 'aut_label': '24.y1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '24.14', 'aut_weyl_index': 144, 'centralizer': '12.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.c1.a1', '12.d1.a1', '12.by1.a1', '12.by1.b1'], 'contains': ['48.a1.a1', '72.by1.a1', '72.cf1.a1', '72.cg1.a1', '72.ci1.a1', '72.ci1.b1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7275, -1, 1616, -1, 5319, -1, 1430, -1], 'generators': [18, 2, 432, 144], 'label': '1296.3190.24.y1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '24.y1.a1', 'projective_image': '432.598', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.y1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 71059991
    {'ambient': '1296.3190', 'aut_centralizer_order': 72, 'aut_label': '24.z1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '24.14', 'aut_weyl_index': 144, 'centralizer': '24.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.c1.a1', '12.e1.a1', '12.cb1.a1', '12.cb1.b1'], 'contains': ['48.c1.a1', '72.bz1.a1', '72.cf1.a1', '72.ch1.a1', '72.cj1.a1'], 'core': '48.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7469, -1, 1335, -1, 5377, -1, 2098, -1], 'generators': [18, 2, 12, 144], 'label': '1296.3190.24.z1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '24.z1.a1', 'projective_image': '432.598', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.z1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 71059992
    {'ambient': '1296.3190', 'aut_centralizer_order': 36, 'aut_label': '24.ba1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '24.14', 'aut_weyl_index': 144, 'centralizer': '24.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.c1.a1', '12.w1.a1'], 'contains': ['48.f1.a1', '72.ca1.a1', '72.cf1.a1', '72.ck1.a1', '72.cl1.a1', '72.cl1.b1'], 'core': '144.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [2478, -1, 3843, -1, 4294, -1, 3306, -1], 'generators': [18, 2, 444, 144], 'label': '1296.3190.24.ba1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.a1', 'old_label': '24.ba1.a1', 'projective_image': '432.598', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.ba1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 71059993
    {'ambient': '1296.3190', 'aut_centralizer_order': 72, 'aut_label': '24.bb1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '24.14', 'aut_weyl_index': 144, 'centralizer': '24.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.c1.a1', '12.f1.a1', '12.cc1.a1', '12.cc1.b1'], 'contains': ['48.d1.a1', '72.cb1.a1', '72.cg1.a1', '72.ch1.a1', '72.ck1.a1'], 'core': '48.d1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7513, -1, 1454, -1, 5261, -1, 2000, -1], 'generators': [18, 12, 432, 144], 'label': '1296.3190.24.bb1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '24.bb1.a1', 'projective_image': '1296.3190', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bb1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 71059994
    {'ambient': '1296.3190', 'aut_centralizer_order': 36, 'aut_label': '24.bc1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '24.14', 'aut_weyl_index': 144, 'centralizer': '24.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.c1.a1', '12.x1.a1'], 'contains': ['48.i1.a1', '72.cc1.a1', '72.cg1.a1', '72.cj1.a1', '72.cl1.a1', '72.cl1.b1'], 'core': '144.d1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [3485, -1, 3311, -1, 4410, -1, 3207, -1], 'generators': [18, 14, 432, 144], 'label': '1296.3190.24.bc1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.a1', 'old_label': '24.bc1.a1', 'projective_image': '1296.3190', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bc1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 71059995
    {'ambient': '1296.3190', 'aut_centralizer_order': 36, 'aut_label': '24.bd1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '24.14', 'aut_weyl_index': 144, 'centralizer': '24.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.c1.a1', '12.y1.a1', '12.cd1.a1', '12.cd1.c1'], 'contains': ['48.l1.a1', '72.cd1.a1', '72.ch1.a1', '72.ci1.a1', '72.cl1.a1'], 'core': '144.f1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7359, -1, 15, -1, 5436, -1, 983, -1], 'generators': [18, 434, 12, 144], 'label': '1296.3190.24.bd1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '24.bd1.a1', 'projective_image': '1296.3190', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bd1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 71059996
    {'ambient': '1296.3190', 'aut_centralizer_order': 36, 'aut_label': '24.bd1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '24.14', 'aut_weyl_index': 144, 'centralizer': '24.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.c1.a1', '12.y1.a1', '12.cd1.b1', '12.cd1.d1'], 'contains': ['48.l1.a1', '72.cd1.b1', '72.ch1.a1', '72.ci1.b1', '72.cl1.b1'], 'core': '144.f1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7359, -1, 459, -1, 5436, -1, 934, -1], 'generators': [18, 866, 12, 144], 'label': '1296.3190.24.bd1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '24.bd1.b1', 'projective_image': '1296.3190', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bd1.b1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 71059997
    {'ambient': '1296.3190', 'aut_centralizer_order': 36, 'aut_label': '24.be1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '12.4', 'aut_weyl_index': 288, 'centralizer': '24.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.c1.a1', '12.z1.a1'], 'contains': ['48.m1.a1', '72.ce1.a1', '72.ci1.a1', '72.cj1.a1', '72.ck1.a1', '72.cl1.b1'], 'core': '432.c1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [2699, -1, 2499, -1, 4352, -1, 3256, -1], 'generators': [18, 434, 444, 144], 'label': '1296.3190.24.be1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.a1', 'old_label': '24.be1.a1', 'projective_image': '1296.3190', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.be1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 71059998
    {'ambient': '1296.3190', 'aut_centralizer_order': 12, 'aut_label': '6.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '288.1040', 'aut_weyl_index': 12, 'centralizer': '72.a1.a1', 'complements': ['216.bo1.a1', '216.bq1.a1', '216.bq1.a2', '216.bs1.a1', '216.bv1.a1', '216.bv1.a2', '216.bw1.a1', '216.by1.a1', '216.by1.a2'], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '3.d1.a1'], 'contains': ['12.b1.a1', '12.e1.a1', '12.g1.a1', '12.cb1.a1', '12.cb1.b1', '18.a1.a1', '18.e1.a1', '18.p1.a1'], 'core': '6.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5446, 8183, 4712, 2395, 6237, 1018, 2301, 1820], 'generators': [3, 144, 12, 18, 216, 2], 'label': '1296.3190.6.a1.a1', 'mobius_quo': 0, 'mobius_sub': 3, 'normal_closure': '6.a1.a1', 'normal_contained_in': ['2.a1.a1'], 'normal_contains': ['12.b1.a1', '12.e1.a1', '12.g1.a1', '18.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '6.a1.a1', 'projective_image': '216.162', 'quotient_action_image': '2.1', 'quotient_action_kernel': '3.1', 'quotient_action_kernel_order': 3, 'quotient_fusion': None, 'short_label': '6.a1.a1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 71059999
    {'ambient': '1296.3190', 'aut_centralizer_order': 36, 'aut_label': '24.be1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '12.4', 'aut_weyl_index': 288, 'centralizer': '24.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.c1.a1', '12.z1.a1'], 'contains': ['48.m1.a1', '72.ce1.b1', '72.ci1.b1', '72.cj1.a1', '72.ck1.a1', '72.cl1.a1'], 'core': '432.c1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [2699, -1, 2533, -1, 4352, -1, 3159, -1], 'generators': [18, 866, 444, 144], 'label': '1296.3190.24.be1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.a1', 'old_label': '24.be1.b1', 'projective_image': '1296.3190', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.be1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 71060000
    {'ambient': '1296.3190', 'aut_centralizer_order': 24, 'aut_label': '24.bf1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '24.14', 'aut_weyl_index': 144, 'centralizer': '36.m1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.d1.a1', '12.ba1.a1', '12.by1.a1', '12.by1.b1'], 'contains': ['48.a1.a1', '72.cm1.a1', '72.cn1.a1', '72.cq1.a1', '72.ct1.a1', '72.ct1.b1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [8617, -1, 1733, -1, 8304, -1, 666, -1], 'generators': [9, 2, 432, 144], 'label': '1296.3190.24.bf1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.k1.a1', 'old_label': '24.bf1.a1', 'projective_image': '432.598', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bf1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 71060001
    {'ambient': '1296.3190', 'aut_centralizer_order': 24, 'aut_label': '24.bg1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '24.14', 'aut_weyl_index': 144, 'centralizer': '36.x1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.d1.a1', '12.bb1.a1', '12.ca1.a1', '12.ca1.b1'], 'contains': ['48.b1.a1', '72.cm1.a1', '72.co1.a1', '72.cr1.a1', '72.cu1.a1', '72.cu1.b1'], 'core': '48.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [8741, -1, 690, -1, 8487, -1, 617, -1], 'generators': [9, 2, 432, 12], 'label': '1296.3190.24.bg1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.n1.a1', 'old_label': '24.bg1.a1', 'projective_image': '432.598', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bg1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 71060002
    {'ambient': '1296.3190', 'aut_centralizer_order': 12, 'aut_label': '24.bh1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '24.14', 'aut_weyl_index': 144, 'centralizer': '72.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.d1.a1', '12.bc1.a1'], 'contains': ['48.e1.a1', '72.cm1.a1', '72.cp1.a1', '72.cs1.a1', '72.cv1.a1', '72.cv1.b1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [8244, -1, 4256, -1, 6968, -1, 2627, -1], 'generators': [9, 2, 432, 156], 'label': '1296.3190.24.bh1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bc1.a1', 'old_label': '24.bh1.a1', 'projective_image': '432.598', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bh1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 71060003
    {'ambient': '1296.3190', 'aut_centralizer_order': 24, 'aut_label': '24.bi1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '72.46', 'aut_weyl_index': 48, 'centralizer': '72.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.d1.a1', '12.g1.a1', '12.cb1.a1', '12.cb1.b1'], 'contains': ['48.c1.a1', '72.cn1.a1', '72.co1.a1', '72.cp1.a1', '72.cw1.a1'], 'core': '48.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8341, -1, 1378, -1, 8365, -1, 1481, -1], 'generators': [9, 2, 12, 144], 'label': '1296.3190.24.bi1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '24.bi1.a1', 'projective_image': '432.598', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bi1.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 71060004
    {'ambient': '1296.3190', 'aut_centralizer_order': 24, 'aut_label': '24.bj1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '72.46', 'aut_weyl_index': 48, 'centralizer': '72.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.d1.a1', '12.h1.a1', '12.cc1.a1', '12.cc1.b1'], 'contains': ['48.d1.a1', '72.cq1.a1', '72.cr1.a1', '72.cs1.a1', '72.cw1.a1'], 'core': '48.d1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8388, -1, 1505, -1, 8244, -1, 1337, -1], 'generators': [9, 432, 12, 144], 'label': '1296.3190.24.bj1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.h1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '24.bj1.a1', 'projective_image': '1296.3190', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bj1.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 71060005
    {'ambient': '1296.3190', 'aut_centralizer_order': 12, 'aut_label': '24.bk1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '72.46', 'aut_weyl_index': 48, 'centralizer': '72.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.d1.a1', '12.bd1.a1', '12.cd1.b1', '12.cd1.c1'], 'contains': ['48.l1.a1', '72.ct1.a1', '72.cu1.a1', '72.cv1.a1', '72.cw1.a1'], 'core': '144.f1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8291, -1, 581, -1, 8427, -1, 464, -1], 'generators': [9, 866, 12, 144], 'label': '1296.3190.24.bk1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '24.bk1.a1', 'projective_image': '1296.3190', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bk1.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 71060006
    {'ambient': '1296.3190', 'aut_centralizer_order': 12, 'aut_label': '24.bk1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '72.46', 'aut_weyl_index': 48, 'centralizer': '72.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.d1.a1', '12.bd1.a1', '12.cd1.a1', '12.cd1.d1'], 'contains': ['48.l1.a1', '72.ct1.b1', '72.cu1.b1', '72.cv1.b1', '72.cw1.a1'], 'core': '144.f1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8291, -1, 502, -1, 8427, -1, 412, -1], 'generators': [9, 434, 12, 144], 'label': '1296.3190.24.bk1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '24.bk1.b1', 'projective_image': '1296.3190', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bk1.b1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 71060007
    {'ambient': '1296.3190', 'aut_centralizer_order': 24, 'aut_label': '24.bl1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '24.14', 'aut_weyl_index': 144, 'centralizer': '72.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.e1.a1', '12.be1.a1', '12.ce1.a1', '12.ce1.b1'], 'contains': ['48.b1.a1', '72.cx1.a1', '72.cy1.a1', '72.db1.a1', '72.dc1.a1'], 'core': '48.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [9630, -1, 2449, -1, 9603, -1, 3675, -1], 'generators': [54, 2, 12, 432], 'label': '1296.3190.24.bl1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.p1.a1', 'old_label': '24.bl1.a1', 'projective_image': '432.598', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bl1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 71060008
    {'ambient': '1296.3190', 'aut_centralizer_order': 24, 'aut_label': '24.bm1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '24.14', 'aut_weyl_index': 144, 'centralizer': '72.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.e1.a1', '12.bf1.a1', '12.cf1.a1', '12.cf1.b1'], 'contains': ['48.c1.a1', '72.cx1.a1', '72.cz1.a1', '72.dd1.a1', '72.de1.a1'], 'core': '48.c1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [9095, -1, 3387, -1, 9544, -1, 3490, -1], 'generators': [54, 2, 12, 144], 'label': '1296.3190.24.bm1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.q1.a1', 'old_label': '24.bm1.a1', 'projective_image': '432.598', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bm1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 71060009
    {'ambient': '1296.3190', 'aut_centralizer_order': 12, 'aut_label': '6.b1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '288.1040', 'aut_weyl_index': 12, 'centralizer': '72.a1.a1', 'complements': ['216.bl1.a1', '216.bn1.a1', '216.br1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '3.a1.a1'], 'contains': ['12.c1.a1', '12.f1.a1', '12.h1.a1', '12.cc1.a1', '12.cc1.b1', '18.a1.a1', '18.f1.a1', '18.q1.a1'], 'core': '6.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5531, 7748, 4759, 2903, 6179, 3317, 2252, 2216], 'generators': [3, 144, 12, 18, 216, 432], 'label': '1296.3190.6.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.c1.a1', '12.f1.a1', '12.h1.a1', '18.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '6.b1.a1', 'projective_image': '648.731', 'quotient_action_image': '2.1', 'quotient_action_kernel': '3.1', 'quotient_action_kernel_order': 3, 'quotient_fusion': None, 'short_label': '6.b1.a1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 71060010
    {'ambient': '1296.3190', 'aut_centralizer_order': 12, 'aut_label': '24.bn1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '24.14', 'aut_weyl_index': 144, 'centralizer': '72.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.e1.a1', '12.bg1.a1', '12.cg1.a1', '12.cg1.b1'], 'contains': ['48.g1.a1', '72.cx1.a1', '72.da1.a1', '72.df1.a1', '72.dg1.a1'], 'core': '144.c1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [9761, -1, 2265, -1, 9944, -1, 4290, -1], 'generators': [54, 2, 12, 576], 'label': '1296.3190.24.bn1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.r1.a1', 'old_label': '24.bn1.a1', 'projective_image': '432.598', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bn1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 71060011
    {'ambient': '1296.3190', 'aut_centralizer_order': 12, 'aut_label': '24.bn1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '24.14', 'aut_weyl_index': 144, 'centralizer': '72.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.e1.a1', '12.bg1.a1', '12.cg1.a2', '12.cg1.b2'], 'contains': ['48.g1.a1', '72.cx1.a1', '72.da1.a2', '72.df1.a2', '72.dg1.a2'], 'core': '144.c1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [9761, -1, 2407, -1, 9944, -1, 4339, -1], 'generators': [54, 2, 12, 1008], 'label': '1296.3190.24.bn1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.r1.a1', 'old_label': '24.bn1.a2', 'projective_image': '432.598', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bn1.a2', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 71060012
    {'ambient': '1296.3190', 'aut_centralizer_order': 24, 'aut_label': '24.bo1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '72.46', 'aut_weyl_index': 48, 'centralizer': '36.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.e1.a1', '12.i1.a1', '12.bz1.a1', '12.bz1.b1'], 'contains': ['48.a1.a1', '72.cy1.a1', '72.cz1.a1', '72.da1.a1', '72.da1.a2', '72.dh1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [9473, -1, 4871, -1, 9134, -1, 3948, -1], 'generators': [54, 2, 144, 432], 'label': '1296.3190.24.bo1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.i1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '24.bo1.a1', 'projective_image': '432.598', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bo1.a1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 71060013
    {'ambient': '1296.3190', 'aut_centralizer_order': 24, 'aut_label': '24.bp1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '72.46', 'aut_weyl_index': 48, 'centralizer': '72.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.e1.a1', '12.j1.a1', '12.ch1.a1', '12.ch1.b1'], 'contains': ['48.d1.a1', '72.db1.a1', '72.dd1.a1', '72.df1.a1', '72.df1.a2', '72.dh1.a1'], 'core': '48.d1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [9545, -1, 3725, -1, 9883, -1, 4189, -1], 'generators': [54, 12, 144, 432], 'label': '1296.3190.24.bp1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.j1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '24.bp1.a1', 'projective_image': '1296.3190', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bp1.a1', 'subgroup_fusion': None, 'weyl_group': '36.13'}
  • id: 71060014
    {'ambient': '1296.3190', 'aut_centralizer_order': 12, 'aut_label': '24.bq1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '72.46', 'aut_weyl_index': 48, 'centralizer': '72.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.e1.a1', '12.bh1.a1'], 'contains': ['48.i1.a1', '72.dc1.a1', '72.de1.a1', '72.dg1.a1', '72.dg1.a2', '72.dh1.a1'], 'core': '144.d1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [7558, -1, 3878, -1, 8182, -1, 5209, -1], 'generators': [54, 14, 144, 432], 'label': '1296.3190.24.bq1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.d1.a1', 'old_label': '24.bq1.a1', 'projective_image': '1296.3190', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bq1.a1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 71060015
    {'ambient': '1296.3190', 'aut_centralizer_order': 8, 'aut_label': '24.br1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '72.46', 'aut_weyl_index': 48, 'centralizer': '108.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.f1.a1', '12.bi1.a1', '12.bz1.a1', '12.bz1.b1'], 'contains': ['48.a1.a1', '72.di1.a1', '72.dj1.a1', '72.dl1.a1', '72.dl1.a2', '72.dp1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [7955, -1, 4983, -1, 5844, -1, 5261, -1], 'generators': [45, 2, 144, 432], 'label': '1296.3190.24.br1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.l1.a1', 'old_label': '24.br1.a1', 'projective_image': '432.598', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.br1.a1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 71060016
    {'ambient': '1296.3190', 'aut_centralizer_order': 8, 'aut_label': '24.bs1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '72.46', 'aut_weyl_index': 48, 'centralizer': '216.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.f1.a1', '12.bj1.a1', '12.ce1.a1', '12.ce1.b1'], 'contains': ['48.b1.a1', '72.di1.a1', '72.dk1.a1', '72.dm1.a1', '72.dq1.a1'], 'core': '48.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [8140, -1, 3154, -1, 6101, -1, 5157, -1], 'generators': [45, 2, 12, 432], 'label': '1296.3190.24.bs1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.p1.a1', 'old_label': '24.bs1.a1', 'projective_image': '432.598', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bs1.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 71060017
    {'ambient': '1296.3190', 'aut_centralizer_order': 4, 'aut_label': '24.bt1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '72.46', 'aut_weyl_index': 48, 'centralizer': '216.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.f1.a1', '12.bk1.a1'], 'contains': ['48.e1.a1', '72.di1.a1', '72.dn1.a1', '72.do1.a1', '72.do1.a2', '72.dr1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [5315, -1, 6435, -1, 4978, -1, 7902, -1], 'generators': [45, 2, 156, 432], 'label': '1296.3190.24.bt1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bk1.a1', 'old_label': '24.bt1.a1', 'projective_image': '432.598', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bt1.a1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 71060018
    {'ambient': '1296.3190', 'aut_centralizer_order': 8, 'aut_label': '24.bu1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '72.46', 'aut_weyl_index': 48, 'centralizer': '216.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.f1.a1', '12.bl1.a1', '12.cf1.a1', '12.cf1.b1'], 'contains': ['48.c1.a1', '72.dj1.a1', '72.dk1.a1', '72.dn1.a1', '72.ds1.a1'], 'core': '48.c1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [8095, -1, 3447, -1, 6039, -1, 5105, -1], 'generators': [45, 2, 12, 144], 'label': '1296.3190.24.bu1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.q1.a1', 'old_label': '24.bu1.a1', 'projective_image': '432.598', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bu1.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 71060019
    {'ambient': '1296.3190', 'aut_centralizer_order': 4, 'aut_label': '24.bv1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '72.46', 'aut_weyl_index': 48, 'centralizer': '216.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.f1.a1', '12.bm1.a1'], 'contains': ['48.f1.a1', '72.dj1.a1', '72.dm1.a1', '72.do1.a1', '72.do1.a2', '72.dt1.a1'], 'core': '144.b1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [2811, -1, 5982, -1, 4916, -1, 7320, -1], 'generators': [45, 2, 444, 144], 'label': '1296.3190.24.bv1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bm1.a1', 'old_label': '24.bv1.a1', 'projective_image': '432.598', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bv1.a1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 71060020
    {'ambient': '1296.3190', 'aut_centralizer_order': 4, 'aut_label': '6.c1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '864.4704', 'aut_weyl_index': 4, 'centralizer': '216.a1.a1', 'complements': ['216.x1.a1', '216.ba1.a1', '216.ba1.b1', '216.bb1.a1', '216.bd1.a1', '216.bd1.b1', '216.bf1.a1', '216.bh1.b1', '216.bh1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '3.a1.a1'], 'contains': ['12.c1.a1', '12.j1.a1', '12.k1.a1', '12.ch1.a1', '12.ch1.b1', '18.k1.a1', '18.t1.a1', '18.u1.a1', '18.v1.a1'], 'core': '6.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6733, 6774, 5415, 3819, 7034, 7403, 4529, 3332], 'generators': [3, 432, 144, 54, 216, 12], 'label': '1296.3190.6.c1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '6.c1.a1', 'normal_contained_in': ['2.b1.a1', '3.a1.a1'], 'normal_contains': ['12.c1.a1', '12.j1.a1', '12.k1.a1'], 'normalizer': '1.a1.a1', 'old_label': '6.c1.a1', 'projective_image': '648.731', 'quotient_action_image': '2.1', 'quotient_action_kernel': '3.1', 'quotient_action_kernel_order': 3, 'quotient_fusion': None, 'short_label': '6.c1.a1', 'subgroup_fusion': None, 'weyl_group': '216.162'}
  • id: 71060021
    {'ambient': '1296.3190', 'aut_centralizer_order': 4, 'aut_label': '24.bw1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '72.46', 'aut_weyl_index': 48, 'centralizer': '216.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.f1.a1', '12.bn1.a1', '12.cg1.a1', '12.cg1.b2'], 'contains': ['48.g1.a1', '72.dk1.a1', '72.dl1.a1', '72.do1.a1', '72.du1.a1'], 'core': '144.c1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [8193, -1, 3224, -1, 6163, -1, 5747, -1], 'generators': [45, 2, 12, 576], 'label': '1296.3190.24.bw1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.r1.a1', 'old_label': '24.bw1.a1', 'projective_image': '432.598', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bw1.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 71060022
    {'ambient': '1296.3190', 'aut_centralizer_order': 4, 'aut_label': '24.bw1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '72.46', 'aut_weyl_index': 48, 'centralizer': '216.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.f1.a1', '12.bn1.a1', '12.cg1.a2', '12.cg1.b1'], 'contains': ['48.g1.a1', '72.dk1.a1', '72.dl1.a2', '72.do1.a2', '72.du1.a2'], 'core': '144.c1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [8193, -1, 3260, -1, 6163, -1, 5799, -1], 'generators': [45, 2, 12, 1008], 'label': '1296.3190.24.bw1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.r1.a1', 'old_label': '24.bw1.a2', 'projective_image': '432.598', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bw1.a2', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 71060023
    {'ambient': '1296.3190', 'aut_centralizer_order': 4, 'aut_label': '24.bx1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '36.13', 'aut_weyl_index': 96, 'centralizer': '216.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.f1.a1', '12.bo1.a1'], 'contains': ['48.h1.a1', '72.dl1.a1', '72.dm1.a1', '72.dn1.a1', '72.do1.a2', '72.dv1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [3317, -1, 6398, -1, 5040, -1, 7850, -1], 'generators': [45, 2, 444, 576], 'label': '1296.3190.24.bx1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bo1.a1', 'old_label': '24.bx1.a1', 'projective_image': '432.598', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bx1.a1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 71060024
    {'ambient': '1296.3190', 'aut_centralizer_order': 4, 'aut_label': '24.bx1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '36.13', 'aut_weyl_index': 96, 'centralizer': '216.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.f1.a1', '12.bo1.a1'], 'contains': ['48.h1.a1', '72.dl1.a2', '72.dm1.a1', '72.dn1.a1', '72.do1.a1', '72.dv1.a2'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [3317, -1, 6358, -1, 5040, -1, 7798, -1], 'generators': [45, 2, 444, 1008], 'label': '1296.3190.24.bx1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bo1.a1', 'old_label': '24.bx1.a2', 'projective_image': '432.598', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bx1.a2', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 71060025
    {'ambient': '1296.3190', 'aut_centralizer_order': 8, 'aut_label': '24.by1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '216.162', 'aut_weyl_index': 16, 'centralizer': '216.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.f1.a1', '12.k1.a1', '12.ch1.a1', '12.ch1.b1'], 'contains': ['48.d1.a1', '72.dp1.a1', '72.dq1.a1', '72.dr1.a1', '72.ds1.a1', '72.dt1.a1', '72.du1.a1', '72.du1.a2', '72.dv1.a1', '72.dv1.a2'], 'core': '48.d1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8047, -1, 4016, -1, 5605, -1, 6557, -1], 'generators': [45, 12, 144, 432], 'label': '1296.3190.24.by1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.k1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '24.by1.a1', 'projective_image': '1296.3190', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.by1.a1', 'subgroup_fusion': None, 'weyl_group': '108.39'}
  • id: 71060026
    {'ambient': '1296.3190', 'aut_centralizer_order': 8, 'aut_label': '27.a1', 'aut_quo_index': None, 'aut_stab_index': 27, 'aut_weyl_group': '16.14', 'aut_weyl_index': 216, 'centralizer': '108.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['9.a1.a1', '9.b1.a1', '9.d1.a1'], 'contains': ['54.a1.a1', '54.e1.a1', '54.i1.a1', '54.p1.a1', '54.t1.a1', '54.z1.a1', '54.bb1.a1', '81.a1.a1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [3829, -1, 7659, -1, 4819, -1, 7303, -1], 'generators': [3, 216, 18, 108, 2], 'label': '1296.3190.27.a1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1.a1', 'old_label': '27.a1.a1', 'projective_image': '216.162', '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: 71060027
    {'ambient': '1296.3190', 'aut_centralizer_order': 8, 'aut_label': '27.b1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '48.51', 'aut_weyl_index': 72, 'centralizer': '108.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['9.a1.a1', '9.c1.a1', '9.e1.a1'], 'contains': ['54.b1.a1', '54.f1.a1', '54.j1.a1', '54.s1.a1', '54.u1.a1', '54.ba1.a1', '54.bc1.a1', '81.a1.a1'], 'core': '108.c1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [3746, -1, 7353, -1, 4762, -1, 7074, -1], 'generators': [3, 432, 18, 108, 216], 'label': '1296.3190.27.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': '648.731', '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: 71060028
    {'ambient': '1296.3190', 'aut_centralizer_order': 8, 'aut_label': '27.c1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '48.51', 'aut_weyl_index': 72, 'centralizer': '108.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['9.b1.a1', '9.c1.a1', '9.f1.a1'], 'contains': ['54.d1.a1', '54.g1.a1', '54.k1.a1', '54.x1.a1', '54.y1.a1', '54.be1.a1', '54.bf1.a1', '81.a1.a1'], 'core': '108.b1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [3129, -1, 7997, -1, 4700, -1, 6937, -1], 'generators': [3, 144, 18, 108, 216], 'label': '1296.3190.27.c1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1.a1', 'old_label': '27.c1.a1', 'projective_image': '648.731', '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': '12.4'}
  • id: 71060029
    {'ambient': '1296.3190', 'aut_centralizer_order': 8, 'aut_label': '27.d1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '48.51', 'aut_weyl_index': 72, 'centralizer': '216.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['9.d1.a1', '9.e1.a1', '9.f1.a1'], 'contains': ['54.m1.a1', '54.n1.a1', '54.o1.a1', '54.q1.a1', '54.v1.a1', '54.bd1.a1', '54.bg1.a1', '81.a1.a1'], 'core': '108.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [5457, -1, 5677, -1, 4933, -1, 6081, -1], 'generators': [3, 12, 18, 108, 216], 'label': '1296.3190.27.d1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.d1.a1', 'old_label': '27.d1.a1', 'projective_image': '648.731', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '27.d1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 71060030
    {'ambient': '1296.3190', 'aut_centralizer_order': 144, 'aut_label': '36.a1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '24.14', 'aut_weyl_index': 144, 'centralizer': '6.f1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['12.a1.a1', '12.b1.a1', '12.r1.a1', '18.p1.a1', '18.s1.a1', '18.w1.a1'], 'contains': ['72.c1.a1', '72.g1.a1', '72.g1.b1', '108.a1.a1', '108.d1.a1'], 'core': '36.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6251, 8600, 3779, 2249, 7752, 1221, 2901, 2475], 'generators': [3, 216, 2, 12], 'label': '1296.3190.36.a1.a1', 'mobius_quo': 0, 'mobius_sub': 18, 'normal_closure': '36.a1.a1', 'normal_contained_in': ['12.b1.a1', '12.a1.a1'], 'normal_contains': ['72.c1.a1', '72.g1.a1', '72.g1.b1', '108.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '36.a1.a1', 'projective_image': '216.162', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.a1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 71060031
    {'ambient': '1296.3190', 'aut_centralizer_order': 12, 'aut_label': '6.d1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '288.1040', 'aut_weyl_index': 12, 'centralizer': '72.b1.a1', 'complements': ['216.be1.a1', '216.bp1.a1', '216.bq1.a1', '216.bq1.a2', '216.bi1.a1', '216.bt1.a1', '216.bv1.a1', '216.bv1.a2', '216.bk1.a1', '216.bx1.a1', '216.by1.a1', '216.by1.a2'], 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1', '3.c1.a1'], 'contains': ['12.a1.a1', '12.m1.a1', '12.n1.a1', '18.b1.a1', '18.l1.a1', '18.w1.a1'], 'core': '6.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1846, 2936, 7896, 7330, 1657, 2154, 7816, 7360], 'generators': [3, 432, 12, 108, 2, 216], 'label': '1296.3190.6.d1.a1', 'mobius_quo': 0, 'mobius_sub': 3, 'normal_closure': '6.d1.a1', 'normal_contained_in': ['2.c1.a1'], 'normal_contains': ['12.a1.a1', '12.m1.a1', '12.n1.a1', '18.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '6.d1.a1', 'projective_image': '216.162', 'quotient_action_image': '2.1', 'quotient_action_kernel': '3.1', 'quotient_action_kernel_order': 3, 'quotient_fusion': None, 'short_label': '6.d1.a1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 71060032
    {'ambient': '1296.3190', 'aut_centralizer_order': 144, 'aut_label': '36.b1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '24.14', 'aut_weyl_index': 144, 'centralizer': '12.d1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['12.a1.a1', '12.c1.a1', '12.s1.a1', '18.b1.a1', '18.q1.a1', '18.t1.a1'], 'contains': ['72.e1.a1', '72.h1.a1', '72.h1.b1', '108.a1.a1', '108.e1.a1'], 'core': '36.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6213, 7693, 4787, 1694, 7321, 2765, 2758, 3216], 'generators': [3, 216, 432, 12], 'label': '1296.3190.36.b1.a1', 'mobius_quo': 0, 'mobius_sub': 6, 'normal_closure': '36.b1.a1', 'normal_contained_in': ['12.a1.a1', '12.c1.a1', '18.b1.a1'], 'normal_contains': ['72.e1.a1', '72.h1.a1', '72.h1.b1', '108.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '36.b1.a1', 'projective_image': '648.731', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.b1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 71060033
    {'ambient': '1296.3190', 'aut_centralizer_order': 144, 'aut_label': '36.c1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '24.14', 'aut_weyl_index': 144, 'centralizer': '12.l1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['12.b1.a1', '12.c1.a1', '12.t1.a1', '18.a1.a1', '18.u1.a1', '18.x1.a1'], 'contains': ['72.f1.a1', '72.i1.a1', '72.i1.b1', '108.a1.a1', '108.f1.a1'], 'core': '36.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6288, 9529, 4121, 741, 7480, 1993, 2673, 1338], 'generators': [3, 216, 144, 12], 'label': '1296.3190.36.c1.a1', 'mobius_quo': 0, 'mobius_sub': 6, 'normal_closure': '36.c1.a1', 'normal_contained_in': ['12.b1.a1', '12.c1.a1', '18.a1.a1'], 'normal_contains': ['72.f1.a1', '72.i1.a1', '72.i1.b1', '108.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '36.c1.a1', 'projective_image': '648.731', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.c1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 71060034
    {'ambient': '1296.3190', 'aut_centralizer_order': 144, 'aut_label': '36.d1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '24.14', 'aut_weyl_index': 144, 'centralizer': '12.a1.a1', 'complements': ['36.dy1.a1', '36.ea1.a1', '36.ea1.a2', '36.dy1.b1', '36.ea1.b1', '36.ea1.b2'], 'conjugacy_class_count': 1, 'contained_in': ['12.d1.a1', '12.e1.a1', '12.w1.a1', '18.e1.a1', '18.bh1.a1', '18.bk1.a1'], 'contains': ['72.b1.a1', '72.cf1.a1', '108.b1.a1', '108.k1.a1'], 'core': '36.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3503, 4181, 7979, 6388, 3778, 6121, 5471, 6439], 'generators': [18, 216, 2, 144], 'label': '1296.3190.36.d1.a1', 'mobius_quo': 0, 'mobius_sub': 18, 'normal_closure': '36.d1.a1', 'normal_contained_in': ['12.d1.a1', '12.e1.a1'], 'normal_contains': ['72.b1.a1', '108.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '36.d1.a1', 'projective_image': '216.162', 'quotient_action_image': '2.1', 'quotient_action_kernel': '18.3', 'quotient_action_kernel_order': 18, 'quotient_fusion': None, 'short_label': '36.d1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 71060035
    {'ambient': '1296.3190', 'aut_centralizer_order': 144, 'aut_label': '36.e1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '24.14', 'aut_weyl_index': 144, 'centralizer': '12.a1.a1', 'complements': ['36.dx1.a1', '36.dx1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['12.d1.a1', '12.f1.a1', '12.x1.a1', '18.c1.a1', '18.f1.a1', '18.bl1.a1'], 'contains': ['72.d1.a1', '72.cg1.a1', '108.b1.a1', '108.l1.a1'], 'core': '36.e1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3815, 3234, 7859, 8110, 3669, 6893, 5360, 7180], 'generators': [18, 216, 432, 144], 'label': '1296.3190.36.e1.a1', 'mobius_quo': 0, 'mobius_sub': 6, 'normal_closure': '36.e1.a1', 'normal_contained_in': ['12.d1.a1', '12.f1.a1', '18.c1.a1'], 'normal_contains': ['72.d1.a1', '108.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '36.e1.a1', 'projective_image': '648.731', 'quotient_action_image': '2.1', 'quotient_action_kernel': '18.3', 'quotient_action_kernel_order': 18, 'quotient_fusion': None, 'short_label': '36.e1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 71060036
    {'ambient': '1296.3190', 'aut_centralizer_order': 144, 'aut_label': '36.f1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '24.14', 'aut_weyl_index': 144, 'centralizer': '24.b1.a1', 'complements': ['36.dp1.a1', '36.dr1.a1', '36.dr1.a2', '36.dp1.b1', '36.dr1.b1', '36.dr1.b2'], 'conjugacy_class_count': 1, 'contained_in': ['12.e1.a1', '12.f1.a1', '12.y1.a1', '18.a1.a1', '18.bi1.a1', '18.bm1.a1'], 'contains': ['72.f1.a1', '72.ch1.a1', '108.b1.a1', '108.m1.a1'], 'core': '36.f1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4752, 5416, 6075, 5513, 4138, 4195, 4836, 4589], 'generators': [18, 216, 12, 144], 'label': '1296.3190.36.f1.a1', 'mobius_quo': 0, 'mobius_sub': 6, 'normal_closure': '36.f1.a1', 'normal_contained_in': ['12.e1.a1', '12.f1.a1', '18.a1.a1'], 'normal_contains': ['72.f1.a1', '108.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '36.f1.a1', 'projective_image': '648.731', 'quotient_action_image': '4.2', 'quotient_action_kernel': '9.2', 'quotient_action_kernel_order': 9, 'quotient_fusion': None, 'short_label': '36.f1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 71060037
    {'ambient': '1296.3190', 'aut_centralizer_order': 48, 'aut_label': '36.g1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '72.46', 'aut_weyl_index': 48, 'centralizer': '72.a1.a1', 'complements': ['36.dp1.a1', '36.dr1.a1', '36.dr1.a2', '36.dp1.b1', '36.dr1.b1', '36.dr1.b2'], 'conjugacy_class_count': 1, 'contained_in': ['12.g1.a1', '12.h1.a1', '12.bd1.a1', '18.a1.a1', '18.ca1.a1', '18.cb1.a1'], 'contains': ['72.f1.a1', '72.cw1.a1', '108.u1.a1', '108.v1.a1', '108.w1.a1'], 'core': '36.g1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5106, 7273, 5734, 3738, 6276, 3795, 4439, 3807], 'generators': [9, 216, 12, 144], 'label': '1296.3190.36.g1.a1', 'mobius_quo': 0, 'mobius_sub': 6, 'normal_closure': '36.g1.a1', 'normal_contained_in': ['12.g1.a1', '12.h1.a1', '18.a1.a1'], 'normal_contains': ['72.f1.a1'], 'normalizer': '1.a1.a1', 'old_label': '36.g1.a1', 'projective_image': '648.731', 'quotient_action_image': '4.2', 'quotient_action_kernel': '9.2', 'quotient_action_kernel_order': 9, 'quotient_fusion': None, 'short_label': '36.g1.a1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 71060038
    {'ambient': '1296.3190', 'aut_centralizer_order': 48, 'aut_label': '36.h1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '72.46', 'aut_weyl_index': 48, 'centralizer': '36.a1.a1', 'complements': ['36.dt1.a1', '36.dv1.a1', '36.dv1.b1', '36.dt1.b1', '36.dv1.c1', '36.dv1.d1'], 'conjugacy_class_count': 1, 'contained_in': ['12.i1.a1', '12.j1.a1', '12.bh1.a1', '18.c1.a1', '18.k1.a1', '18.bt1.a1'], 'contains': ['72.d1.a1', '72.dh1.a1', '108.ba1.a1', '108.bb1.a1', '108.bc1.a1'], 'core': '36.h1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6934, 2602, 7232, 7714, 6615, 8838, 6004, 7564], 'generators': [54, 216, 144, 432], 'label': '1296.3190.36.h1.a1', 'mobius_quo': 0, 'mobius_sub': 6, 'normal_closure': '36.h1.a1', 'normal_contained_in': ['12.i1.a1', '12.j1.a1', '18.c1.a1'], 'normal_contains': ['72.d1.a1'], 'normalizer': '1.a1.a1', 'old_label': '36.h1.a1', 'projective_image': '648.731', 'quotient_action_image': '2.1', 'quotient_action_kernel': '18.3', 'quotient_action_kernel_order': 18, 'quotient_fusion': None, 'short_label': '36.h1.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 71060039
    {'ambient': '1296.3190', 'aut_centralizer_order': 144, 'aut_label': '36.i1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '24.14', 'aut_weyl_index': 144, 'centralizer': '12.b1.a1', 'complements': ['36.dw1.a1', '36.dw1.b1', '36.dz1.a1', '36.ea1.a1', '36.ea1.a2', '36.dz1.b1', '36.ea1.b1', '36.ea1.b2'], 'conjugacy_class_count': 1, 'contained_in': ['12.l1.a1', '12.m1.a1', '12.bq1.a1', '18.l1.a1', '18.ba1.a1', '18.bp1.a1'], 'contains': ['72.a1.a1', '108.c1.a1', '108.bl1.a1'], 'core': '36.i1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1264, 921, 8694, 9157, 893, 7292, 9562, 8411], 'generators': [108, 2, 216, 432], 'label': '1296.3190.36.i1.a1', 'mobius_quo': 0, 'mobius_sub': 18, 'normal_closure': '36.i1.a1', 'normal_contained_in': ['12.l1.a1', '12.m1.a1'], 'normal_contains': ['72.a1.a1', '108.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '36.i1.a1', 'projective_image': '216.162', 'quotient_action_image': '2.1', 'quotient_action_kernel': '18.3', 'quotient_action_kernel_order': 18, 'quotient_fusion': None, 'short_label': '36.i1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 71060040
    {'ambient': '1296.3190', 'aut_centralizer_order': 144, 'aut_label': '36.j1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '24.14', 'aut_weyl_index': 144, 'centralizer': '12.b1.a1', 'complements': ['36.dt1.a1', '36.dv1.a1', '36.dv1.b1', '36.dt1.b1', '36.dv1.c1', '36.dv1.d1', '36.dx1.a1', '36.dx1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['12.l1.a1', '12.o1.a1', '12.bu1.a1', '18.c1.a1', '18.n1.a1', '18.bx1.a1'], 'contains': ['72.d1.a1', '108.c1.a1', '108.bo1.a1'], 'core': '36.j1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [839, 2001, 9767, 8549, 770, 7734, 9036, 7987], 'generators': [108, 144, 216, 432], 'label': '1296.3190.36.j1.a1', 'mobius_quo': 0, 'mobius_sub': 6, 'normal_closure': '36.j1.a1', 'normal_contained_in': ['12.l1.a1', '12.o1.a1', '18.c1.a1'], 'normal_contains': ['72.d1.a1', '108.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '36.j1.a1', 'projective_image': '648.731', 'quotient_action_image': '2.1', 'quotient_action_kernel': '18.3', 'quotient_action_kernel_order': 18, 'quotient_fusion': None, 'short_label': '36.j1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 71060041
    {'ambient': '1296.3190', 'aut_centralizer_order': 144, 'aut_label': '36.k1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '24.14', 'aut_weyl_index': 144, 'centralizer': '24.c1.a1', 'complements': ['36.dm1.a1', '36.do1.a1', '36.do1.b1', '36.dm1.b1', '36.do1.c1', '36.do1.d1', '36.dq1.a1', '36.dr1.a1', '36.dr1.a2', '36.dq1.b1', '36.dr1.b1', '36.dr1.b2'], 'conjugacy_class_count': 1, 'contained_in': ['12.m1.a1', '12.o1.a1', '12.bv1.a1', '18.b1.a1', '18.bb1.a1', '18.by1.a1'], 'contains': ['72.e1.a1', '108.c1.a1', '108.bq1.a1'], 'core': '36.k1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1663, 3760, 9181, 6782, 1017, 5722, 7693, 6056], 'generators': [108, 12, 216, 432], 'label': '1296.3190.36.k1.a1', 'mobius_quo': 0, 'mobius_sub': 6, 'normal_closure': '36.k1.a1', 'normal_contained_in': ['12.m1.a1', '12.o1.a1', '18.b1.a1'], 'normal_contains': ['72.e1.a1', '108.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '36.k1.a1', 'projective_image': '648.731', 'quotient_action_image': '4.2', 'quotient_action_kernel': '9.2', 'quotient_action_kernel_order': 9, 'quotient_fusion': None, 'short_label': '36.k1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 71060042
    {'ambient': '1296.3190', 'aut_centralizer_order': 12, 'aut_label': '6.e1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '288.1040', 'aut_weyl_index': 12, 'centralizer': '72.b1.a1', 'complements': ['216.x1.a1', '216.ba1.a1', '216.ba1.b1', '216.bl1.a1', '216.bb1.a1', '216.bd1.a1', '216.bd1.b1', '216.bn1.a1', '216.bf1.a1', '216.bh1.b1', '216.bh1.a1', '216.br1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1', '3.a1.a1'], 'contains': ['12.c1.a1', '12.o1.a1', '12.p1.a1', '18.b1.a1', '18.n1.a1', '18.x1.a1'], 'core': '6.e1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1769, 3821, 9062, 6099, 1567, 3843, 7568, 6749], 'generators': [3, 432, 12, 108, 144, 216], 'label': '1296.3190.6.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.c1.a1', '12.o1.a1', '12.p1.a1', '18.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '6.e1.a1', 'projective_image': '648.731', 'quotient_action_image': '2.1', 'quotient_action_kernel': '3.1', 'quotient_action_kernel_order': 3, 'quotient_fusion': None, 'short_label': '6.e1.a1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 71060043
    {'ambient': '1296.3190', 'aut_centralizer_order': 48, 'aut_label': '36.l1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '72.46', 'aut_weyl_index': 48, 'centralizer': '72.b1.a1', 'complements': ['36.dm1.a1', '36.do1.a1', '36.do1.b1', '36.dm1.b1', '36.do1.c1', '36.do1.d1', '36.dq1.a1', '36.dr1.a1', '36.dr1.a2', '36.dq1.b1', '36.dr1.b1', '36.dr1.b2'], 'conjugacy_class_count': 1, 'contained_in': ['12.n1.a1', '12.p1.a1', '12.bw1.a1', '18.b1.a1', '18.bg1.a1', '18.bs1.a1'], 'contains': ['72.e1.a1', '108.bn1.a1', '108.br1.a1', '108.bv1.a1'], 'core': '36.l1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1758, 4525, 8793, 6063, 1551, 4522, 7598, 5700], 'generators': [111, 216, 12, 432], 'label': '1296.3190.36.l1.a1', 'mobius_quo': 0, 'mobius_sub': 6, 'normal_closure': '36.l1.a1', 'normal_contained_in': ['12.n1.a1', '12.p1.a1', '18.b1.a1'], 'normal_contains': ['72.e1.a1'], 'normalizer': '1.a1.a1', 'old_label': '36.l1.a1', 'projective_image': '648.731', 'quotient_action_image': '4.2', 'quotient_action_kernel': '9.2', 'quotient_action_kernel_order': 9, 'quotient_fusion': None, 'short_label': '36.l1.a1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 71060044
    {'ambient': '1296.3190', 'aut_centralizer_order': 144, 'aut_label': '36.m1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '8.5', 'aut_weyl_index': 432, 'centralizer': '6.k1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.a1.a1', '12.q1.a1', '18.d1.a1', '18.h1.a1', '18.l1.a1'], 'contains': ['72.a1.a1', '72.bn1.a1', '72.bn1.b1', '108.d1.a1', '108.e1.a1', '108.g1.a1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6083, -1, 5465, -1, 7280, -1, 2792, -1], 'generators': [3, 216, 2, 432], 'label': '1296.3190.36.m1.a1', 'mobius_quo': None, 'mobius_sub': 6, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '36.m1.a1', 'projective_image': '216.162', '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': '2.1'}
  • id: 71060045
    {'ambient': '1296.3190', 'aut_centralizer_order': 144, 'aut_label': '36.n1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '8.5', 'aut_weyl_index': 432, 'centralizer': '6.m1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.b1.a1', '12.q1.a1', '18.e1.a1', '18.i1.a1', '18.m1.a1'], 'contains': ['72.b1.a1', '72.bo1.a1', '72.bo1.b1', '108.d1.a1', '108.f1.a1', '108.h1.a1'], 'core': '72.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6046, -1, 5565, -1, 7043, -1, 2935, -1], 'generators': [3, 216, 2, 144], 'label': '1296.3190.36.n1.a1', 'mobius_quo': None, 'mobius_sub': 6, 'normal_closure': '12.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '36.n1.a1', 'projective_image': '216.162', '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': '2.1'}
  • id: 71060046
    {'ambient': '1296.3190', 'aut_centralizer_order': 72, 'aut_label': '36.o1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '8.5', 'aut_weyl_index': 432, 'centralizer': '12.q1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.q1.a1', '12.r1.a1', '18.j1.a1'], 'contains': ['72.j1.a1', '72.bp1.a1', '72.bp1.b1', '108.d1.a1', '108.i1.a1', '108.j1.a1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [6538, -1, 5222, -1, 7975, -1, 3078, -1], 'generators': [3, 216, 2, 576], 'label': '1296.3190.36.o1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.l1.a1', 'old_label': '36.o1.a1', 'projective_image': '216.162', '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': '2.1'}
  • id: 71060047
    {'ambient': '1296.3190', 'aut_centralizer_order': 144, 'aut_label': '36.p1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '8.5', 'aut_weyl_index': 432, 'centralizer': '12.q1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.c1.a1', '12.q1.a1', '18.f1.a1', '18.k1.a1', '18.n1.a1'], 'contains': ['72.d1.a1', '72.bq1.a1', '72.bq1.b1', '108.e1.a1', '108.f1.a1', '108.i1.a1'], 'core': '72.d1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6115, -1, 5548, -1, 7249, -1, 3053, -1], 'generators': [3, 216, 144, 432], 'label': '1296.3190.36.p1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '12.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '36.p1.a1', 'projective_image': '648.731', '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': '4.2'}
  • id: 71060048
    {'ambient': '1296.3190', 'aut_centralizer_order': 72, 'aut_label': '36.q1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '8.5', 'aut_weyl_index': 432, 'centralizer': '12.q1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.q1.a1', '12.s1.a1', '18.o1.a1'], 'contains': ['72.n1.a1', '72.br1.a1', '72.br1.b1', '108.e1.a1', '108.h1.a1', '108.j1.a1'], 'core': '216.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [5991, -1, 6322, -1, 7012, -1, 2818, -1], 'generators': [3, 216, 146, 432], 'label': '1296.3190.36.q1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.m1.a1', 'old_label': '36.q1.a1', 'projective_image': '648.731', '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': '2.1'}
  • id: 71060049
    {'ambient': '1296.3190', 'aut_centralizer_order': 72, 'aut_label': '36.r1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '8.5', 'aut_weyl_index': 432, 'centralizer': '12.q1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.q1.a1', '12.t1.a1', '18.g1.a1'], 'contains': ['72.r1.a1', '72.bs1.a1', '72.bs1.b1', '108.f1.a1', '108.g1.a1', '108.j1.a1'], 'core': '216.c1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [6147, -1, 2038, -1, 7712, -1, 1520, -1], 'generators': [3, 216, 434, 144], 'label': '1296.3190.36.r1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.k1.a1', 'old_label': '36.r1.a1', 'projective_image': '648.731', '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': '2.1'}
  • id: 71060050
    {'ambient': '1296.3190', 'aut_centralizer_order': 72, 'aut_label': '36.s1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '4.2', 'aut_weyl_index': 864, 'centralizer': '12.q1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.q1.a1', '12.u1.a1'], 'contains': ['72.z1.a1', '72.bt1.a1', '72.bt1.b1', '108.g1.a1', '108.h1.a1', '108.i1.a1', '108.j1.a1'], 'core': '648.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [6348, -1, 3237, -1, 7793, -1, 2344, -1], 'generators': [3, 216, 434, 576], 'label': '1296.3190.36.s1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.q1.a1', 'old_label': '36.s1.a1', 'projective_image': '648.731', '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': '1.1'}
  • id: 71060051
    {'ambient': '1296.3190', 'aut_centralizer_order': 72, 'aut_label': '36.t1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '24.14', 'aut_weyl_index': 144, 'centralizer': '12.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.a1.a1', '12.t1.a1', '12.u1.a1', '18.r1.a1'], 'contains': ['72.v1.a1', '72.bu1.a1', '72.bu1.b1', '108.a1.a1', '108.g1.a1'], 'core': '108.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [6472, -1, 676, -1, 7834, -1, 1384, -1], 'generators': [3, 216, 434, 12], 'label': '1296.3190.36.t1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '36.t1.a1', 'projective_image': '648.731', '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': '6.1'}
  • id: 71060052
    {'ambient': '1296.3190', 'aut_centralizer_order': 72, 'aut_label': '36.u1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '24.14', 'aut_weyl_index': 144, 'centralizer': '12.l1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.b1.a1', '12.s1.a1', '12.u1.a1', '18.y1.a1'], 'contains': ['72.w1.a1', '72.bv1.a1', '72.bv1.b1', '108.a1.a1', '108.h1.a1'], 'core': '108.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [6177, -1, 5254, -1, 7371, -1, 2715, -1], 'generators': [3, 216, 146, 12], 'label': '1296.3190.36.u1.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.u1.a1', 'projective_image': '648.731', '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': '6.1'}
  • id: 71060053
    {'ambient': '1296.3190', 'aut_centralizer_order': 12, 'aut_label': '6.f1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '288.1040', 'aut_weyl_index': 12, 'centralizer': '36.a1.a1', 'complements': ['216.e1.a1', '216.e1.b1', '216.bj1.a1', '216.bk1.a1', '216.bu1.a1', '216.bw1.a1', '216.bx1.a1', '216.by1.a1', '216.by1.a2'], 'conjugacy_class_count': 1, 'contained_in': ['2.d1.a1', '3.b1.a1'], 'contains': ['12.d1.a1', '12.i1.a1', '12.l1.a1', '18.c1.a1', '18.ba1.a1', '18.bh1.a1'], 'core': '6.f1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2854, 835, 7943, 9157, 4224, 9602, 7260, 9472], 'generators': [18, 432, 144, 108, 2, 216], 'label': '1296.3190.6.f1.a1', 'mobius_quo': 0, 'mobius_sub': 3, 'normal_closure': '6.f1.a1', 'normal_contained_in': ['2.d1.a1'], 'normal_contains': ['12.d1.a1', '12.i1.a1', '12.l1.a1', '18.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '6.f1.a1', 'projective_image': '216.162', 'quotient_action_image': '1.1', 'quotient_action_kernel': '6.1', 'quotient_action_kernel_order': 6, 'quotient_fusion': None, 'short_label': '6.f1.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 71060054
    {'ambient': '1296.3190', 'aut_centralizer_order': 72, 'aut_label': '36.v1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '24.14', 'aut_weyl_index': 144, 'centralizer': '24.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.c1.a1', '12.r1.a1', '12.u1.a1', '18.v1.a1'], 'contains': ['72.x1.a1', '72.bw1.a1', '72.bw1.b1', '108.a1.a1', '108.i1.a1'], 'core': '108.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [6569, -1, 3513, -1, 8125, -1, 3113, -1], 'generators': [3, 216, 576, 12], 'label': '1296.3190.36.v1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '36.v1.a1', 'projective_image': '648.731', '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: 71060055
    {'ambient': '1296.3190', 'aut_centralizer_order': 36, 'aut_label': '36.w1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '24.14', 'aut_weyl_index': 144, 'centralizer': '24.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.r1.a1', '12.s1.a1', '12.t1.a1', '12.u1.a1'], 'contains': ['72.y1.a1', '72.bx1.a1', '72.bx1.b1', '108.a1.a1', '108.j1.a1'], 'core': '108.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [6508, -1, 789, -1, 7884, -1, 2310, -1], 'generators': [3, 216, 578, 12], 'label': '1296.3190.36.w1.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.w1.a1', 'projective_image': '648.731', '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': '6.1'}
  • id: 71060056
    {'ambient': '1296.3190', 'aut_centralizer_order': 144, 'aut_label': '36.x1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '8.5', 'aut_weyl_index': 432, 'centralizer': '6.n1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.d1.a1', '12.v1.a1', '18.d1.a1', '18.ba1.a1', '18.bd1.a1'], 'contains': ['72.a1.a1', '72.by1.a1', '108.k1.a1', '108.l1.a1', '108.n1.a1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4038, -1, 7363, -1, 4097, -1, 5394, -1], 'generators': [18, 216, 2, 432], 'label': '1296.3190.36.x1.a1', 'mobius_quo': None, 'mobius_sub': 6, 'normal_closure': '12.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1.a1', 'old_label': '36.x1.a1', 'projective_image': '216.162', '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': '2.1'}
  • id: 71060057
    {'ambient': '1296.3190', 'aut_centralizer_order': 144, 'aut_label': '36.y1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '8.5', 'aut_weyl_index': 432, 'centralizer': '12.v1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.e1.a1', '12.v1.a1', '18.p1.a1', '18.z1.a1', '18.be1.a1'], 'contains': ['72.c1.a1', '72.bz1.a1', '108.k1.a1', '108.m1.a1', '108.o1.a1'], 'core': '72.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4977, -1, 5760, -1, 4506, -1, 5326, -1], 'generators': [18, 216, 2, 12], 'label': '1296.3190.36.y1.a1', 'mobius_quo': None, 'mobius_sub': 6, 'normal_closure': '12.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1.a1', 'old_label': '36.y1.a1', 'projective_image': '216.162', '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: 71060058
    {'ambient': '1296.3190', 'aut_centralizer_order': 72, 'aut_label': '36.z1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '8.5', 'aut_weyl_index': 432, 'centralizer': '12.v1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.v1.a1', '12.w1.a1', '18.bf1.a1'], 'contains': ['72.k1.a1', '72.ca1.a1', '108.k1.a1', '108.p1.a1', '108.q1.a1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [69, -1, 7438, -1, 2764, -1, 5531, -1], 'generators': [18, 216, 2, 444], 'label': '1296.3190.36.z1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.v1.a1', 'old_label': '36.z1.a1', 'projective_image': '216.162', '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': '2.1'}
  • id: 71060059
    {'ambient': '1296.3190', 'aut_centralizer_order': 144, 'aut_label': '36.ba1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '8.5', 'aut_weyl_index': 432, 'centralizer': '12.v1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.f1.a1', '12.v1.a1', '18.q1.a1', '18.bb1.a1', '18.bg1.a1'], 'contains': ['72.e1.a1', '72.cb1.a1', '108.l1.a1', '108.m1.a1', '108.p1.a1'], 'core': '72.e1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4783, -1, 6128, -1, 4066, -1, 5300, -1], 'generators': [18, 216, 12, 432], 'label': '1296.3190.36.ba1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '12.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1.a1', 'old_label': '36.ba1.a1', 'projective_image': '648.731', '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': '4.2'}
  • id: 71060060
    {'ambient': '1296.3190', 'aut_centralizer_order': 72, 'aut_label': '36.bb1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '8.5', 'aut_weyl_index': 432, 'centralizer': '12.v1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.v1.a1', '12.x1.a1', '18.bc1.a1'], 'contains': ['72.o1.a1', '72.cc1.a1', '108.l1.a1', '108.o1.a1', '108.q1.a1'], 'core': '216.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [306, -1, 6162, -1, 2927, -1, 5505, -1], 'generators': [18, 216, 14, 432], 'label': '1296.3190.36.bb1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.u1.a1', 'old_label': '36.bb1.a1', 'projective_image': '648.731', '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': '2.1'}
  • id: 71060061
    {'ambient': '1296.3190', 'aut_centralizer_order': 72, 'aut_label': '36.bc1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '8.5', 'aut_weyl_index': 432, 'centralizer': '12.v1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.v1.a1', '12.y1.a1', '18.r1.a1'], 'contains': ['72.v1.a1', '72.cd1.a1', '72.cd1.b1', '108.m1.a1', '108.n1.a1', '108.q1.a1'], 'core': '216.d1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [4248, -1, 3202, -1, 4697, -1, 2135, -1], 'generators': [18, 216, 434, 12], 'label': '1296.3190.36.bc1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.n1.a1', 'old_label': '36.bc1.a1', 'projective_image': '648.731', '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': '2.1'}
  • id: 71060062
    {'ambient': '1296.3190', 'aut_centralizer_order': 72, 'aut_label': '36.bd1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '4.2', 'aut_weyl_index': 864, 'centralizer': '12.v1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.v1.a1', '12.z1.a1'], 'contains': ['72.ba1.a1', '72.ce1.a1', '72.ce1.b1', '108.n1.a1', '108.o1.a1', '108.p1.a1', '108.q1.a1'], 'core': '648.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [284, -1, 6197, -1, 2795, -1, 4605, -1], 'generators': [18, 216, 434, 444], 'label': '1296.3190.36.bd1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.v1.a1', 'old_label': '36.bd1.a1', 'projective_image': '648.731', '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': '1.1'}
  • id: 71060063
    {'ambient': '1296.3190', 'aut_centralizer_order': 72, 'aut_label': '36.be1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '24.14', 'aut_weyl_index': 144, 'centralizer': '12.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.d1.a1', '12.y1.a1', '12.z1.a1', '18.g1.a1'], 'contains': ['72.r1.a1', '72.ci1.a1', '72.ci1.b1', '108.b1.a1', '108.n1.a1'], 'core': '108.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3289, -1, 5173, -1, 4657, -1, 2169, -1], 'generators': [18, 216, 434, 144], 'label': '1296.3190.36.be1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '36.be1.a1', 'projective_image': '648.731', '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': '6.1'}
  • id: 71060064
    {'ambient': '1296.3190', 'aut_centralizer_order': 2, 'aut_label': '2.b1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '1728.47915', 'aut_weyl_index': 2, 'centralizer': '216.a1.a1', 'complements': ['648.c1.a1', '648.d1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1', '4.d1.a1', '4.e1.a1', '4.i1.a1', '4.i1.b1', '6.c1.a1', '6.l1.a1', '6.p1.a1', '6.q1.a1', '6.r1.a1'], 'core': '2.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6640, 6696, 5081, 3728, 6968, 7139, 4467, 3655], 'generators': [3, 144, 12, 54, 432, 216, 2], 'label': '1296.3190.2.b1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.b1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.a1.a1', '4.d1.a1', '4.e1.a1', '6.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.b1.a1', 'projective_image': '216.162', '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': '216.162'}
  • id: 71060065
    {'ambient': '1296.3190', 'aut_centralizer_order': 12, 'aut_label': '6.g1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '288.1040', 'aut_weyl_index': 12, 'centralizer': '72.c1.a1', 'complements': ['216.q1.a1', '216.t1.a1', '216.u1.a1', '216.w1.a1', '216.q1.b1', '216.t1.b1', '216.u1.b1', '216.w1.b1', '216.bf1.a1', '216.bh1.b1', '216.bh1.a1', '216.br1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['2.d1.a1', '3.a1.a1'], 'contains': ['12.f1.a1', '12.j1.a1', '12.o1.a1', '18.c1.a1', '18.bb1.a1', '18.bi1.a1'], 'core': '6.g1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4197, 2338, 7435, 7893, 4363, 9105, 6340, 8518], 'generators': [18, 432, 144, 108, 12, 216], 'label': '1296.3190.6.g1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '6.g1.a1', 'normal_contained_in': ['2.d1.a1', '3.a1.a1'], 'normal_contains': ['12.f1.a1', '12.j1.a1', '12.o1.a1', '18.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '6.g1.a1', 'projective_image': '648.731', 'quotient_action_image': '2.1', 'quotient_action_kernel': '3.1', 'quotient_action_kernel_order': 3, 'quotient_fusion': None, 'short_label': '6.g1.a1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 71060066
    {'ambient': '1296.3190', 'aut_centralizer_order': 72, 'aut_label': '36.bf1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '24.14', 'aut_weyl_index': 144, 'centralizer': '24.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.e1.a1', '12.x1.a1', '12.z1.a1', '18.bj1.a1'], 'contains': ['72.s1.a1', '72.cj1.a1', '108.b1.a1', '108.o1.a1'], 'core': '108.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2831, -1, 6569, -1, 2886, -1, 5429, -1], 'generators': [18, 216, 14, 144], 'label': '1296.3190.36.bf1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.a1', 'old_label': '36.bf1.a1', 'projective_image': '648.731', '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': '12.4'}
  • id: 71060067
    {'ambient': '1296.3190', 'aut_centralizer_order': 72, 'aut_label': '36.bg1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '24.14', 'aut_weyl_index': 144, 'centralizer': '24.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.f1.a1', '12.w1.a1', '12.z1.a1', '18.bn1.a1'], 'contains': ['72.t1.a1', '72.ck1.a1', '108.b1.a1', '108.p1.a1'], 'core': '108.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [501, -1, 8008, -1, 2723, -1, 5657, -1], 'generators': [18, 216, 444, 144], 'label': '1296.3190.36.bg1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.e1.a1', 'old_label': '36.bg1.a1', 'projective_image': '648.731', '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': '12.4'}
  • id: 71060068
    {'ambient': '1296.3190', 'aut_centralizer_order': 36, 'aut_label': '36.bh1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '24.14', 'aut_weyl_index': 144, 'centralizer': '24.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.w1.a1', '12.x1.a1', '12.y1.a1', '12.z1.a1'], 'contains': ['72.u1.a1', '72.cl1.a1', '72.cl1.b1', '108.b1.a1', '108.q1.a1'], 'core': '108.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [1941, -1, 6958, -1, 2836, -1, 4486, -1], 'generators': [18, 216, 446, 144], 'label': '1296.3190.36.bh1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.a1', 'old_label': '36.bh1.a1', 'projective_image': '648.731', '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: 71060069
    {'ambient': '1296.3190', 'aut_centralizer_order': 48, 'aut_label': '36.bi1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '8.5', 'aut_weyl_index': 432, 'centralizer': '18.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.ba1.a1', '12.bb1.a1', '12.bc1.a1', '18.d1.a1', '18.bo1.a1', '18.bp1.a1'], 'contains': ['72.a1.a1', '72.cm1.a1', '108.r1.a1', '108.s1.a1', '108.t1.a1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [4602, -1, 7067, -1, 5941, -1, 4896, -1], 'generators': [9, 216, 2, 432], 'label': '1296.3190.36.bi1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '36.bi1.a1', 'projective_image': '216.162', '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': '2.1'}
  • id: 71060070
    {'ambient': '1296.3190', 'aut_centralizer_order': 48, 'aut_label': '36.bj1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '24.14', 'aut_weyl_index': 144, 'centralizer': '36.m1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.g1.a1', '12.ba1.a1', '18.e1.a1', '18.br1.a1', '18.bu1.a1'], 'contains': ['72.b1.a1', '72.cn1.a1', '108.r1.a1', '108.u1.a1'], 'core': '72.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4381, -1, 6850, -1, 5982, -1, 4973, -1], 'generators': [9, 216, 2, 144], 'label': '1296.3190.36.bj1.a1', 'mobius_quo': None, 'mobius_sub': 6, 'normal_closure': '12.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '36.bj1.a1', 'projective_image': '216.162', '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': '12.4'}
  • id: 71060071
    {'ambient': '1296.3190', 'aut_centralizer_order': 48, 'aut_label': '36.bk1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '24.14', 'aut_weyl_index': 144, 'centralizer': '36.x1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.g1.a1', '12.bb1.a1', '18.p1.a1', '18.bq1.a1', '18.bv1.a1'], 'contains': ['72.c1.a1', '72.co1.a1', '108.r1.a1', '108.v1.a1'], 'core': '72.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5571, -1, 5401, -1, 6332, -1, 4571, -1], 'generators': [9, 216, 2, 12], 'label': '1296.3190.36.bk1.a1', 'mobius_quo': None, 'mobius_sub': 6, 'normal_closure': '12.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1.a1', 'old_label': '36.bk1.a1', 'projective_image': '216.162', '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': '12.4'}
  • id: 71060072
    {'ambient': '1296.3190', 'aut_centralizer_order': 24, 'aut_label': '36.bl1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '24.14', 'aut_weyl_index': 144, 'centralizer': '72.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.g1.a1', '12.bc1.a1', '18.bw1.a1'], 'contains': ['72.l1.a1', '72.cp1.a1', '108.r1.a1', '108.w1.a1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [4448, -1, 8557, -1, 5206, -1, 5058, -1], 'generators': [9, 216, 2, 156], 'label': '1296.3190.36.bl1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.bf1.a1', 'old_label': '36.bl1.a1', 'projective_image': '216.162', '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': '12.4'}
  • id: 71060073
    {'ambient': '1296.3190', 'aut_centralizer_order': 48, 'aut_label': '36.bm1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '24.14', 'aut_weyl_index': 144, 'centralizer': '36.m1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.h1.a1', '12.ba1.a1', '18.f1.a1', '18.bt1.a1', '18.bx1.a1'], 'contains': ['72.d1.a1', '72.cq1.a1', '108.s1.a1', '108.u1.a1'], 'core': '72.d1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4844, -1, 6912, -1, 5901, -1, 4930, -1], 'generators': [9, 216, 432, 144], 'label': '1296.3190.36.bm1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '12.h1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '36.bm1.a1', 'projective_image': '648.731', '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': '12.4'}
  • id: 71060074
    {'ambient': '1296.3190', 'aut_centralizer_order': 48, 'aut_label': '36.bn1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '24.14', 'aut_weyl_index': 144, 'centralizer': '36.x1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.h1.a1', '12.bb1.a1', '18.q1.a1', '18.bs1.a1', '18.by1.a1'], 'contains': ['72.e1.a1', '72.cr1.a1', '108.s1.a1', '108.v1.a1'], 'core': '72.e1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5165, -1, 5623, -1, 6219, -1, 4529, -1], 'generators': [9, 216, 432, 12], 'label': '1296.3190.36.bn1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '12.h1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1.a1', 'old_label': '36.bn1.a1', 'projective_image': '648.731', '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': '12.4'}
  • id: 71060075
    {'ambient': '1296.3190', 'aut_centralizer_order': 24, 'aut_label': '36.bo1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '24.14', 'aut_weyl_index': 144, 'centralizer': '72.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.h1.a1', '12.bc1.a1', '18.bz1.a1'], 'contains': ['72.p1.a1', '72.cs1.a1', '108.s1.a1', '108.w1.a1'], 'core': '216.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [4664, -1, 8603, -1, 5156, -1, 5015, -1], 'generators': [9, 216, 432, 156], 'label': '1296.3190.36.bo1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.h1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.bf1.a1', 'old_label': '36.bo1.a1', 'projective_image': '648.731', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.bo1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 71060076
    {'ambient': '1296.3190', 'aut_centralizer_order': 4, 'aut_label': '6.h1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '864.4704', 'aut_weyl_index': 4, 'centralizer': '216.a1.a1', 'complements': ['216.bl1.a1', '216.bn1.a1', '216.q1.a1', '216.t1.a1', '216.u1.a1', '216.w1.a1', '216.q1.b1', '216.t1.b1', '216.u1.b1', '216.w1.b1', '216.bf1.a1', '216.bh1.b1', '216.bh1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['2.e1.a1', '3.a1.a1'], 'contains': ['12.f1.a1', '12.k1.a1', '12.p1.a1', '18.bg1.a1', '18.bl1.a1', '18.bm1.a1', '18.bn1.a1'], 'core': '6.h1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4247, 4614, 8110, 5253, 3433, 5928, 6633, 5333], 'generators': [111, 432, 144, 18, 216, 12], 'label': '1296.3190.6.h1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '6.h1.a1', 'normal_contained_in': ['2.e1.a1', '3.a1.a1'], 'normal_contains': ['12.f1.a1', '12.k1.a1', '12.p1.a1'], 'normalizer': '1.a1.a1', 'old_label': '6.h1.a1', 'projective_image': '648.731', 'quotient_action_image': '2.1', 'quotient_action_kernel': '3.1', 'quotient_action_kernel_order': 3, 'quotient_fusion': None, 'short_label': '6.h1.a1', 'subgroup_fusion': None, 'weyl_group': '216.162'}
  • id: 71060077
    {'ambient': '1296.3190', 'aut_centralizer_order': 24, 'aut_label': '36.bp1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '24.14', 'aut_weyl_index': 144, 'centralizer': '36.m1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.ba1.a1', '12.bd1.a1', '18.g1.a1'], 'contains': ['72.r1.a1', '72.ct1.a1', '72.ct1.b1', '108.t1.a1', '108.u1.a1'], 'core': '216.c1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [5017, -1, 2875, -1, 6913, -1, 1120, -1], 'generators': [9, 216, 434, 144], 'label': '1296.3190.36.bp1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.k1.a1', 'old_label': '36.bp1.a1', 'projective_image': '648.731', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.bp1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 71060078
    {'ambient': '1296.3190', 'aut_centralizer_order': 24, 'aut_label': '36.bq1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '24.14', 'aut_weyl_index': 144, 'centralizer': '36.x1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bb1.a1', '12.bd1.a1', '18.r1.a1'], 'contains': ['72.v1.a1', '72.cu1.a1', '72.cu1.b1', '108.t1.a1', '108.v1.a1'], 'core': '216.d1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [5265, -1, 2522, -1, 7612, -1, 1078, -1], 'generators': [9, 216, 434, 12], 'label': '1296.3190.36.bq1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.n1.a1', 'old_label': '36.bq1.a1', 'projective_image': '648.731', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.bq1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 71060079
    {'ambient': '1296.3190', 'aut_centralizer_order': 12, 'aut_label': '36.br1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '24.14', 'aut_weyl_index': 144, 'centralizer': '72.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bc1.a1', '12.bd1.a1'], 'contains': ['72.bb1.a1', '72.cv1.a1', '72.cv1.b1', '108.t1.a1', '108.w1.a1'], 'core': '648.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [4927, -1, 5955, -1, 5788, -1, 3018, -1], 'generators': [9, 216, 434, 156], 'label': '1296.3190.36.br1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bc1.a1', 'old_label': '36.br1.a1', 'projective_image': '648.731', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.br1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 71060080
    {'ambient': '1296.3190', 'aut_centralizer_order': 48, 'aut_label': '36.bs1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '8.5', 'aut_weyl_index': 432, 'centralizer': '36.bs1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.be1.a1', '12.bf1.a1', '12.bg1.a1', '18.s1.a1', '18.z1.a1', '18.bq1.a1'], 'contains': ['72.c1.a1', '72.cx1.a1', '108.x1.a1', '108.y1.a1', '108.z1.a1'], 'core': '72.c1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [7042, -1, 4739, -1, 6872, -1, 5923, -1], 'generators': [54, 216, 2, 12], 'label': '1296.3190.36.bs1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.d1.a1', 'old_label': '36.bs1.a1', 'projective_image': '216.162', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.bs1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 71060081
    {'ambient': '1296.3190', 'aut_centralizer_order': 48, 'aut_label': '36.bt1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '24.14', 'aut_weyl_index': 144, 'centralizer': '36.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.i1.a1', '12.be1.a1', '18.h1.a1', '18.ba1.a1', '18.bo1.a1'], 'contains': ['72.a1.a1', '72.cy1.a1', '108.x1.a1', '108.ba1.a1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6893, -1, 7114, -1, 6672, -1, 6195, -1], 'generators': [54, 216, 2, 432], 'label': '1296.3190.36.bt1.a1', 'mobius_quo': None, 'mobius_sub': 6, 'normal_closure': '12.i1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1.a1', 'old_label': '36.bt1.a1', 'projective_image': '216.162', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.bt1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 71060082
    {'ambient': '1296.3190', 'aut_centralizer_order': 48, 'aut_label': '36.bu1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '24.14', 'aut_weyl_index': 144, 'centralizer': '36.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.i1.a1', '12.bf1.a1', '18.i1.a1', '18.bh1.a1', '18.br1.a1'], 'contains': ['72.b1.a1', '72.cz1.a1', '108.x1.a1', '108.bb1.a1'], 'core': '72.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6856, -1, 7779, -1, 6559, -1, 6596, -1], 'generators': [54, 216, 2, 144], 'label': '1296.3190.36.bu1.a1', 'mobius_quo': None, 'mobius_sub': 6, 'normal_closure': '12.i1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.d1.a1', 'old_label': '36.bu1.a1', 'projective_image': '216.162', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.bu1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 71060083
    {'ambient': '1296.3190', 'aut_centralizer_order': 24, 'aut_label': '36.bv1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '24.14', 'aut_weyl_index': 144, 'centralizer': '36.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.i1.a1', '12.bg1.a1', '18.j1.a1'], 'contains': ['72.j1.a1', '72.da1.a1', '72.da1.a2', '108.x1.a1', '108.bc1.a1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [7192, -1, 5321, -1, 7935, -1, 5699, -1], 'generators': [54, 216, 2, 576], 'label': '1296.3190.36.bv1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.i1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.r1.a1', 'old_label': '36.bv1.a1', 'projective_image': '216.162', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.bv1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 71060084
    {'ambient': '1296.3190', 'aut_centralizer_order': 48, 'aut_label': '36.bw1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '24.14', 'aut_weyl_index': 144, 'centralizer': '72.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.j1.a1', '12.be1.a1', '18.t1.a1', '18.bb1.a1', '18.bs1.a1'], 'contains': ['72.e1.a1', '72.db1.a1', '108.y1.a1', '108.ba1.a1'], 'core': '72.e1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7013, -1, 5792, -1, 6832, -1, 5889, -1], 'generators': [54, 216, 12, 432], 'label': '1296.3190.36.bw1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '12.j1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1.a1', 'old_label': '36.bw1.a1', 'projective_image': '648.731', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.bw1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 71060085
    {'ambient': '1296.3190', 'aut_centralizer_order': 24, 'aut_label': '36.bx1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '24.14', 'aut_weyl_index': 144, 'centralizer': '72.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.be1.a1', '12.bh1.a1', '18.bc1.a1'], 'contains': ['72.o1.a1', '72.dc1.a1', '108.z1.a1', '108.ba1.a1'], 'core': '216.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [6819, -1, 6105, -1, 5737, -1, 6783, -1], 'generators': [54, 216, 14, 432], 'label': '1296.3190.36.bx1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.u1.a1', 'old_label': '36.bx1.a1', 'projective_image': '648.731', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.bx1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 71060086
    {'ambient': '1296.3190', 'aut_centralizer_order': 48, 'aut_label': '36.by1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '24.14', 'aut_weyl_index': 144, 'centralizer': '72.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.j1.a1', '12.bf1.a1', '18.u1.a1', '18.bi1.a1', '18.ca1.a1'], 'contains': ['72.f1.a1', '72.dd1.a1', '108.y1.a1', '108.bb1.a1'], 'core': '72.f1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6975, -1, 5901, -1, 6722, -1, 5846, -1], 'generators': [54, 216, 12, 144], 'label': '1296.3190.36.by1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '12.j1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.d1.a1', 'old_label': '36.by1.a1', 'projective_image': '648.731', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.by1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 71060087
    {'ambient': '1296.3190', 'aut_centralizer_order': 4, 'aut_label': '6.i1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '864.4704', 'aut_weyl_index': 4, 'centralizer': '216.a1.a1', 'complements': ['216.x1.a1', '216.ba1.a1', '216.ba1.b1', '216.bb1.a1', '216.bd1.a1', '216.bd1.b1', '216.q1.a1', '216.t1.a1', '216.u1.a1', '216.w1.a1', '216.q1.b1', '216.t1.b1', '216.u1.b1', '216.w1.b1', '216.br1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['2.f1.a1', '3.a1.a1'], 'contains': ['12.h1.a1', '12.j1.a1', '12.p1.a1', '18.bs1.a1', '18.bt1.a1', '18.ca1.a1'], 'core': '6.i1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4996, 5371, 6626, 4840, 5439, 4900, 5935, 5734], 'generators': [111, 432, 144, 54, 216, 12], 'label': '1296.3190.6.i1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '6.i1.a1', 'normal_contained_in': ['2.f1.a1', '3.a1.a1'], 'normal_contains': ['12.j1.a1', '12.h1.a1', '12.p1.a1'], 'normalizer': '1.a1.a1', 'old_label': '6.i1.a1', 'projective_image': '648.731', 'quotient_action_image': '2.1', 'quotient_action_kernel': '3.1', 'quotient_action_kernel_order': 3, 'quotient_fusion': None, 'short_label': '6.i1.a1', 'subgroup_fusion': None, 'weyl_group': '216.162'}
  • id: 71060088
    {'ambient': '1296.3190', 'aut_centralizer_order': 24, 'aut_label': '36.bz1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '24.14', 'aut_weyl_index': 144, 'centralizer': '72.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bf1.a1', '12.bh1.a1', '18.bj1.a1'], 'contains': ['72.s1.a1', '72.de1.a1', '108.z1.a1', '108.bb1.a1'], 'core': '216.c1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [6782, -1, 6238, -1, 5687, -1, 6469, -1], 'generators': [54, 216, 14, 144], 'label': '1296.3190.36.bz1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.w1.a1', 'old_label': '36.bz1.a1', 'projective_image': '648.731', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.bz1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 71060089
    {'ambient': '1296.3190', 'aut_centralizer_order': 24, 'aut_label': '36.ca1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '24.14', 'aut_weyl_index': 144, 'centralizer': '72.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.j1.a1', '12.bg1.a1', '18.v1.a1'], 'contains': ['72.x1.a1', '72.df1.a1', '72.df1.a2', '108.y1.a1', '108.bc1.a1'], 'core': '216.d1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [7229, -1, 4575, -1, 8016, -1, 5565, -1], 'generators': [54, 216, 12, 576], 'label': '1296.3190.36.ca1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.j1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.r1.a1', 'old_label': '36.ca1.a1', 'projective_image': '648.731', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.ca1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 71060090
    {'ambient': '1296.3190', 'aut_centralizer_order': 12, 'aut_label': '36.cb1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '24.14', 'aut_weyl_index': 144, 'centralizer': '72.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bg1.a1', '12.bh1.a1'], 'contains': ['72.bg1.a1', '72.dg1.a1', '72.dg1.a2', '108.z1.a1', '108.bc1.a1'], 'core': '648.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [7072, -1, 5292, -1, 7562, -1, 5957, -1], 'generators': [54, 216, 14, 576], 'label': '1296.3190.36.cb1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bg1.a1', 'old_label': '36.cb1.a1', 'projective_image': '648.731', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.cb1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 71060091
    {'ambient': '1296.3190', 'aut_centralizer_order': 16, 'aut_label': '36.cc1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '24.14', 'aut_weyl_index': 144, 'centralizer': '108.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bi1.a1', '12.bj1.a1', '12.bk1.a1', '18.h1.a1', '18.bd1.a1', '18.bp1.a1'], 'contains': ['72.a1.a1', '72.di1.a1', '108.bd1.a1', '108.be1.a1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [4090, -1, 8179, -1, 3435, -1, 7223, -1], 'generators': [45, 216, 2, 432], 'label': '1296.3190.36.cc1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '36.cc1.a1', 'projective_image': '216.162', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.cc1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 71060092
    {'ambient': '1296.3190', 'aut_centralizer_order': 16, 'aut_label': '36.cd1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '24.14', 'aut_weyl_index': 144, 'centralizer': '108.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bi1.a1', '12.bl1.a1', '12.bm1.a1', '18.i1.a1', '18.bk1.a1', '18.bu1.a1'], 'contains': ['72.b1.a1', '72.dj1.a1', '108.bd1.a1', '108.bf1.a1'], 'core': '72.b1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [3551, -1, 8444, -1, 3384, -1, 7129, -1], 'generators': [45, 216, 2, 144], 'label': '1296.3190.36.cd1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1.a1', 'old_label': '36.cd1.a1', 'projective_image': '216.162', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.cd1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 71060093
    {'ambient': '1296.3190', 'aut_centralizer_order': 16, 'aut_label': '36.ce1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '24.14', 'aut_weyl_index': 144, 'centralizer': '108.x1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bj1.a1', '12.bl1.a1', '12.bn1.a1', '18.s1.a1', '18.be1.a1', '18.bv1.a1'], 'contains': ['72.c1.a1', '72.dk1.a1', '108.bd1.a1', '108.bg1.a1'], 'core': '72.c1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [5402, -1, 6637, -1, 4465, -1, 6153, -1], 'generators': [45, 216, 2, 12], 'label': '1296.3190.36.ce1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.d1.a1', 'old_label': '36.ce1.a1', 'projective_image': '216.162', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.ce1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 71060094
    {'ambient': '1296.3190', 'aut_centralizer_order': 8, 'aut_label': '36.cf1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '24.14', 'aut_weyl_index': 144, 'centralizer': '108.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bi1.a1', '12.bn1.a1', '12.bo1.a1', '18.j1.a1'], 'contains': ['72.j1.a1', '72.dl1.a1', '72.dl1.a2', '108.bd1.a1', '108.bh1.a1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [5053, -1, 9336, -1, 4239, -1, 6639, -1], 'generators': [45, 216, 2, 576], 'label': '1296.3190.36.cf1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.j1.a1', 'old_label': '36.cf1.a1', 'projective_image': '216.162', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.cf1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 71060095
    {'ambient': '1296.3190', 'aut_centralizer_order': 8, 'aut_label': '36.cg1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '24.14', 'aut_weyl_index': 144, 'centralizer': '216.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bj1.a1', '12.bm1.a1', '12.bo1.a1', '18.bf1.a1'], 'contains': ['72.k1.a1', '72.dm1.a1', '108.bd1.a1', '108.bi1.a1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [1989, -1, 8374, -1, 2673, -1, 8354, -1], 'generators': [45, 216, 2, 444], 'label': '1296.3190.36.cg1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bf1.a1', 'old_label': '36.cg1.a1', 'projective_image': '216.162', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.cg1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 71060096
    {'ambient': '1296.3190', 'aut_centralizer_order': 8, 'aut_label': '36.ch1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '24.14', 'aut_weyl_index': 144, 'centralizer': '216.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bk1.a1', '12.bl1.a1', '12.bo1.a1', '18.bw1.a1'], 'contains': ['72.l1.a1', '72.dn1.a1', '108.bd1.a1', '108.bj1.a1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [3127, -1, 9539, -1, 2388, -1, 8885, -1], 'generators': [45, 216, 2, 156], 'label': '1296.3190.36.ch1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bw1.a1', 'old_label': '36.ch1.a1', 'projective_image': '216.162', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.ch1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 71060097
    {'ambient': '1296.3190', 'aut_centralizer_order': 4, 'aut_label': '36.ci1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '24.14', 'aut_weyl_index': 144, 'centralizer': '216.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bk1.a1', '12.bm1.a1', '12.bn1.a1', '12.bo1.a1'], 'contains': ['72.m1.a1', '72.do1.a1', '72.do1.a2', '108.bd1.a1', '108.bk1.a1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [2993, -1, 9374, -1, 2560, -1, 8446, -1], 'generators': [45, 216, 2, 588], 'label': '1296.3190.36.ci1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.ci1.a1', 'old_label': '36.ci1.a1', 'projective_image': '216.162', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.ci1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 71060098
    {'ambient': '1296.3190', 'aut_centralizer_order': 4, 'aut_label': '6.j1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '864.4704', 'aut_weyl_index': 4, 'centralizer': '216.a1.a1', 'complements': ['216.x1.a1', '216.ba1.a1', '216.ba1.b1', '216.bl1.a1', '216.bb1.a1', '216.bd1.a1', '216.bd1.b1', '216.bn1.a1', '216.q1.a1', '216.t1.a1', '216.u1.a1', '216.w1.a1', '216.q1.b1', '216.t1.b1', '216.u1.b1', '216.w1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['2.g1.a1', '3.a1.a1'], 'contains': ['12.h1.a1', '12.k1.a1', '12.o1.a1', '18.bx1.a1', '18.by1.a1', '18.bz1.a1', '18.cb1.a1'], 'core': '6.j1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4149, 6214, 8534, 4346, 3227, 6375, 6686, 4320], 'generators': [9, 432, 144, 108, 216, 12], 'label': '1296.3190.6.j1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '6.j1.a1', 'normal_contained_in': ['2.g1.a1', '3.a1.a1'], 'normal_contains': ['12.h1.a1', '12.k1.a1', '12.o1.a1'], 'normalizer': '1.a1.a1', 'old_label': '6.j1.a1', 'projective_image': '648.731', 'quotient_action_image': '2.1', 'quotient_action_kernel': '3.1', 'quotient_action_kernel_order': 3, 'quotient_fusion': None, 'short_label': '6.j1.a1', 'subgroup_fusion': None, 'weyl_group': '216.162'}
  • id: 71060099
    {'ambient': '1296.3190', 'aut_centralizer_order': 16, 'aut_label': '36.cj1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '72.46', 'aut_weyl_index': 48, 'centralizer': '108.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.k1.a1', '12.bi1.a1', '18.k1.a1', '18.bl1.a1', '18.bx1.a1'], 'contains': ['72.d1.a1', '72.dp1.a1', '108.be1.a1', '108.bf1.a1', '108.bh1.a1'], 'core': '72.d1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4182, -1, 9137, -1, 3550, -1, 7029, -1], 'generators': [45, 216, 144, 432], 'label': '1296.3190.36.cj1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '12.k1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '36.cj1.a1', 'projective_image': '648.731', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.cj1.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 71060100
    {'ambient': '1296.3190', 'aut_centralizer_order': 16, 'aut_label': '36.ck1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '72.46', 'aut_weyl_index': 48, 'centralizer': '216.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.k1.a1', '12.bj1.a1', '18.t1.a1', '18.bg1.a1', '18.by1.a1'], 'contains': ['72.e1.a1', '72.dq1.a1', '108.be1.a1', '108.bg1.a1', '108.bi1.a1'], 'core': '72.e1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4884, -1, 7180, -1, 3926, -1, 6372, -1], 'generators': [45, 216, 12, 432], 'label': '1296.3190.36.ck1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '12.k1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1.a1', 'old_label': '36.ck1.a1', 'projective_image': '648.731', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.ck1.a1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 71060101
    {'ambient': '1296.3190', 'aut_centralizer_order': 8, 'aut_label': '36.cl1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '72.46', 'aut_weyl_index': 48, 'centralizer': '216.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.k1.a1', '12.bk1.a1', '18.bz1.a1'], 'contains': ['72.p1.a1', '72.dr1.a1', '108.be1.a1', '108.bj1.a1', '108.bk1.a1'], 'core': '216.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [3086, -1, 9828, -1, 2332, -1, 9222, -1], 'generators': [45, 216, 156, 432], 'label': '1296.3190.36.cl1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.k1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.bf1.a1', 'old_label': '36.cl1.a1', 'projective_image': '648.731', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.cl1.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 71060102
    {'ambient': '1296.3190', 'aut_centralizer_order': 16, 'aut_label': '36.cm1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '72.46', 'aut_weyl_index': 48, 'centralizer': '216.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.k1.a1', '12.bl1.a1', '18.u1.a1', '18.bm1.a1', '18.cb1.a1'], 'contains': ['72.f1.a1', '72.ds1.a1', '108.bf1.a1', '108.bg1.a1', '108.bj1.a1'], 'core': '72.f1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4293, -1, 8041, -1, 3612, -1, 6271, -1], 'generators': [45, 216, 12, 144], 'label': '1296.3190.36.cm1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '12.k1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.d1.a1', 'old_label': '36.cm1.a1', 'projective_image': '648.731', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.cm1.a1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 71060103
    {'ambient': '1296.3190', 'aut_centralizer_order': 8, 'aut_label': '36.cn1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '72.46', 'aut_weyl_index': 48, 'centralizer': '216.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.k1.a1', '12.bm1.a1', '18.bn1.a1'], 'contains': ['72.t1.a1', '72.dt1.a1', '108.bf1.a1', '108.bi1.a1', '108.bk1.a1'], 'core': '216.c1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2276, -1, 9101, -1, 2616, -1, 8684, -1], 'generators': [45, 216, 444, 144], 'label': '1296.3190.36.cn1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.k1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.ba1.a1', 'old_label': '36.cn1.a1', 'projective_image': '648.731', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.cn1.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 71060104
    {'ambient': '1296.3190', 'aut_centralizer_order': 8, 'aut_label': '36.co1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '72.46', 'aut_weyl_index': 48, 'centralizer': '216.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.k1.a1', '12.bn1.a1', '18.v1.a1'], 'contains': ['72.x1.a1', '72.du1.a1', '72.du1.a2', '108.bg1.a1', '108.bh1.a1', '108.bk1.a1'], 'core': '216.d1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [5818, -1, 6270, -1, 4854, -1, 6686, -1], 'generators': [45, 216, 12, 576], 'label': '1296.3190.36.co1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.k1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.r1.a1', 'old_label': '36.co1.a1', 'projective_image': '648.731', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.co1.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 71060105
    {'ambient': '1296.3190', 'aut_centralizer_order': 8, 'aut_label': '36.cp1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '36.13', 'aut_weyl_index': 96, 'centralizer': '216.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.k1.a1', '12.bo1.a1'], 'contains': ['72.bi1.a1', '72.dv1.a1', '72.dv1.a2', '108.bh1.a1', '108.bi1.a1', '108.bj1.a1', '108.bk1.a1'], 'core': '648.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [2738, -1, 9448, -1, 2503, -1, 9141, -1], 'generators': [45, 216, 444, 576], 'label': '1296.3190.36.cp1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.k1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bo1.a1', 'old_label': '36.cp1.a1', 'projective_image': '648.731', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.cp1.a1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 71060106
    {'ambient': '1296.3190', 'aut_centralizer_order': 48, 'aut_label': '36.cq1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '24.14', 'aut_weyl_index': 144, 'centralizer': '36.n1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.n1.a1', '12.bp1.a1', '18.l1.a1', '18.bd1.a1', '18.bo1.a1'], 'contains': ['72.a1.a1', '108.bm1.a1', '108.bn1.a1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [1710, -1, 7697, -1, 1666, -1, 8307, -1], 'generators': [111, 2, 216, 432], 'label': '1296.3190.36.cq1.a1', 'mobius_quo': None, 'mobius_sub': 6, 'normal_closure': '12.n1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '36.cq1.a1', 'projective_image': '216.162', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.cq1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 71060107
    {'ambient': '1296.3190', 'aut_centralizer_order': 144, 'aut_label': '36.cr1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '8.5', 'aut_weyl_index': 432, 'centralizer': '6.s1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.l1.a1', '12.br1.a1', '18.m1.a1', '18.bh1.a1', '18.bu1.a1'], 'contains': ['72.b1.a1', '108.bl1.a1', '108.bo1.a1', '108.bs1.a1'], 'core': '72.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [543, -1, 9024, -1, 832, -1, 9510, -1], 'generators': [108, 2, 144, 216], 'label': '1296.3190.36.cr1.a1', 'mobius_quo': None, 'mobius_sub': 6, 'normal_closure': '12.l1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.d1.a1', 'old_label': '36.cr1.a1', 'projective_image': '216.162', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.cr1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 71060108
    {'ambient': '1296.3190', 'aut_centralizer_order': 48, 'aut_label': '36.cs1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '8.5', 'aut_weyl_index': 432, 'centralizer': '18.m1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bp1.a1', '12.bs1.a1', '12.bt1.a1', '18.m1.a1', '18.bk1.a1', '18.br1.a1'], 'contains': ['72.b1.a1', '108.bm1.a1', '108.bp1.a1', '108.bt1.a1'], 'core': '72.b1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [1019, -1, 8988, -1, 1437, -1, 8787, -1], 'generators': [111, 2, 144, 216], 'label': '1296.3190.36.cs1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '4.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1.a1', 'old_label': '36.cs1.a1', 'projective_image': '216.162', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.cs1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 71060109
    {'ambient': '1296.3190', 'aut_centralizer_order': 12, 'aut_label': '6.k1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '96.230', 'aut_weyl_index': 36, 'centralizer': '36.m1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '3.b1.a1'], 'contains': ['12.d1.a1', '12.q1.a1', '12.ba1.a1', '12.by1.a1', '12.by1.b1', '18.d1.a1', '18.e1.a1', '18.f1.a1', '18.g1.a1'], 'core': '12.d1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5385, -1, 5371, -1, 6100, -1, 2203, -1], 'generators': [3, 144, 432, 18, 216, 2], 'label': '1296.3190.6.k1.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.k1.a1', 'projective_image': '216.162', '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': '12.4'}
  • id: 71060110
    {'ambient': '1296.3190', 'aut_centralizer_order': 144, 'aut_label': '36.ct1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '8.5', 'aut_weyl_index': 432, 'centralizer': '12.br1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.m1.a1', '12.br1.a1', '18.w1.a1', '18.z1.a1', '18.bv1.a1'], 'contains': ['72.c1.a1', '108.bl1.a1', '108.bq1.a1', '108.bu1.a1'], 'core': '72.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [1573, -1, 8130, -1, 1078, -1, 8838, -1], 'generators': [108, 2, 12, 216], 'label': '1296.3190.36.ct1.a1', 'mobius_quo': None, 'mobius_sub': 6, 'normal_closure': '12.m1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.d1.a1', 'old_label': '36.ct1.a1', 'projective_image': '216.162', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.ct1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 71060111
    {'ambient': '1296.3190', 'aut_centralizer_order': 48, 'aut_label': '36.cu1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '24.14', 'aut_weyl_index': 144, 'centralizer': '36.cr1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.n1.a1', '12.bs1.a1', '18.w1.a1', '18.be1.a1', '18.bq1.a1'], 'contains': ['72.c1.a1', '108.bm1.a1', '108.br1.a1'], 'core': '72.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [2149, -1, 7285, -1, 1791, -1, 7176, -1], 'generators': [111, 2, 216, 12], 'label': '1296.3190.36.cu1.a1', 'mobius_quo': None, 'mobius_sub': 6, 'normal_closure': '12.n1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.d1.a1', 'old_label': '36.cu1.a1', 'projective_image': '216.162', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.cu1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 71060112
    {'ambient': '1296.3190', 'aut_centralizer_order': 24, 'aut_label': '36.cv1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '24.14', 'aut_weyl_index': 144, 'centralizer': '72.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.n1.a1', '12.bt1.a1', '18.bf1.a1'], 'contains': ['72.k1.a1', '108.bm1.a1', '108.bv1.a1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [104, -1, 8078, -1, 1498, -1, 9275, -1], 'generators': [111, 2, 216, 444], 'label': '1296.3190.36.cv1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.n1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.ba1.a1', 'old_label': '36.cv1.a1', 'projective_image': '216.162', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.cv1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 71060113
    {'ambient': '1296.3190', 'aut_centralizer_order': 72, 'aut_label': '36.cw1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '8.5', 'aut_weyl_index': 432, 'centralizer': '12.br1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bq1.a1', '12.br1.a1', '18.bw1.a1'], 'contains': ['72.l1.a1', '108.bl1.a1', '108.bw1.a1', '108.bx1.a1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [385, -1, 9615, -1, 336, -1, 9874, -1], 'generators': [108, 2, 156, 216], 'label': '1296.3190.36.cw1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.bh1.a1', 'old_label': '36.cw1.a1', 'projective_image': '216.162', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.cw1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 71060114
    {'ambient': '1296.3190', 'aut_centralizer_order': 48, 'aut_label': '36.cx1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '24.14', 'aut_weyl_index': 144, 'centralizer': '36.n1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.p1.a1', '12.bp1.a1', '18.n1.a1', '18.bl1.a1', '18.bt1.a1'], 'contains': ['72.d1.a1', '108.bn1.a1', '108.bp1.a1'], 'core': '72.d1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [1618, -1, 9287, -1, 1603, -1, 8133, -1], 'generators': [111, 144, 216, 432], 'label': '1296.3190.36.cx1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '12.p1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '36.cx1.a1', 'projective_image': '648.731', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.cx1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 71060115
    {'ambient': '1296.3190', 'aut_centralizer_order': 72, 'aut_label': '36.cy1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '24.14', 'aut_weyl_index': 144, 'centralizer': '12.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.l1.a1', '12.bv1.a1', '12.bx1.a1', '18.o1.a1'], 'contains': ['72.n1.a1', '108.c1.a1', '108.bs1.a1'], 'core': '108.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [737, -1, 9953, -1, 151, -1, 9769, -1], 'generators': [108, 146, 216, 432], 'label': '1296.3190.36.cy1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.l1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '36.cy1.a1', 'projective_image': '648.731', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.cy1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 71060116
    {'ambient': '1296.3190', 'aut_centralizer_order': 24, 'aut_label': '36.cz1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '24.14', 'aut_weyl_index': 144, 'centralizer': '36.n1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bp1.a1', '12.bw1.a1', '18.o1.a1'], 'contains': ['72.n1.a1', '108.bn1.a1', '108.bt1.a1'], 'core': '216.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [1496, -1, 9917, -1, 522, -1, 9089, -1], 'generators': [111, 146, 216, 432], 'label': '1296.3190.36.cz1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.m1.a1', 'old_label': '36.cz1.a1', 'projective_image': '648.731', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.cz1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 71060117
    {'ambient': '1296.3190', 'aut_centralizer_order': 72, 'aut_label': '36.da1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '24.14', 'aut_weyl_index': 144, 'centralizer': '24.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.m1.a1', '12.bu1.a1', '12.bx1.a1', '18.bc1.a1'], 'contains': ['72.o1.a1', '108.c1.a1', '108.bu1.a1'], 'core': '108.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [204, -1, 8831, -1, 707, -1, 9666, -1], 'generators': [108, 14, 216, 432], 'label': '1296.3190.36.da1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.m1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.a1', 'old_label': '36.da1.a1', 'projective_image': '648.731', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.da1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 71060118
    {'ambient': '1296.3190', 'aut_centralizer_order': 72, 'aut_label': '36.db1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '24.14', 'aut_weyl_index': 144, 'centralizer': '24.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.o1.a1', '12.bq1.a1', '12.bx1.a1', '18.bz1.a1'], 'contains': ['72.p1.a1', '108.c1.a1', '108.bw1.a1'], 'core': '108.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [782, -1, 9880, -1, 275, -1, 9822, -1], 'generators': [108, 156, 216, 432], 'label': '1296.3190.36.db1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.o1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.g1.a1', 'old_label': '36.db1.a1', 'projective_image': '648.731', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.db1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 71060119
    {'ambient': '1296.3190', 'aut_centralizer_order': 36, 'aut_label': '36.dc1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '24.14', 'aut_weyl_index': 144, 'centralizer': '24.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bq1.a1', '12.bu1.a1', '12.bv1.a1', '12.bx1.a1'], 'contains': ['72.q1.a1', '108.c1.a1', '108.bx1.a1'], 'core': '108.c1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [681, -1, 9989, -1, 89, -1, 9925, -1], 'generators': [108, 158, 216, 432], 'label': '1296.3190.36.dc1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.f1.a1', 'old_label': '36.dc1.a1', 'projective_image': '648.731', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.dc1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 71060120
    {'ambient': '1296.3190', 'aut_centralizer_order': 4, 'aut_label': '6.l1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '288.1040', 'aut_weyl_index': 12, 'centralizer': '108.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '3.b1.a1'], 'contains': ['12.i1.a1', '12.q1.a1', '12.bi1.a1', '12.bz1.a1', '12.bz1.b1', '18.h1.a1', '18.i1.a1', '18.j1.a1', '18.k1.a1'], 'core': '12.i1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6556, -1, 6095, -1, 6827, -1, 4681, -1], 'generators': [3, 432, 144, 54, 216, 2], 'label': '1296.3190.6.l1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '6.l1.a1', 'projective_image': '216.162', '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': '36.10'}
  • id: 71060121
    {'ambient': '1296.3190', 'aut_centralizer_order': 144, 'aut_label': '36.dd1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '8.5', 'aut_weyl_index': 432, 'centralizer': '12.br1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.o1.a1', '12.br1.a1', '18.x1.a1', '18.bi1.a1', '18.cb1.a1'], 'contains': ['72.f1.a1', '108.bo1.a1', '108.bq1.a1', '108.bw1.a1'], 'core': '72.f1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [1063, -1, 8867, -1, 955, -1, 7641, -1], 'generators': [108, 12, 144, 216], 'label': '1296.3190.36.dd1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '12.o1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.d1.a1', 'old_label': '36.dd1.a1', 'projective_image': '648.731', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.dd1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 71060122
    {'ambient': '1296.3190', 'aut_centralizer_order': 48, 'aut_label': '36.de1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '24.14', 'aut_weyl_index': 144, 'centralizer': '36.cr1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.p1.a1', '12.bs1.a1', '18.x1.a1', '18.bm1.a1', '18.ca1.a1'], 'contains': ['72.f1.a1', '108.bp1.a1', '108.br1.a1'], 'core': '72.f1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [2041, -1, 8738, -1, 1728, -1, 7081, -1], 'generators': [111, 144, 216, 12], 'label': '1296.3190.36.de1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '12.p1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.d1.a1', 'old_label': '36.de1.a1', 'projective_image': '648.731', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.de1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 71060123
    {'ambient': '1296.3190', 'aut_centralizer_order': 72, 'aut_label': '36.df1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '8.5', 'aut_weyl_index': 432, 'centralizer': '12.br1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.br1.a1', '12.bu1.a1', '18.bj1.a1'], 'contains': ['72.s1.a1', '108.bo1.a1', '108.bu1.a1', '108.bx1.a1'], 'core': '216.c1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [25, -1, 8912, -1, 646, -1, 9614, -1], 'generators': [108, 14, 144, 216], 'label': '1296.3190.36.df1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.w1.a1', 'old_label': '36.df1.a1', 'projective_image': '648.731', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.df1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 71060124
    {'ambient': '1296.3190', 'aut_centralizer_order': 24, 'aut_label': '36.dg1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '24.14', 'aut_weyl_index': 144, 'centralizer': '72.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.p1.a1', '12.bt1.a1', '18.bn1.a1'], 'contains': ['72.t1.a1', '108.bp1.a1', '108.bv1.a1'], 'core': '216.c1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [340, -1, 9217, -1, 1375, -1, 9327, -1], 'generators': [111, 144, 216, 444], 'label': '1296.3190.36.dg1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.p1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.ba1.a1', 'old_label': '36.dg1.a1', 'projective_image': '648.731', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.dg1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 71060125
    {'ambient': '1296.3190', 'aut_centralizer_order': 72, 'aut_label': '36.dh1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '8.5', 'aut_weyl_index': 432, 'centralizer': '12.br1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.br1.a1', '12.bv1.a1', '18.y1.a1'], 'contains': ['72.w1.a1', '108.bq1.a1', '108.bs1.a1', '108.bx1.a1'], 'core': '216.d1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [461, -1, 9686, -1, 213, -1, 9717, -1], 'generators': [108, 146, 12, 216], 'label': '1296.3190.36.dh1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.s1.a1', 'old_label': '36.dh1.a1', 'projective_image': '648.731', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.dh1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 71060126
    {'ambient': '1296.3190', 'aut_centralizer_order': 24, 'aut_label': '36.di1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '24.14', 'aut_weyl_index': 144, 'centralizer': '36.cr1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bs1.a1', '12.bw1.a1', '18.y1.a1'], 'contains': ['72.w1.a1', '108.br1.a1', '108.bt1.a1'], 'core': '216.d1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [1859, -1, 9651, -1, 584, -1, 7745, -1], 'generators': [111, 146, 216, 12], 'label': '1296.3190.36.di1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.s1.a1', 'old_label': '36.di1.a1', 'projective_image': '648.731', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.di1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 71060127
    {'ambient': '1296.3190', 'aut_centralizer_order': 72, 'aut_label': '36.dj1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '4.2', 'aut_weyl_index': 864, 'centralizer': '12.br1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.br1.a1', '12.bx1.a1'], 'contains': ['72.bd1.a1', '108.bs1.a1', '108.bu1.a1', '108.bw1.a1', '108.bx1.a1'], 'core': '648.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [159, -1, 9580, -1, 27, -1, 9977, -1], 'generators': [108, 146, 156, 216], 'label': '1296.3190.36.dj1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.br1.a1', 'old_label': '36.dj1.a1', 'projective_image': '648.731', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.dj1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 71060128
    {'ambient': '1296.3190', 'aut_centralizer_order': 12, 'aut_label': '36.dk1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '24.14', 'aut_weyl_index': 144, 'centralizer': '72.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bt1.a1', '12.bw1.a1'], 'contains': ['72.be1.a1', '108.bt1.a1', '108.bv1.a1'], 'core': '648.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [250, -1, 9723, -1, 459, -1, 9431, -1], 'generators': [111, 146, 216, 444], 'label': '1296.3190.36.dk1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bt1.a1', 'old_label': '36.dk1.a1', 'projective_image': '648.731', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.dk1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 71060129
    {'ambient': '1296.3190', 'aut_centralizer_order': 24, 'aut_label': '36.dl1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '4.2', 'aut_weyl_index': 864, 'centralizer': '18.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.by1.a1', '12.ca1.a1', '18.d1.a1'], 'contains': ['72.bn1.a1', '72.by1.a1', '72.cm1.a1', '108.by1.a1', '108.bz1.a1', '108.ca1.a1', '108.ca1.b1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [9117, -1, 1222, -1, 8633, -1, 554, -1], 'generators': [3, 18, 2, 432], 'label': '1296.3190.36.dl1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.d1.a1', 'old_label': '36.dl1.a1', 'projective_image': '432.598', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.dl1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 71060130
    {'ambient': '1296.3190', 'aut_centralizer_order': 24, 'aut_label': '36.dl1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '4.2', 'aut_weyl_index': 864, 'centralizer': '18.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.by1.b1', '12.ca1.b1', '18.d1.a1'], 'contains': ['72.bn1.b1', '72.by1.a1', '72.cm1.a1', '108.by1.b1', '108.bz1.b1', '108.ca1.c1', '108.ca1.d1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [9117, -1, 2323, -1, 8633, -1, 580, -1], 'generators': [219, 18, 2, 432], 'label': '1296.3190.36.dl1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.d1.a1', 'old_label': '36.dl1.b1', 'projective_image': '432.598', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.dl1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 71060131
    {'ambient': '1296.3190', 'aut_centralizer_order': 12, 'aut_label': '6.m1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '96.230', 'aut_weyl_index': 36, 'centralizer': '36.n1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1', '3.b1.a1'], 'contains': ['12.l1.a1', '12.q1.a1', '12.bp1.a1', '18.l1.a1', '18.m1.a1', '18.n1.a1', '18.o1.a1'], 'core': '12.l1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [1371, -1, 9142, -1, 1371, -1, 8223, -1], 'generators': [3, 432, 216, 108, 2, 144], 'label': '1296.3190.6.m1.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.m1.a1', 'projective_image': '216.162', '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': '12.4'}
  • id: 71060132
    {'ambient': '1296.3190', 'aut_centralizer_order': 24, 'aut_label': '36.dm1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '12.4', 'aut_weyl_index': 288, 'centralizer': '36.m1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.by1.a1', '12.cb1.a1', '18.e1.a1'], 'contains': ['72.bo1.a1', '72.cf1.a1', '72.cn1.a1', '108.by1.a1', '108.cb1.a1'], 'core': '144.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [8835, -1, 1417, -1, 8592, -1, 1205, -1], 'generators': [3, 18, 2, 144], 'label': '1296.3190.36.dm1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.k1.a1', 'old_label': '36.dm1.a1', 'projective_image': '432.598', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.dm1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 71060133
    {'ambient': '1296.3190', 'aut_centralizer_order': 24, 'aut_label': '36.dm1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '12.4', 'aut_weyl_index': 288, 'centralizer': '36.m1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.by1.b1', '12.cb1.b1', '18.e1.a1'], 'contains': ['72.bo1.b1', '72.cf1.a1', '72.cn1.a1', '108.by1.b1', '108.cb1.b1'], 'core': '144.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [8835, -1, 2346, -1, 8592, -1, 1290, -1], 'generators': [219, 18, 2, 144], 'label': '1296.3190.36.dm1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.k1.a1', 'old_label': '36.dm1.b1', 'projective_image': '432.598', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.dm1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 71060134
    {'ambient': '1296.3190', 'aut_centralizer_order': 24, 'aut_label': '36.dn1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '12.4', 'aut_weyl_index': 288, 'centralizer': '36.m1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.by1.a1', '12.cc1.a1', '18.f1.a1'], 'contains': ['72.bq1.a1', '72.cg1.a1', '72.cq1.a1', '108.bz1.a1', '108.cb1.a1'], 'core': '144.d1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [8918, -1, 1335, -1, 8542, -1, 803, -1], 'generators': [3, 18, 432, 144], 'label': '1296.3190.36.dn1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.k1.a1', 'old_label': '36.dn1.a1', 'projective_image': '1296.3190', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.dn1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 71060135
    {'ambient': '1296.3190', 'aut_centralizer_order': 24, 'aut_label': '36.dn1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '12.4', 'aut_weyl_index': 288, 'centralizer': '36.m1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.by1.b1', '12.cc1.b1', '18.f1.a1'], 'contains': ['72.bq1.b1', '72.cg1.a1', '72.cq1.a1', '108.bz1.b1', '108.cb1.b1'], 'core': '144.d1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [8918, -1, 1973, -1, 8542, -1, 888, -1], 'generators': [219, 18, 432, 144], 'label': '1296.3190.36.dn1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.k1.a1', 'old_label': '36.dn1.b1', 'projective_image': '1296.3190', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.dn1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 71060136
    {'ambient': '1296.3190', 'aut_centralizer_order': 12, 'aut_label': '36.do1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '12.4', 'aut_weyl_index': 288, 'centralizer': '36.m1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.by1.a1', '12.cd1.a1', '18.g1.a1'], 'contains': ['72.bs1.a1', '72.ci1.a1', '72.ct1.b1', '108.ca1.a1', '108.cb1.a1'], 'core': '432.c1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [8559, -1, 1169, -1, 8724, -1, 103, -1], 'generators': [3, 18, 434, 144], 'label': '1296.3190.36.do1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.k1.a1', 'old_label': '36.do1.a1', 'projective_image': '1296.3190', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.do1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 71060137
    {'ambient': '1296.3190', 'aut_centralizer_order': 12, 'aut_label': '36.do1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '12.4', 'aut_weyl_index': 288, 'centralizer': '36.m1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.by1.a1', '12.cd1.b1', '18.g1.a1'], 'contains': ['72.bs1.a1', '72.ci1.b1', '72.ct1.a1', '108.ca1.b1', '108.cb1.a1'], 'core': '432.c1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [8559, -1, 1199, -1, 8724, -1, 146, -1], 'generators': [3, 18, 866, 144], 'label': '1296.3190.36.do1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.k1.a1', 'old_label': '36.do1.b1', 'projective_image': '1296.3190', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.do1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 71060138
    {'ambient': '1296.3190', 'aut_centralizer_order': 12, 'aut_label': '36.do1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '12.4', 'aut_weyl_index': 288, 'centralizer': '36.m1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.by1.b1', '12.cd1.c1', '18.g1.a1'], 'contains': ['72.bs1.b1', '72.ci1.a1', '72.ct1.a1', '108.ca1.c1', '108.cb1.b1'], 'core': '432.c1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [8559, -1, 1926, -1, 8724, -1, 315, -1], 'generators': [219, 18, 434, 144], 'label': '1296.3190.36.do1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.k1.a1', 'old_label': '36.do1.c1', 'projective_image': '1296.3190', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.do1.c1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 71060139
    {'ambient': '1296.3190', 'aut_centralizer_order': 12, 'aut_label': '36.do1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '12.4', 'aut_weyl_index': 288, 'centralizer': '36.m1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.by1.b1', '12.cd1.d1', '18.g1.a1'], 'contains': ['72.bs1.b1', '72.ci1.b1', '72.ct1.b1', '108.ca1.d1', '108.cb1.b1'], 'core': '432.c1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [8559, -1, 1897, -1, 8724, -1, 273, -1], 'generators': [219, 18, 866, 144], 'label': '1296.3190.36.do1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.k1.a1', 'old_label': '36.do1.d1', 'projective_image': '1296.3190', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.do1.d1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 71060140
    {'ambient': '1296.3190', 'aut_centralizer_order': 8, 'aut_label': '36.dp1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '12.4', 'aut_weyl_index': 288, 'centralizer': '108.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bz1.a1', '12.ce1.a1', '18.h1.a1'], 'contains': ['72.bn1.a1', '72.cy1.a1', '72.di1.a1', '108.cc1.a1', '108.cd1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [9504, -1, 4432, -1, 9077, -1, 3536, -1], 'generators': [3, 54, 2, 432], 'label': '1296.3190.36.dp1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.h1.a1', 'old_label': '36.dp1.a1', 'projective_image': '432.598', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.dp1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 71060141
    {'ambient': '1296.3190', 'aut_centralizer_order': 8, 'aut_label': '36.dp1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '12.4', 'aut_weyl_index': 288, 'centralizer': '108.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bz1.b1', '12.ce1.b1', '18.h1.a1'], 'contains': ['72.bn1.b1', '72.cy1.a1', '72.di1.a1', '108.cc1.b1', '108.cd1.b1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [9504, -1, 5025, -1, 9077, -1, 3764, -1], 'generators': [219, 54, 2, 432], 'label': '1296.3190.36.dp1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.h1.a1', 'old_label': '36.dp1.b1', 'projective_image': '432.598', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.dp1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 71060142
    {'ambient': '1296.3190', 'aut_centralizer_order': 12, 'aut_label': '6.n1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '96.230', 'aut_weyl_index': 36, 'centralizer': '36.x1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '3.c1.a1'], 'contains': ['12.a1.a1', '12.v1.a1', '12.bb1.a1', '12.ca1.a1', '12.ca1.b1', '18.d1.a1', '18.p1.a1', '18.q1.a1', '18.r1.a1'], 'core': '12.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5488, -1, 3492, -1, 6301, -1, 2154, -1], 'generators': [3, 12, 432, 18, 216, 2], 'label': '1296.3190.6.n1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1.a1', 'old_label': '6.n1.a1', 'projective_image': '216.162', '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': '12.4'}
  • id: 71060143
    {'ambient': '1296.3190', 'aut_centralizer_order': 8, 'aut_label': '36.dq1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '12.4', 'aut_weyl_index': 288, 'centralizer': '108.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bz1.a1', '12.cf1.a1', '18.i1.a1'], 'contains': ['72.bo1.a1', '72.cz1.a1', '72.dj1.a1', '108.cc1.a1', '108.ce1.a1'], 'core': '144.b1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [9077, -1, 4374, -1, 8965, -1, 3445, -1], 'generators': [3, 54, 2, 144], 'label': '1296.3190.36.dq1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.i1.a1', 'old_label': '36.dq1.a1', 'projective_image': '432.598', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.dq1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 71060144
    {'ambient': '1296.3190', 'aut_centralizer_order': 8, 'aut_label': '36.dq1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '12.4', 'aut_weyl_index': 288, 'centralizer': '108.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bz1.b1', '12.cf1.b1', '18.i1.a1'], 'contains': ['72.bo1.b1', '72.cz1.a1', '72.dj1.a1', '108.cc1.b1', '108.ce1.b1'], 'core': '144.b1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [9077, -1, 4970, -1, 8965, -1, 3721, -1], 'generators': [219, 54, 2, 144], 'label': '1296.3190.36.dq1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.i1.a1', 'old_label': '36.dq1.b1', 'projective_image': '432.598', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.dq1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 71060145
    {'ambient': '1296.3190', 'aut_centralizer_order': 4, 'aut_label': '36.dr1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '12.4', 'aut_weyl_index': 288, 'centralizer': '108.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bz1.a1', '12.cg1.a1', '18.j1.a1'], 'contains': ['72.bp1.a1', '72.da1.a1', '72.dl1.a1', '108.cc1.a1', '108.cf1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [9838, -1, 4895, -1, 9718, -1, 3858, -1], 'generators': [3, 54, 2, 576], 'label': '1296.3190.36.dr1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.j1.a1', 'old_label': '36.dr1.a1', 'projective_image': '432.598', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.dr1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 71060146
    {'ambient': '1296.3190', 'aut_centralizer_order': 4, 'aut_label': '36.dr1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '12.4', 'aut_weyl_index': 288, 'centralizer': '108.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bz1.a1', '12.cg1.a2', '18.j1.a1'], 'contains': ['72.bp1.a1', '72.da1.a2', '72.dl1.a2', '108.cc1.a1', '108.cf1.a2'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [9838, -1, 4924, -1, 9718, -1, 3901, -1], 'generators': [3, 54, 2, 1008], 'label': '1296.3190.36.dr1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.j1.a1', 'old_label': '36.dr1.a2', 'projective_image': '432.598', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.dr1.a2', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 71060147
    {'ambient': '1296.3190', 'aut_centralizer_order': 4, 'aut_label': '36.dr1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '12.4', 'aut_weyl_index': 288, 'centralizer': '108.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bz1.b1', '12.cg1.b1', '18.j1.a1'], 'contains': ['72.bp1.b1', '72.da1.a1', '72.dl1.a2', '108.cc1.b1', '108.cf1.b1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [9838, -1, 5136, -1, 9718, -1, 4099, -1], 'generators': [219, 54, 2, 576], 'label': '1296.3190.36.dr1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.j1.a1', 'old_label': '36.dr1.b1', 'projective_image': '432.598', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.dr1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 71060148
    {'ambient': '1296.3190', 'aut_centralizer_order': 4, 'aut_label': '36.dr1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '12.4', 'aut_weyl_index': 288, 'centralizer': '108.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bz1.b1', '12.cg1.b2', '18.j1.a1'], 'contains': ['72.bp1.b1', '72.da1.a2', '72.dl1.a1', '108.cc1.b1', '108.cf1.b2'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [9838, -1, 5107, -1, 9718, -1, 4141, -1], 'generators': [219, 54, 2, 1008], 'label': '1296.3190.36.dr1.b2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.j1.a1', 'old_label': '36.dr1.b2', 'projective_image': '432.598', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.dr1.b2', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 71060149
    {'ambient': '1296.3190', 'aut_centralizer_order': 8, 'aut_label': '36.ds1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '36.10', 'aut_weyl_index': 96, 'centralizer': '108.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bz1.a1', '12.ch1.a1', '18.k1.a1'], 'contains': ['72.bq1.a1', '72.dh1.a1', '72.dp1.a1', '108.cd1.a1', '108.ce1.a1', '108.cf1.a1', '108.cf1.a2'], 'core': '144.d1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [9425, -1, 4837, -1, 9021, -1, 3811, -1], 'generators': [3, 54, 144, 432], 'label': '1296.3190.36.ds1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.l1.a1', 'old_label': '36.ds1.a1', 'projective_image': '1296.3190', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.ds1.a1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 71060150
    {'ambient': '1296.3190', 'aut_centralizer_order': 8, 'aut_label': '36.ds1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '36.10', 'aut_weyl_index': 96, 'centralizer': '108.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bz1.b1', '12.ch1.b1', '18.k1.a1'], 'contains': ['72.bq1.b1', '72.dh1.a1', '72.dp1.a1', '108.cd1.b1', '108.ce1.b1', '108.cf1.b1', '108.cf1.b2'], 'core': '144.d1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [9425, -1, 5057, -1, 9021, -1, 4052, -1], 'generators': [219, 54, 144, 432], 'label': '1296.3190.36.ds1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.l1.a1', 'old_label': '36.ds1.b1', 'projective_image': '1296.3190', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.ds1.b1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 71060151
    {'ambient': '1296.3190', 'aut_centralizer_order': 24, 'aut_label': '36.dt1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '12.4', 'aut_weyl_index': 288, 'centralizer': '36.x1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.ca1.a1', '12.cb1.a1', '18.p1.a1'], 'contains': ['72.g1.a1', '72.bz1.a1', '72.co1.a1', '108.by1.a1', '108.cg1.a1'], 'core': '72.g1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [9708, -1, 867, -1, 8805, -1, 1163, -1], 'generators': [3, 18, 2, 12], 'label': '1296.3190.36.dt1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.n1.a1', 'old_label': '36.dt1.a1', 'projective_image': '432.598', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.dt1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 71060152
    {'ambient': '1296.3190', 'aut_centralizer_order': 24, 'aut_label': '36.dt1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '12.4', 'aut_weyl_index': 288, 'centralizer': '36.x1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.ca1.b1', '12.cb1.b1', '18.p1.a1'], 'contains': ['72.g1.b1', '72.bz1.a1', '72.co1.a1', '108.by1.b1', '108.cg1.b1'], 'core': '72.g1.b1', 'coset_action_label': None, 'count': 6, 'diagramx': [9708, -1, 954, -1, 8805, -1, 1247, -1], 'generators': [219, 18, 2, 12], 'label': '1296.3190.36.dt1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.n1.a1', 'old_label': '36.dt1.b1', 'projective_image': '432.598', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.dt1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 71060153
    {'ambient': '1296.3190', 'aut_centralizer_order': 6, 'aut_label': '6.o1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '288.1040', 'aut_weyl_index': 12, 'centralizer': '72.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1'], 'contains': ['12.t1.a1', '12.y1.a1', '12.bd1.a1', '12.cd1.a1', '12.cd1.b1', '12.cd1.c1', '12.cd1.d1', '18.a1.a1', '18.g1.a1', '18.r1.a1'], 'core': '18.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [5608, -1, 790, -1, 6960, -1, 905, -1], 'generators': [3, 144, 12, 18, 216, 434], 'label': '1296.3190.6.o1.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.o1.a1', 'projective_image': '648.731', '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': '36.10'}
  • id: 71060154
    {'ambient': '1296.3190', 'aut_centralizer_order': 24, 'aut_label': '36.du1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '12.4', 'aut_weyl_index': 288, 'centralizer': '36.x1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.ca1.a1', '12.cc1.a1', '18.q1.a1'], 'contains': ['72.h1.a1', '72.cb1.a1', '72.cr1.a1', '108.bz1.a1', '108.cg1.a1'], 'core': '72.h1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [9263, -1, 1085, -1, 8673, -1, 761, -1], 'generators': [3, 18, 432, 12], 'label': '1296.3190.36.du1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.n1.a1', 'old_label': '36.du1.a1', 'projective_image': '1296.3190', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.du1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 71060155
    {'ambient': '1296.3190', 'aut_centralizer_order': 24, 'aut_label': '36.du1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '12.4', 'aut_weyl_index': 288, 'centralizer': '36.x1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.ca1.b1', '12.cc1.b1', '18.q1.a1'], 'contains': ['72.h1.b1', '72.cb1.a1', '72.cr1.a1', '108.bz1.b1', '108.cg1.b1'], 'core': '72.h1.b1', 'coset_action_label': None, 'count': 6, 'diagramx': [9263, -1, 1124, -1, 8673, -1, 846, -1], 'generators': [219, 18, 432, 12], 'label': '1296.3190.36.du1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.n1.a1', 'old_label': '36.du1.b1', 'projective_image': '1296.3190', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.du1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 71060156
    {'ambient': '1296.3190', 'aut_centralizer_order': 12, 'aut_label': '36.dv1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '12.4', 'aut_weyl_index': 288, 'centralizer': '36.x1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.ca1.a1', '12.cd1.a1', '18.r1.a1'], 'contains': ['72.bu1.a1', '72.cd1.a1', '72.cu1.b1', '108.ca1.a1', '108.cg1.a1'], 'core': '216.e1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [8728, -1, 203, -1, 8855, -1, 18, -1], 'generators': [3, 18, 434, 12], 'label': '1296.3190.36.dv1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.n1.a1', 'old_label': '36.dv1.a1', 'projective_image': '1296.3190', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.dv1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 71060157
    {'ambient': '1296.3190', 'aut_centralizer_order': 12, 'aut_label': '36.dv1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '12.4', 'aut_weyl_index': 288, 'centralizer': '36.x1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.ca1.a1', '12.cd1.b1', '18.r1.a1'], 'contains': ['72.bu1.a1', '72.cd1.b1', '72.cu1.a1', '108.ca1.b1', '108.cg1.a1'], 'core': '216.e1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [8728, -1, 157, -1, 8855, -1, 61, -1], 'generators': [3, 18, 866, 12], 'label': '1296.3190.36.dv1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.n1.a1', 'old_label': '36.dv1.b1', 'projective_image': '1296.3190', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.dv1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 71060158
    {'ambient': '1296.3190', 'aut_centralizer_order': 12, 'aut_label': '36.dv1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '12.4', 'aut_weyl_index': 288, 'centralizer': '36.x1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.ca1.b1', '12.cd1.c1', '18.r1.a1'], 'contains': ['72.bu1.b1', '72.cd1.a1', '72.cu1.a1', '108.ca1.c1', '108.cg1.b1'], 'core': '216.e1.b1', 'coset_action_label': None, 'count': 6, 'diagramx': [8728, -1, 278, -1, 8855, -1, 230, -1], 'generators': [219, 18, 434, 12], 'label': '1296.3190.36.dv1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.n1.a1', 'old_label': '36.dv1.c1', 'projective_image': '1296.3190', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.dv1.c1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 71060159
    {'ambient': '1296.3190', 'aut_centralizer_order': 12, 'aut_label': '36.dv1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '12.4', 'aut_weyl_index': 288, 'centralizer': '36.x1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.ca1.b1', '12.cd1.d1', '18.r1.a1'], 'contains': ['72.bu1.b1', '72.cd1.b1', '72.cu1.b1', '108.ca1.d1', '108.cg1.b1'], 'core': '216.e1.b1', 'coset_action_label': None, 'count': 6, 'diagramx': [8728, -1, 240, -1, 8855, -1, 188, -1], 'generators': [219, 18, 866, 12], 'label': '1296.3190.36.dv1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.n1.a1', 'old_label': '36.dv1.d1', 'projective_image': '1296.3190', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.dv1.d1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 71060160
    {'ambient': '1296.3190', 'aut_centralizer_order': 24, 'aut_label': '36.dw1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '36.10', 'aut_weyl_index': 96, 'centralizer': '72.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.cb1.a1', '12.cc1.a1', '12.cd1.a1', '12.cd1.b1', '18.a1.a1'], 'contains': ['72.i1.a1', '72.ch1.a1', '72.cw1.a1', '108.cb1.a1', '108.cg1.a1'], 'core': '72.i1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8985, -1, 891, -1, 8765, -1, 503, -1], 'generators': [3, 18, 12, 144], 'label': '1296.3190.36.dw1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '36.dw1.a1', 'projective_image': '1296.3190', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.dw1.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 71060161
    {'ambient': '1296.3190', 'aut_centralizer_order': 24, 'aut_label': '36.dw1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '36.10', 'aut_weyl_index': 96, 'centralizer': '72.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.cb1.b1', '12.cc1.b1', '12.cd1.c1', '12.cd1.d1', '18.a1.a1'], 'contains': ['72.i1.b1', '72.ch1.a1', '72.cw1.a1', '108.cb1.b1', '108.cg1.b1'], 'core': '72.i1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [8985, -1, 996, -1, 8765, -1, 528, -1], 'generators': [219, 18, 12, 144], 'label': '1296.3190.36.dw1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '36.dw1.b1', 'projective_image': '1296.3190', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.dw1.b1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 71060162
    {'ambient': '1296.3190', 'aut_centralizer_order': 8, 'aut_label': '36.dx1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '12.4', 'aut_weyl_index': 288, 'centralizer': '108.x1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.ce1.a1', '12.cf1.a1', '12.cg1.a1', '12.cg1.a2', '18.s1.a1'], 'contains': ['72.g1.a1', '72.cx1.a1', '72.dk1.a1', '108.cc1.a1', '108.ch1.a1'], 'core': '72.g1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [9793, -1, 1753, -1, 9827, -1, 3402, -1], 'generators': [3, 54, 2, 12], 'label': '1296.3190.36.dx1.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': '36.dx1.a1', 'projective_image': '432.598', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.dx1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 71060163
    {'ambient': '1296.3190', 'aut_centralizer_order': 8, 'aut_label': '36.dx1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '12.4', 'aut_weyl_index': 288, 'centralizer': '108.x1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.ce1.b1', '12.cf1.b1', '12.cg1.b1', '12.cg1.b2', '18.s1.a1'], 'contains': ['72.g1.b1', '72.cx1.a1', '72.dk1.a1', '108.cc1.b1', '108.ch1.b1'], 'core': '72.g1.b1', 'coset_action_label': None, 'count': 18, 'diagramx': [9793, -1, 2266, -1, 9827, -1, 3629, -1], 'generators': [219, 54, 2, 12], 'label': '1296.3190.36.dx1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.s1.a1', 'old_label': '36.dx1.b1', 'projective_image': '432.598', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.dx1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 71060164
    {'ambient': '1296.3190', 'aut_centralizer_order': 4, 'aut_label': '6.p1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '288.1040', 'aut_weyl_index': 12, 'centralizer': '216.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '3.c1.a1'], 'contains': ['12.a1.a1', '12.be1.a1', '12.bj1.a1', '12.ce1.a1', '12.ce1.b1', '18.h1.a1', '18.s1.a1', '18.t1.a1'], 'core': '12.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6661, -1, 5048, -1, 7108, -1, 4418, -1], 'generators': [3, 432, 12, 54, 216, 2], 'label': '1296.3190.6.p1.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.p1.a1', 'projective_image': '216.162', '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': '72.46'}
  • id: 71060165
    {'ambient': '1296.3190', 'aut_centralizer_order': 8, 'aut_label': '36.dy1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '36.10', 'aut_weyl_index': 96, 'centralizer': '216.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.ce1.a1', '12.ch1.a1', '18.t1.a1'], 'contains': ['72.h1.a1', '72.db1.a1', '72.dq1.a1', '108.cd1.a1', '108.ch1.a1'], 'core': '72.h1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [9599, -1, 3380, -1, 9677, -1, 3368, -1], 'generators': [3, 54, 12, 432], 'label': '1296.3190.36.dy1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.p1.a1', 'old_label': '36.dy1.a1', 'projective_image': '1296.3190', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.dy1.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 71060166
    {'ambient': '1296.3190', 'aut_centralizer_order': 8, 'aut_label': '36.dy1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '36.10', 'aut_weyl_index': 96, 'centralizer': '216.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.ce1.b1', '12.ch1.b1', '18.t1.a1'], 'contains': ['72.h1.b1', '72.db1.a1', '72.dq1.a1', '108.cd1.b1', '108.ch1.b1'], 'core': '72.h1.b1', 'coset_action_label': None, 'count': 6, 'diagramx': [9599, -1, 3926, -1, 9677, -1, 3596, -1], 'generators': [219, 54, 12, 432], 'label': '1296.3190.36.dy1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.p1.a1', 'old_label': '36.dy1.b1', 'projective_image': '1296.3190', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.dy1.b1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 71060167
    {'ambient': '1296.3190', 'aut_centralizer_order': 8, 'aut_label': '36.dz1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '36.10', 'aut_weyl_index': 96, 'centralizer': '216.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.cf1.a1', '12.ch1.a1', '18.u1.a1'], 'contains': ['72.i1.a1', '72.dd1.a1', '72.ds1.a1', '108.ce1.a1', '108.ch1.a1'], 'core': '72.i1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [9181, -1, 3353, -1, 9647, -1, 3343, -1], 'generators': [3, 54, 12, 144], 'label': '1296.3190.36.dz1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.q1.a1', 'old_label': '36.dz1.a1', 'projective_image': '1296.3190', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.dz1.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 71060168
    {'ambient': '1296.3190', 'aut_centralizer_order': 8, 'aut_label': '36.dz1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '36.10', 'aut_weyl_index': 96, 'centralizer': '216.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.cf1.b1', '12.ch1.b1', '18.u1.a1'], 'contains': ['72.i1.b1', '72.dd1.a1', '72.ds1.a1', '108.ce1.b1', '108.ch1.b1'], 'core': '72.i1.b1', 'coset_action_label': None, 'count': 6, 'diagramx': [9181, -1, 3907, -1, 9647, -1, 3570, -1], 'generators': [219, 54, 12, 144], 'label': '1296.3190.36.dz1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.q1.a1', 'old_label': '36.dz1.b1', 'projective_image': '1296.3190', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.dz1.b1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 71060169
    {'ambient': '1296.3190', 'aut_centralizer_order': 4, 'aut_label': '36.ea1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '36.10', 'aut_weyl_index': 96, 'centralizer': '216.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.cg1.a1', '12.ch1.a1', '18.v1.a1'], 'contains': ['72.bw1.a1', '72.df1.a1', '72.du1.a1', '108.cf1.a1', '108.ch1.a1'], 'core': '216.e1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [9990, -1, 3406, -1, 9988, -1, 3987, -1], 'generators': [3, 54, 12, 576], 'label': '1296.3190.36.ea1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.r1.a1', 'old_label': '36.ea1.a1', 'projective_image': '1296.3190', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.ea1.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 71060170
    {'ambient': '1296.3190', 'aut_centralizer_order': 4, 'aut_label': '36.ea1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '36.10', 'aut_weyl_index': 96, 'centralizer': '216.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.cg1.a2', '12.ch1.a1', '18.v1.a1'], 'contains': ['72.bw1.a1', '72.df1.a2', '72.du1.a2', '108.cf1.a2', '108.ch1.a1'], 'core': '216.e1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [9990, -1, 3457, -1, 9988, -1, 4012, -1], 'generators': [3, 54, 12, 1008], 'label': '1296.3190.36.ea1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.r1.a1', 'old_label': '36.ea1.a2', 'projective_image': '1296.3190', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.ea1.a2', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 71060171
    {'ambient': '1296.3190', 'aut_centralizer_order': 4, 'aut_label': '36.ea1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '36.10', 'aut_weyl_index': 96, 'centralizer': '216.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.cg1.b1', '12.ch1.b1', '18.v1.a1'], 'contains': ['72.bw1.b1', '72.df1.a1', '72.du1.a2', '108.cf1.b1', '108.ch1.b1'], 'core': '216.e1.b1', 'coset_action_label': None, 'count': 6, 'diagramx': [9990, -1, 3990, -1, 9988, -1, 4228, -1], 'generators': [219, 54, 12, 576], 'label': '1296.3190.36.ea1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.r1.a1', 'old_label': '36.ea1.b1', 'projective_image': '1296.3190', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.ea1.b1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 71060172
    {'ambient': '1296.3190', 'aut_centralizer_order': 4, 'aut_label': '36.ea1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '36.10', 'aut_weyl_index': 96, 'centralizer': '216.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.cg1.b2', '12.ch1.b1', '18.v1.a1'], 'contains': ['72.bw1.b1', '72.df1.a2', '72.du1.a1', '108.cf1.b2', '108.ch1.b1'], 'core': '216.e1.b1', 'coset_action_label': None, 'count': 6, 'diagramx': [9990, -1, 4012, -1, 9988, -1, 4253, -1], 'generators': [219, 54, 12, 1008], 'label': '1296.3190.36.ea1.b2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.r1.a1', 'old_label': '36.ea1.b2', 'projective_image': '1296.3190', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.ea1.b2', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 71060173
    {'ambient': '1296.3190', 'aut_centralizer_order': 432, 'aut_label': '48.a1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '8.5', 'aut_weyl_index': 432, 'centralizer': '4.a1.a1', 'complements': ['27.d1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '24.a1.a1', '24.s1.a1', '24.s1.b1', '24.y1.a1', '24.bf1.a1', '24.bo1.a1', '24.br1.a1'], 'contains': ['144.a1.a1', '144.b1.a1', '144.d1.a1', '144.g1.a1', '144.k1.a1', '144.o1.a1', '144.w1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7987, 5174, 3665, 5286, 7289, 5204, 3700, 5152], 'generators': [2, 144, 432], 'label': '1296.3190.48.a1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '48.a1.a1', 'normal_contained_in': ['16.a1.a1', '24.a1.a1'], 'normal_contains': ['144.b1.a1', '144.a1.a1', '144.d1.a1'], 'normalizer': '1.a1.a1', 'old_label': '48.a1.a1', 'projective_image': '432.598', 'quotient_action_image': '4.2', 'quotient_action_kernel': '12.4', 'quotient_action_kernel_order': 12, 'quotient_fusion': None, 'short_label': '48.a1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 71060174
    {'ambient': '1296.3190', 'aut_centralizer_order': 432, 'aut_label': '48.b1', 'aut_quo_index': 8, 'aut_stab_index': 1, 'aut_weyl_group': '8.5', 'aut_weyl_index': 432, 'centralizer': '4.b1.a1', 'complements': ['27.c1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '24.b1.a1', '24.e1.a1', '24.e1.b1', '24.x1.a1', '24.bg1.a1', '24.bl1.a1', '24.bs1.a1'], 'contains': ['144.a1.a1', '144.c1.a1', '144.e1.a1', '144.h1.a1', '144.l1.a1', '144.s1.a1', '144.x1.a1'], 'core': '48.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7725, 5931, 828, 3659, 7320, 3692, 3674, 3909], 'generators': [2, 12, 432], 'label': '1296.3190.48.b1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '48.b1.a1', 'normal_contained_in': ['16.a1.a1', '24.b1.a1', '24.e1.a1', '24.e1.b1'], 'normal_contains': ['144.a1.a1', '144.c1.a1', '144.e1.a1'], 'normalizer': '1.a1.a1', 'old_label': '48.b1.a1', 'projective_image': '432.598', 'quotient_action_image': '4.2', 'quotient_action_kernel': '12.4', 'quotient_action_kernel_order': 12, 'quotient_fusion': None, 'short_label': '48.b1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 71060175
    {'ambient': '1296.3190', 'aut_centralizer_order': 6, 'aut_label': '2.c1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '576.8675', 'aut_weyl_index': 6, 'centralizer': '72.b1.a1', 'complements': ['648.c1.a1', '648.e1.a1', '648.d1.a1', '648.f1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1', '4.f1.a1', '4.g1.a1', '6.d1.a1', '6.e1.a1', '6.m1.a1', '6.s1.a1', '6.t1.a1'], 'core': '2.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1769, 3613, 8429, 6324, 1567, 4057, 7738, 6622], 'generators': [3, 12, 216, 108, 432, 2, 144], 'label': '1296.3190.2.c1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.c1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.a1.a1', '4.f1.a1', '4.g1.a1', '6.d1.a1', '6.e1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.c1.a1', 'projective_image': '216.162', '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': '72.46'}
  • id: 71060176
    {'ambient': '1296.3190', 'aut_centralizer_order': 4, 'aut_label': '6.q1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '288.1040', 'aut_weyl_index': 12, 'centralizer': '216.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '3.d1.a1'], 'contains': ['12.b1.a1', '12.bf1.a1', '12.bl1.a1', '12.cf1.a1', '12.cf1.b1', '18.i1.a1', '18.s1.a1', '18.u1.a1'], 'core': '12.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6619, -1, 5081, -1, 6902, -1, 4368, -1], 'generators': [3, 144, 12, 54, 216, 2], 'label': '1296.3190.6.q1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.d1.a1', 'old_label': '6.q1.a1', 'projective_image': '216.162', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.q1.a1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 71060177
    {'ambient': '1296.3190', 'aut_centralizer_order': 432, 'aut_label': '48.c1', 'aut_quo_index': 4, 'aut_stab_index': 1, 'aut_weyl_group': '8.5', 'aut_weyl_index': 432, 'centralizer': '4.f1.a1', 'complements': ['27.b1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '24.c1.a1', '24.f1.a1', '24.f1.b1', '24.z1.a1', '24.bi1.a1', '24.bm1.a1', '24.bu1.a1'], 'contains': ['144.b1.a1', '144.c1.a1', '144.f1.a1', '144.i1.a1', '144.p1.a1', '144.t1.a1', '144.ba1.a1'], 'core': '48.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7701, 7236, 1646, 3445, 7157, 3116, 3768, 3492], 'generators': [2, 12, 144], 'label': '1296.3190.48.c1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '48.c1.a1', 'normal_contained_in': ['16.a1.a1', '24.c1.a1', '24.f1.a1', '24.f1.b1'], 'normal_contains': ['144.b1.a1', '144.c1.a1', '144.f1.a1'], 'normalizer': '1.a1.a1', 'old_label': '48.c1.a1', 'projective_image': '432.598', 'quotient_action_image': '4.2', 'quotient_action_kernel': '12.1', 'quotient_action_kernel_order': 12, 'quotient_fusion': None, 'short_label': '48.c1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 71060178
    {'ambient': '1296.3190', 'aut_centralizer_order': 432, 'aut_label': '48.d1', 'aut_quo_index': 8, 'aut_stab_index': 1, 'aut_weyl_group': '8.5', 'aut_weyl_index': 432, 'centralizer': '8.a1.a1', 'complements': ['27.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '24.d1.a1', '24.g1.a1', '24.g1.b1', '24.bb1.a1', '24.bj1.a1', '24.bp1.a1', '24.by1.a1'], 'contains': ['144.d1.a1', '144.e1.a1', '144.f1.a1', '144.m1.a1', '144.q1.a1', '144.u1.a1', '144.bf1.a1'], 'core': '48.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8113, 6370, 2384, 3031, 7126, 4269, 4720, 3701], 'generators': [12, 144, 432], 'label': '1296.3190.48.d1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '48.d1.a1', 'normal_contained_in': ['16.a1.a1', '24.d1.a1', '24.g1.a1', '24.g1.b1'], 'normal_contains': ['144.d1.a1', '144.e1.a1', '144.f1.a1'], 'normalizer': '1.a1.a1', 'old_label': '48.d1.a1', 'projective_image': '1296.3190', 'quotient_action_image': '8.5', 'quotient_action_kernel': '6.2', 'quotient_action_kernel_order': 6, 'quotient_fusion': None, 'short_label': '48.d1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 71060179
    {'ambient': '1296.3190', 'aut_centralizer_order': 216, 'aut_label': '48.e1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '8.5', 'aut_weyl_index': 432, 'centralizer': '8.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '24.h1.a1', '24.bh1.a1', '24.bt1.a1'], 'contains': ['144.a1.a1', '144.i1.a1', '144.j1.a1', '144.m1.a1', '144.n1.a1', '144.y1.a1', '144.z1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [5158, -1, 5856, -1, 5292, -1, 5948, -1], 'generators': [2, 156, 432], 'label': '1296.3190.48.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.g1.a1', 'old_label': '48.e1.a1', 'projective_image': '432.598', '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': '4.2'}
  • id: 71060180
    {'ambient': '1296.3190', 'aut_centralizer_order': 216, 'aut_label': '48.f1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '8.5', 'aut_weyl_index': 432, 'centralizer': '8.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '24.i1.a1', '24.ba1.a1', '24.bv1.a1'], 'contains': ['144.b1.a1', '144.h1.a1', '144.j1.a1', '144.q1.a1', '144.r1.a1', '144.bb1.a1', '144.bc1.a1'], 'core': '144.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2605, -1, 5301, -1, 4960, -1, 5871, -1], 'generators': [2, 444, 144], 'label': '1296.3190.48.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.e1.a1', 'old_label': '48.f1.a1', 'projective_image': '432.598', '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': '4.2'}
  • id: 71060181
    {'ambient': '1296.3190', 'aut_centralizer_order': 216, 'aut_label': '48.g1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '8.5', 'aut_weyl_index': 432, 'centralizer': '8.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '24.j1.a1', '24.t1.a1', '24.t1.b1', '24.bn1.a1', '24.bn1.a2', '24.bw1.a1', '24.bw1.a2'], 'contains': ['144.c1.a1', '144.g1.a1', '144.j1.a1', '144.u1.a1', '144.v1.a1', '144.bd1.a1', '144.be1.a1'], 'core': '144.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7757, -1, 1755, -1, 7351, -1, 4745, -1], 'generators': [2, 12, 576], 'label': '1296.3190.48.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '48.g1.a1', 'projective_image': '432.598', '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': '4.2'}
  • id: 71060182
    {'ambient': '1296.3190', 'aut_centralizer_order': 216, 'aut_label': '48.h1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '4.2', 'aut_weyl_index': 864, 'centralizer': '8.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '24.k1.a1', '24.bx1.a1', '24.bx1.a2'], 'contains': ['144.g1.a1', '144.h1.a1', '144.i1.a1', '144.j1.a1', '144.bf1.a1', '144.bg1.a1', '144.bh1.a1', '144.bi1.a1', '144.bj1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [3589, -1, 6493, -1, 5174, -1, 6779, -1], 'generators': [2, 444, 576], 'label': '1296.3190.48.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.e1.a1', 'old_label': '48.h1.a1', 'projective_image': '432.598', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.h1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 71060183
    {'ambient': '1296.3190', 'aut_centralizer_order': 216, 'aut_label': '48.i1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '8.5', 'aut_weyl_index': 432, 'centralizer': '8.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '24.l1.a1', '24.bc1.a1', '24.bq1.a1'], 'contains': ['144.d1.a1', '144.l1.a1', '144.n1.a1', '144.p1.a1', '144.r1.a1', '144.bd1.a1', '144.bg1.a1'], 'core': '144.d1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3666, -1, 3024, -1, 5323, -1, 5197, -1], 'generators': [14, 144, 432], 'label': '1296.3190.48.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.a1', 'old_label': '48.i1.a1', 'projective_image': '1296.3190', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.i1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 71060184
    {'ambient': '1296.3190', 'aut_centralizer_order': 216, 'aut_label': '48.j1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '8.5', 'aut_weyl_index': 432, 'centralizer': '8.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '24.m1.a1', '24.u1.a1', '24.u1.b1'], 'contains': ['144.e1.a1', '144.k1.a1', '144.n1.a1', '144.t1.a1', '144.v1.a1', '144.bb1.a1', '144.bh1.a1'], 'core': '144.e1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7131, -1, 2846, -1, 7034, -1, 4012, -1], 'generators': [146, 12, 432], 'label': '1296.3190.48.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '48.j1.a1', 'projective_image': '1296.3190', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.j1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 71060185
    {'ambient': '1296.3190', 'aut_centralizer_order': 216, 'aut_label': '48.k1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '4.2', 'aut_weyl_index': 864, 'centralizer': '8.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '24.n1.a1'], 'contains': ['144.k1.a1', '144.l1.a1', '144.m1.a1', '144.n1.a1', '144.ba1.a1', '144.bc1.a1', '144.be1.a1', '144.bi1.a1', '144.bj1.a1'], 'core': '432.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [4104, -1, 4771, -1, 5235, -1, 5897, -1], 'generators': [146, 156, 432], 'label': '1296.3190.48.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.f1.a1', 'old_label': '48.k1.a1', 'projective_image': '1296.3190', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.k1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 71060186
    {'ambient': '1296.3190', 'aut_centralizer_order': 216, 'aut_label': '48.l1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '8.5', 'aut_weyl_index': 432, 'centralizer': '8.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '24.o1.a1', '24.v1.a1', '24.v1.b1', '24.bd1.a1', '24.bd1.b1', '24.bk1.a1', '24.bk1.b1'], 'contains': ['144.f1.a1', '144.o1.a1', '144.r1.a1', '144.s1.a1', '144.v1.a1', '144.y1.a1', '144.bi1.a1'], 'core': '144.f1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7257, -1, 11, -1, 7095, -1, 2004, -1], 'generators': [434, 12, 144], 'label': '1296.3190.48.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '48.l1.a1', 'projective_image': '1296.3190', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.l1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 71060187
    {'ambient': '1296.3190', 'aut_centralizer_order': 2, 'aut_label': '6.r1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '288.1040', 'aut_weyl_index': 12, 'centralizer': '216.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1'], 'contains': ['12.r1.a1', '12.bg1.a1', '12.bn1.a1', '12.cg1.a1', '12.cg1.a2', '12.cg1.b1', '12.cg1.b2', '18.j1.a1', '18.s1.a1', '18.v1.a1'], 'core': '36.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [6796, -1, 4096, -1, 7901, -1, 4467, -1], 'generators': [3, 576, 12, 54, 216, 2], 'label': '1296.3190.6.r1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.r1.a1', 'old_label': '6.r1.a1', 'projective_image': '216.162', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.r1.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 71060188
    {'ambient': '1296.3190', 'aut_centralizer_order': 216, 'aut_label': '48.m1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '4.2', 'aut_weyl_index': 864, 'centralizer': '8.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '24.p1.a1', '24.be1.a1', '24.be1.b1'], 'contains': ['144.o1.a1', '144.p1.a1', '144.q1.a1', '144.r1.a1', '144.x1.a1', '144.z1.a1', '144.be1.a1', '144.bh1.a1', '144.bj1.a1'], 'core': '432.c1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [2752, -1, 2500, -1, 5143, -1, 5487, -1], 'generators': [434, 444, 144], 'label': '1296.3190.48.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.a1', 'old_label': '48.m1.a1', 'projective_image': '1296.3190', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.m1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 71060189
    {'ambient': '1296.3190', 'aut_centralizer_order': 216, 'aut_label': '48.n1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '4.2', 'aut_weyl_index': 864, 'centralizer': '8.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '24.q1.a1', '24.w1.a1', '24.w1.b1'], 'contains': ['144.s1.a1', '144.t1.a1', '144.u1.a1', '144.v1.a1', '144.w1.a1', '144.z1.a1', '144.bc1.a1', '144.bg1.a1', '144.bj1.a1'], 'core': '432.d1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [7169, -1, 631, -1, 7065, -1, 4651, -1], 'generators': [434, 12, 576], 'label': '1296.3190.48.n1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '48.n1.a1', 'projective_image': '1296.3190', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.n1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 71060190
    {'ambient': '1296.3190', 'aut_centralizer_order': 216, 'aut_label': '48.o1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1728, 'centralizer': '8.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '24.r1.a1'], 'contains': ['144.w1.a1', '144.x1.a1', '144.y1.a1', '144.z1.a1', '144.ba1.a1', '144.bb1.a1', '144.bc1.a1', '144.bd1.a1', '144.be1.a1', '144.bf1.a1', '144.bg1.a1', '144.bh1.a1', '144.bi1.a1'], 'core': '1296.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [3521, -1, 3823, -1, 5204, -1, 5923, -1], 'generators': [434, 444, 576], 'label': '1296.3190.48.o1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.a1.a1', 'old_label': '48.o1.a1', 'projective_image': '1296.3190', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.o1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 71060191
    {'ambient': '1296.3190', 'aut_centralizer_order': 48, 'aut_label': '54.a1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '8.5', 'aut_weyl_index': 432, 'centralizer': '18.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.d1.a1', '18.e1.a1', '18.p1.a1', '27.a1.a1'], 'contains': ['108.d1.a1', '108.k1.a1', '108.r1.a1', '108.by1.a1', '108.by1.b1', '162.a1.a1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [5660, -1, 5644, -1, 6504, -1, 2215, -1], 'generators': [3, 18, 216, 2], 'label': '1296.3190.54.a1.a1', 'mobius_quo': None, 'mobius_sub': 3, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '54.a1.a1', 'projective_image': '216.162', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 71060192
    {'ambient': '1296.3190', 'aut_centralizer_order': 48, 'aut_label': '54.b1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '8.5', 'aut_weyl_index': 432, 'centralizer': '18.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.d1.a1', '18.f1.a1', '18.q1.a1', '27.b1.a1'], 'contains': ['108.e1.a1', '108.l1.a1', '108.s1.a1', '108.bz1.a1', '108.bz1.b1', '162.a1.a1'], 'core': '216.b1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [5704, -1, 5551, -1, 6387, -1, 1655, -1], 'generators': [3, 18, 216, 432], 'label': '1296.3190.54.b1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '6.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '54.b1.a1', 'projective_image': '648.731', '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: 71060193
    {'ambient': '1296.3190', 'aut_centralizer_order': 24, 'aut_label': '54.c1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '8.5', 'aut_weyl_index': 432, 'centralizer': '18.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.d1.a1', '18.g1.a1', '18.r1.a1'], 'contains': ['108.g1.a1', '108.n1.a1', '108.t1.a1', '108.ca1.a1', '108.ca1.b1', '108.ca1.c1', '108.ca1.d1', '162.a1.a1'], 'core': '648.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [5862, -1, 1648, -1, 7204, -1, 361, -1], 'generators': [3, 18, 216, 434], 'label': '1296.3190.54.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.d1.a1', 'old_label': '54.c1.a1', 'projective_image': '648.731', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.c1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 71060194
    {'ambient': '1296.3190', 'aut_centralizer_order': 48, 'aut_label': '54.d1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '24.14', 'aut_weyl_index': 144, 'centralizer': '36.m1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.a1.a1', '18.e1.a1', '18.f1.a1', '18.g1.a1', '27.c1.a1'], 'contains': ['108.b1.a1', '108.f1.a1', '108.u1.a1', '108.cb1.a1', '108.cb1.b1', '162.a1.a1'], 'core': '108.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5788, -1, 5501, -1, 6445, -1, 1606, -1], 'generators': [3, 18, 216, 144], 'label': '1296.3190.54.d1.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.d1.a1', 'projective_image': '648.731', '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: 71060195
    {'ambient': '1296.3190', 'aut_centralizer_order': 16, 'aut_label': '54.e1', 'aut_quo_index': None, 'aut_stab_index': 27, 'aut_weyl_group': '8.5', 'aut_weyl_index': 432, 'centralizer': '54.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.h1.a1', '18.i1.a1', '18.j1.a1', '18.s1.a1', '27.a1.a1'], 'contains': ['108.d1.a1', '108.x1.a1', '108.bd1.a1', '108.cc1.a1', '108.cc1.b1', '162.b1.a1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [6677, -1, 6058, -1, 7426, -1, 4741, -1], 'generators': [3, 54, 216, 2], 'label': '1296.3190.54.e1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1.a1', 'old_label': '54.e1.a1', 'projective_image': '216.162', '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: 71060196
    {'ambient': '1296.3190', 'aut_centralizer_order': 16, 'aut_label': '54.f1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '24.14', 'aut_weyl_index': 144, 'centralizer': '108.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.h1.a1', '18.k1.a1', '18.t1.a1', '27.b1.a1'], 'contains': ['108.e1.a1', '108.ba1.a1', '108.be1.a1', '108.cd1.a1', '108.cd1.b1', '162.b1.a1'], 'core': '216.b1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [6592, -1, 6412, -1, 7146, -1, 4692, -1], 'generators': [3, 54, 216, 432], 'label': '1296.3190.54.f1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '6.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '54.f1.a1', 'projective_image': '648.731', '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: 71060197
    {'ambient': '1296.3190', 'aut_centralizer_order': 16, 'aut_label': '54.g1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '24.14', 'aut_weyl_index': 144, 'centralizer': '108.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.i1.a1', '18.k1.a1', '18.u1.a1', '27.c1.a1'], 'contains': ['108.f1.a1', '108.bb1.a1', '108.bf1.a1', '108.ce1.a1', '108.ce1.b1', '162.b1.a1'], 'core': '216.c1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [6634, -1, 6109, -1, 7087, -1, 4643, -1], 'generators': [3, 54, 216, 144], 'label': '1296.3190.54.g1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '6.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1.a1', 'old_label': '54.g1.a1', 'projective_image': '648.731', '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: 71060198
    {'ambient': '1296.3190', 'aut_centralizer_order': 12, 'aut_label': '6.s1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '96.230', 'aut_weyl_index': 36, 'centralizer': '36.cr1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1', '3.d1.a1'], 'contains': ['12.b1.a1', '12.br1.a1', '12.bs1.a1', '18.m1.a1', '18.w1.a1', '18.x1.a1', '18.y1.a1'], 'core': '12.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [1910, -1, 8240, -1, 1478, -1, 7668, -1], 'generators': [3, 12, 216, 108, 2, 144], 'label': '1296.3190.6.s1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.d1.a1', 'old_label': '6.s1.a1', 'projective_image': '216.162', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.s1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 71060199
    {'ambient': '1296.3190', 'aut_centralizer_order': 8, 'aut_label': '54.h1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '24.14', 'aut_weyl_index': 144, 'centralizer': '108.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.j1.a1', '18.k1.a1', '18.v1.a1'], 'contains': ['108.i1.a1', '108.bc1.a1', '108.bh1.a1', '108.cf1.a1', '108.cf1.a2', '108.cf1.b1', '108.cf1.b2', '162.b1.a1'], 'core': '648.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [6763, -1, 5426, -1, 8071, -1, 4790, -1], 'generators': [3, 54, 216, 576], 'label': '1296.3190.54.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.j1.a1', 'old_label': '54.h1.a1', 'projective_image': '648.731', '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': '6.1'}
  • id: 71060200
    {'ambient': '1296.3190', 'aut_centralizer_order': 48, 'aut_label': '54.i1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '8.5', 'aut_weyl_index': 432, 'centralizer': '18.m1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.l1.a1', '18.m1.a1', '18.w1.a1', '27.a1.a1'], 'contains': ['108.d1.a1', '108.bl1.a1', '108.bm1.a1', '162.c1.a1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [1566, -1, 8362, -1, 1263, -1, 8932, -1], 'generators': [3, 108, 2, 216], 'label': '1296.3190.54.i1.a1', 'mobius_quo': None, 'mobius_sub': 3, 'normal_closure': '6.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1.a1', 'old_label': '54.i1.a1', 'projective_image': '216.162', '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': '2.1'}
  • id: 71060201
    {'ambient': '1296.3190', 'aut_centralizer_order': 48, 'aut_label': '54.j1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '24.14', 'aut_weyl_index': 144, 'centralizer': '36.n1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.b1.a1', '18.l1.a1', '18.n1.a1', '18.o1.a1', '27.b1.a1'], 'contains': ['108.c1.a1', '108.e1.a1', '108.bn1.a1', '162.c1.a1'], 'core': '108.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [1063, -1, 9521, -1, 1140, -1, 8984, -1], 'generators': [3, 108, 216, 432], 'label': '1296.3190.54.j1.a1', 'mobius_quo': None, 'mobius_sub': 3, 'normal_closure': '18.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '54.j1.a1', 'projective_image': '648.731', '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': '12.4'}
  • id: 71060202
    {'ambient': '1296.3190', 'aut_centralizer_order': 48, 'aut_label': '54.k1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '8.5', 'aut_weyl_index': 432, 'centralizer': '18.m1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.m1.a1', '18.n1.a1', '18.x1.a1', '27.c1.a1'], 'contains': ['108.f1.a1', '108.bo1.a1', '108.bp1.a1', '162.c1.a1'], 'core': '216.c1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [987, -1, 9171, -1, 1202, -1, 8736, -1], 'generators': [3, 108, 144, 216], 'label': '1296.3190.54.k1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '6.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1.a1', 'old_label': '54.k1.a1', 'projective_image': '648.731', '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': '2.1'}
  • id: 71060203
    {'ambient': '1296.3190', 'aut_centralizer_order': 24, 'aut_label': '54.l1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '8.5', 'aut_weyl_index': 432, 'centralizer': '18.m1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.m1.a1', '18.o1.a1', '18.y1.a1'], 'contains': ['108.h1.a1', '108.bs1.a1', '108.bt1.a1', '162.c1.a1'], 'core': '648.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [516, -1, 9832, -1, 397, -1, 9379, -1], 'generators': [3, 108, 146, 216], 'label': '1296.3190.54.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.m1.a1', 'old_label': '54.l1.a1', 'projective_image': '648.731', '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': '1.1'}
  • id: 71060204
    {'ambient': '1296.3190', 'aut_centralizer_order': 48, 'aut_label': '54.m1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '24.14', 'aut_weyl_index': 144, 'centralizer': '36.x1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.a1.a1', '18.p1.a1', '18.q1.a1', '18.r1.a1', '27.d1.a1'], 'contains': ['108.a1.a1', '108.m1.a1', '108.v1.a1', '108.cg1.a1', '108.cg1.b1', '162.a1.a1'], 'core': '108.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5999, -1, 4152, -1, 6777, -1, 1557, -1], 'generators': [3, 18, 216, 12], 'label': '1296.3190.54.m1.a1', 'mobius_quo': None, 'mobius_sub': 3, 'normal_closure': '18.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1.a1', 'old_label': '54.m1.a1', 'projective_image': '648.731', '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': '12.4'}
  • id: 71060205
    {'ambient': '1296.3190', 'aut_centralizer_order': 16, 'aut_label': '54.n1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '24.14', 'aut_weyl_index': 144, 'centralizer': '108.x1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.s1.a1', '18.t1.a1', '18.u1.a1', '18.v1.a1', '27.d1.a1'], 'contains': ['108.a1.a1', '108.y1.a1', '108.bg1.a1', '108.ch1.a1', '108.ch1.b1', '162.b1.a1'], 'core': '108.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [6721, -1, 5301, -1, 7667, -1, 4388, -1], 'generators': [3, 54, 216, 12], 'label': '1296.3190.54.n1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '6.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.d1.a1', 'old_label': '54.n1.a1', 'projective_image': '648.731', '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': '12.4'}
  • id: 71060206
    {'ambient': '1296.3190', 'aut_centralizer_order': 48, 'aut_label': '54.o1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '24.14', 'aut_weyl_index': 144, 'centralizer': '36.cr1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.b1.a1', '18.w1.a1', '18.x1.a1', '18.y1.a1', '27.d1.a1'], 'contains': ['108.a1.a1', '108.bq1.a1', '108.br1.a1', '162.c1.a1'], 'core': '108.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [1770, -1, 8998, -1, 1319, -1, 7559, -1], 'generators': [3, 108, 216, 12], 'label': '1296.3190.54.o1.a1', 'mobius_quo': None, 'mobius_sub': 3, 'normal_closure': '18.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.d1.a1', 'old_label': '54.o1.a1', 'projective_image': '648.731', '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': '12.4'}
  • id: 71060207
    {'ambient': '1296.3190', 'aut_centralizer_order': 48, 'aut_label': '54.p1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '8.5', 'aut_weyl_index': 432, 'centralizer': '36.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.z1.a1', '18.ba1.a1', '18.bh1.a1', '27.a1.a1'], 'contains': ['108.k1.a1', '108.x1.a1', '108.bl1.a1', '162.d1.a1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [2211, -1, 7599, -1, 4188, -1, 8042, -1], 'generators': [18, 108, 2, 216], 'label': '1296.3190.54.p1.a1', 'mobius_quo': None, 'mobius_sub': 3, 'normal_closure': '6.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.d1.a1', 'old_label': '54.p1.a1', 'projective_image': '216.162', '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': '4.2'}
  • id: 71060208
    {'ambient': '1296.3190', 'aut_centralizer_order': 48, 'aut_label': '54.q1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '8.5', 'aut_weyl_index': 432, 'centralizer': '72.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.z1.a1', '18.bb1.a1', '18.bi1.a1', '27.d1.a1'], 'contains': ['108.m1.a1', '108.y1.a1', '108.bq1.a1', '162.d1.a1'], 'core': '216.d1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [3996, -1, 5837, -1, 4547, -1, 6081, -1], 'generators': [18, 108, 12, 216], 'label': '1296.3190.54.q1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '6.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.d1.a1', 'old_label': '54.q1.a1', 'projective_image': '648.731', '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': '8.5'}
  • id: 71060209
    {'ambient': '1296.3190', 'aut_centralizer_order': 6, 'aut_label': '6.t1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '288.1040', 'aut_weyl_index': 12, 'centralizer': '72.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1'], 'contains': ['12.s1.a1', '12.bv1.a1', '12.bw1.a1', '18.b1.a1', '18.o1.a1', '18.y1.a1'], 'core': '18.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1635, -1, 9679, -1, 831, -1, 8147, -1], 'generators': [3, 432, 12, 108, 146, 216], 'label': '1296.3190.6.t1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '6.t1.a1', 'projective_image': '648.731', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.t1.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 71060210
    {'ambient': '1296.3190', 'aut_centralizer_order': 24, 'aut_label': '54.r1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '8.5', 'aut_weyl_index': 432, 'centralizer': '72.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.z1.a1', '18.bc1.a1', '18.bj1.a1'], 'contains': ['108.o1.a1', '108.z1.a1', '108.bu1.a1', '162.d1.a1'], 'core': '648.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [33, -1, 6364, -1, 2968, -1, 8085, -1], 'generators': [18, 108, 14, 216], 'label': '1296.3190.54.r1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.z1.a1', 'old_label': '54.r1.a1', 'projective_image': '648.731', '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: 71060211
    {'ambient': '1296.3190', 'aut_centralizer_order': 48, 'aut_label': '54.s1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '24.14', 'aut_weyl_index': 144, 'centralizer': '36.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.c1.a1', '18.ba1.a1', '18.bb1.a1', '18.bc1.a1', '27.b1.a1'], 'contains': ['108.c1.a1', '108.l1.a1', '108.ba1.a1', '162.d1.a1'], 'core': '108.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [1812, -1, 7460, -1, 3974, -1, 7523, -1], 'generators': [18, 108, 216, 432], 'label': '1296.3190.54.s1.a1', 'mobius_quo': None, 'mobius_sub': 3, 'normal_closure': '18.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1.a1', 'old_label': '54.s1.a1', 'projective_image': '648.731', '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: 71060212
    {'ambient': '1296.3190', 'aut_centralizer_order': 16, 'aut_label': '54.t1', 'aut_quo_index': None, 'aut_stab_index': 27, 'aut_weyl_group': '8.5', 'aut_weyl_index': 432, 'centralizer': '108.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.bd1.a1', '18.be1.a1', '18.bf1.a1', '18.bk1.a1', '27.a1.a1'], 'contains': ['108.k1.a1', '108.bd1.a1', '108.bm1.a1', '162.e1.a1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [4335, -1, 7810, -1, 3172, -1, 8259, -1], 'generators': [111, 18, 2, 216], 'label': '1296.3190.54.t1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1.a1', 'old_label': '54.t1.a1', 'projective_image': '216.162', '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: 71060213
    {'ambient': '1296.3190', 'aut_centralizer_order': 16, 'aut_label': '54.u1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '24.14', 'aut_weyl_index': 144, 'centralizer': '108.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.bd1.a1', '18.bg1.a1', '18.bl1.a1', '27.b1.a1'], 'contains': ['108.l1.a1', '108.be1.a1', '108.bn1.a1', '162.e1.a1'], 'core': '216.b1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [3892, -1, 7691, -1, 3215, -1, 7494, -1], 'generators': [111, 18, 216, 432], 'label': '1296.3190.54.u1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '6.h1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '54.u1.a1', 'projective_image': '648.731', '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: 71060214
    {'ambient': '1296.3190', 'aut_centralizer_order': 16, 'aut_label': '54.v1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '24.14', 'aut_weyl_index': 144, 'centralizer': '216.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.be1.a1', '18.bg1.a1', '18.bm1.a1', '27.d1.a1'], 'contains': ['108.m1.a1', '108.bg1.a1', '108.br1.a1', '162.e1.a1'], 'core': '216.d1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [5306, -1, 6489, -1, 3283, -1, 6117, -1], 'generators': [111, 18, 216, 12], 'label': '1296.3190.54.v1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '6.h1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.d1.a1', 'old_label': '54.v1.a1', 'projective_image': '648.731', '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: 71060215
    {'ambient': '1296.3190', 'aut_centralizer_order': 8, 'aut_label': '54.w1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '24.14', 'aut_weyl_index': 144, 'centralizer': '216.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.bf1.a1', '18.bg1.a1', '18.bn1.a1'], 'contains': ['108.p1.a1', '108.bi1.a1', '108.bv1.a1', '162.e1.a1'], 'core': '648.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [148, -1, 7727, -1, 2284, -1, 9182, -1], 'generators': [111, 18, 216, 444], 'label': '1296.3190.54.w1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.h1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bf1.a1', 'old_label': '54.w1.a1', 'projective_image': '648.731', '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: 71060216
    {'ambient': '1296.3190', 'aut_centralizer_order': 48, 'aut_label': '54.x1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '24.14', 'aut_weyl_index': 144, 'centralizer': '36.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.c1.a1', '18.bh1.a1', '18.bi1.a1', '18.bj1.a1', '27.c1.a1'], 'contains': ['108.b1.a1', '108.bb1.a1', '108.bo1.a1', '162.d1.a1'], 'core': '108.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [1191, -1, 7921, -1, 3820, -1, 7438, -1], 'generators': [18, 108, 216, 144], 'label': '1296.3190.54.x1.a1', 'mobius_quo': None, 'mobius_sub': 3, 'normal_closure': '18.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.d1.a1', 'old_label': '54.x1.a1', 'projective_image': '648.731', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.x1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 71060217
    {'ambient': '1296.3190', 'aut_centralizer_order': 16, 'aut_label': '54.y1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '24.14', 'aut_weyl_index': 144, 'centralizer': '108.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.bk1.a1', '18.bl1.a1', '18.bm1.a1', '18.bn1.a1', '27.c1.a1'], 'contains': ['108.b1.a1', '108.bf1.a1', '108.bp1.a1', '162.e1.a1'], 'core': '108.b1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [3026, -1, 8472, -1, 3130, -1, 7466, -1], 'generators': [111, 18, 216, 144], 'label': '1296.3190.54.y1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '6.h1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1.a1', 'old_label': '54.y1.a1', 'projective_image': '648.731', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.y1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 71060218
    {'ambient': '1296.3190', 'aut_centralizer_order': 16, 'aut_label': '54.z1', 'aut_quo_index': None, 'aut_stab_index': 27, 'aut_weyl_group': '8.5', 'aut_weyl_index': 432, 'centralizer': '108.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.bo1.a1', '18.bq1.a1', '18.br1.a1', '27.a1.a1'], 'contains': ['108.r1.a1', '108.x1.a1', '108.bm1.a1', '162.f1.a1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [4529, -1, 7384, -1, 5559, -1, 6981, -1], 'generators': [111, 54, 2, 216], 'label': '1296.3190.54.z1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1.a1', 'old_label': '54.z1.a1', 'projective_image': '216.162', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.z1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 71060219
    {'ambient': '1296.3190', 'aut_centralizer_order': 16, 'aut_label': '54.ba1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '24.14', 'aut_weyl_index': 144, 'centralizer': '108.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.bo1.a1', '18.bs1.a1', '18.bt1.a1', '27.b1.a1'], 'contains': ['108.s1.a1', '108.ba1.a1', '108.bn1.a1', '162.f1.a1'], 'core': '216.b1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [4658, -1, 7351, -1, 5516, -1, 6896, -1], 'generators': [111, 54, 216, 432], 'label': '1296.3190.54.ba1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '6.i1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '54.ba1.a1', 'projective_image': '648.731', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.ba1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 71060220
    {'ambient': '1296.3190', 'aut_centralizer_order': 12, 'aut_label': '6.u1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '96.230', 'aut_weyl_index': 36, 'centralizer': '72.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.d1.a1', '3.c1.a1'], 'contains': ['12.m1.a1', '12.v1.a1', '12.be1.a1', '18.z1.a1', '18.ba1.a1', '18.bb1.a1', '18.bc1.a1'], 'core': '12.m1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3400, -1, 5971, -1, 4434, -1, 7030, -1], 'generators': [18, 432, 216, 108, 2, 12], 'label': '1296.3190.6.u1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1.a1', 'old_label': '6.u1.a1', 'projective_image': '216.162', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.u1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 71060221
    {'ambient': '1296.3190', 'aut_centralizer_order': 16, 'aut_label': '54.bb1', 'aut_quo_index': None, 'aut_stab_index': 27, 'aut_weyl_group': '8.5', 'aut_weyl_index': 432, 'centralizer': '108.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.bp1.a1', '18.bu1.a1', '18.bv1.a1', '18.bw1.a1', '27.a1.a1'], 'contains': ['108.r1.a1', '108.bd1.a1', '108.bl1.a1', '162.g1.a1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [3861, -1, 8623, -1, 3054, -1, 8636, -1], 'generators': [9, 108, 2, 216], 'label': '1296.3190.54.bb1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1.a1', 'old_label': '54.bb1.a1', 'projective_image': '216.162', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.bb1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 71060222
    {'ambient': '1296.3190', 'aut_centralizer_order': 16, 'aut_label': '54.bc1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '24.14', 'aut_weyl_index': 144, 'centralizer': '108.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.bp1.a1', '18.bx1.a1', '18.by1.a1', '18.bz1.a1', '27.b1.a1'], 'contains': ['108.c1.a1', '108.s1.a1', '108.be1.a1', '162.g1.a1'], 'core': '108.c1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [3102, -1, 8924, -1, 3011, -1, 8223, -1], 'generators': [9, 108, 216, 432], 'label': '1296.3190.54.bc1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '6.j1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '54.bc1.a1', 'projective_image': '648.731', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.bc1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 71060223
    {'ambient': '1296.3190', 'aut_centralizer_order': 16, 'aut_label': '54.bd1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '24.14', 'aut_weyl_index': 144, 'centralizer': '216.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.bq1.a1', '18.bs1.a1', '18.ca1.a1', '27.d1.a1'], 'contains': ['108.v1.a1', '108.y1.a1', '108.br1.a1', '162.f1.a1'], 'core': '216.d1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [5419, -1, 5794, -1, 5644, -1, 6045, -1], 'generators': [111, 54, 216, 12], 'label': '1296.3190.54.bd1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '6.i1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.d1.a1', 'old_label': '54.bd1.a1', 'projective_image': '648.731', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.bd1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 71060224
    {'ambient': '1296.3190', 'aut_centralizer_order': 16, 'aut_label': '54.be1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '24.14', 'aut_weyl_index': 144, 'centralizer': '108.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.br1.a1', '18.bt1.a1', '18.ca1.a1', '27.c1.a1'], 'contains': ['108.u1.a1', '108.bb1.a1', '108.bp1.a1', '162.f1.a1'], 'core': '216.c1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [4602, -1, 7973, -1, 5482, -1, 6867, -1], 'generators': [111, 54, 216, 144], 'label': '1296.3190.54.be1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '6.i1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1.a1', 'old_label': '54.be1.a1', 'projective_image': '648.731', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.be1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 71060225
    {'ambient': '1296.3190', 'aut_centralizer_order': 16, 'aut_label': '54.bf1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '24.14', 'aut_weyl_index': 144, 'centralizer': '108.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.bu1.a1', '18.bx1.a1', '18.cb1.a1', '27.c1.a1'], 'contains': ['108.u1.a1', '108.bf1.a1', '108.bo1.a1', '162.g1.a1'], 'core': '216.c1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [2907, -1, 8590, -1, 3096, -1, 7410, -1], 'generators': [9, 108, 216, 144], 'label': '1296.3190.54.bf1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '6.j1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1.a1', 'old_label': '54.bf1.a1', 'projective_image': '648.731', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.bf1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 71060226
    {'ambient': '1296.3190', 'aut_centralizer_order': 16, 'aut_label': '54.bg1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '24.14', 'aut_weyl_index': 144, 'centralizer': '216.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.bv1.a1', '18.by1.a1', '18.cb1.a1', '27.d1.a1'], 'contains': ['108.v1.a1', '108.bg1.a1', '108.bq1.a1', '162.g1.a1'], 'core': '216.d1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [5331, -1, 7860, -1, 3249, -1, 6230, -1], 'generators': [9, 108, 216, 12], 'label': '1296.3190.54.bg1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '6.j1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.d1.a1', 'old_label': '54.bg1.a1', 'projective_image': '648.731', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.bg1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 71060227
    {'ambient': '1296.3190', 'aut_centralizer_order': 8, 'aut_label': '54.bh1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '24.14', 'aut_weyl_index': 144, 'centralizer': '216.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.bw1.a1', '18.bz1.a1', '18.cb1.a1'], 'contains': ['108.w1.a1', '108.bj1.a1', '108.bw1.a1', '162.g1.a1'], 'core': '648.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [2149, -1, 9615, -1, 2073, -1, 9471, -1], 'generators': [9, 108, 216, 156], 'label': '1296.3190.54.bh1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.j1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bw1.a1', 'old_label': '54.bh1.a1', 'projective_image': '648.731', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.bh1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 71060228
    {'ambient': '1296.3190', 'aut_centralizer_order': 864, 'aut_label': '72.a1', 'aut_quo_index': 8, 'aut_stab_index': 1, 'aut_weyl_group': '4.2', 'aut_weyl_index': 864, 'centralizer': '2.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['24.a1.a1', '24.b1.a1', '24.h1.a1', '36.i1.a1', '36.m1.a1', '36.x1.a1', '36.bi1.a1', '36.bt1.a1', '36.cc1.a1', '36.cq1.a1'], 'contains': ['144.a1.a1', '216.a1.a1', '216.b1.a1', '216.f1.a1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4064, 3585, 7538, 7447, 3770, 5683, 6327, 6302], 'generators': [216, 2, 432], 'label': '1296.3190.72.a1.a1', 'mobius_quo': -1, 'mobius_sub': -72, 'normal_closure': '72.a1.a1', 'normal_contained_in': ['24.a1.a1', '24.b1.a1', '36.i1.a1'], 'normal_contains': ['144.a1.a1', '216.a1.a1', '216.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '72.a1.a1', 'projective_image': '216.162', 'quotient_action_image': '2.1', 'quotient_action_kernel': '36.10', 'quotient_action_kernel_order': 36, 'quotient_fusion': None, 'short_label': '72.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 71060229
    {'ambient': '1296.3190', 'aut_centralizer_order': 864, 'aut_label': '72.b1', 'aut_quo_index': 8, 'aut_stab_index': 1, 'aut_weyl_group': '4.2', 'aut_weyl_index': 864, 'centralizer': '2.c1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['24.a1.a1', '24.c1.a1', '24.i1.a1', '36.d1.a1', '36.n1.a1', '36.bj1.a1', '36.bu1.a1', '36.cd1.a1', '36.cr1.a1', '36.cs1.a1'], 'contains': ['144.b1.a1', '216.a1.a1', '216.c1.a1', '216.g1.a1'], 'core': '72.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3609, 4342, 8253, 5625, 3475, 4916, 6455, 5429], 'generators': [216, 2, 144], 'label': '1296.3190.72.b1.a1', 'mobius_quo': -1, 'mobius_sub': -72, 'normal_closure': '72.b1.a1', 'normal_contained_in': ['24.a1.a1', '24.c1.a1', '36.d1.a1'], 'normal_contains': ['144.b1.a1', '216.a1.a1', '216.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '72.b1.a1', 'projective_image': '216.162', 'quotient_action_image': '2.1', 'quotient_action_kernel': '36.10', 'quotient_action_kernel_order': 36, 'quotient_fusion': None, 'short_label': '72.b1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 71060230
    {'ambient': '1296.3190', 'aut_centralizer_order': 864, 'aut_label': '72.c1', 'aut_quo_index': 8, 'aut_stab_index': 1, 'aut_weyl_group': '4.2', 'aut_weyl_index': 864, 'centralizer': '2.d1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['24.b1.a1', '24.c1.a1', '24.j1.a1', '36.a1.a1', '36.y1.a1', '36.bk1.a1', '36.bs1.a1', '36.ce1.a1', '36.ct1.a1', '36.cu1.a1'], 'contains': ['144.c1.a1', '216.a1.a1', '216.d1.a1', '216.h1.a1'], 'core': '72.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5011, 6415, 6250, 4444, 4461, 3404, 6025, 4531], 'generators': [216, 2, 12], 'label': '1296.3190.72.c1.a1', 'mobius_quo': -1, 'mobius_sub': -72, 'normal_closure': '72.c1.a1', 'normal_contained_in': ['24.c1.a1', '24.b1.a1', '36.a1.a1'], 'normal_contains': ['144.c1.a1', '216.a1.a1', '216.d1.a1'], 'normalizer': '1.a1.a1', 'old_label': '72.c1.a1', 'projective_image': '216.162', 'quotient_action_image': '2.1', 'quotient_action_kernel': '36.10', 'quotient_action_kernel_order': 36, 'quotient_fusion': None, 'short_label': '72.c1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 71060231
    {'ambient': '1296.3190', 'aut_centralizer_order': 4, 'aut_label': '6.v1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '288.1040', 'aut_weyl_index': 12, 'centralizer': '216.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.e1.a1', '3.c1.a1'], 'contains': ['12.n1.a1', '12.v1.a1', '12.bj1.a1', '18.bd1.a1', '18.be1.a1', '18.bf1.a1', '18.bg1.a1'], 'core': '12.n1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4385, -1, 6413, -1, 3501, -1, 6576, -1], 'generators': [111, 432, 12, 18, 2, 216], 'label': '1296.3190.6.v1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1.a1', 'old_label': '6.v1.a1', 'projective_image': '216.162', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.v1.a1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 71060232
    {'ambient': '1296.3190', 'aut_centralizer_order': 864, 'aut_label': '72.d1', 'aut_quo_index': 24, 'aut_stab_index': 1, 'aut_weyl_group': '4.2', 'aut_weyl_index': 864, 'centralizer': '4.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['24.a1.a1', '24.d1.a1', '24.l1.a1', '36.e1.a1', '36.h1.a1', '36.j1.a1', '36.p1.a1', '36.bm1.a1', '36.cj1.a1', '36.cx1.a1'], 'contains': ['144.d1.a1', '216.b1.a1', '216.c1.a1', '216.i1.a1'], 'core': '72.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4414, 3963, 7841, 7092, 3681, 6291, 6284, 5957], 'generators': [216, 144, 432], 'label': '1296.3190.72.d1.a1', 'mobius_quo': -1, 'mobius_sub': -24, 'normal_closure': '72.d1.a1', 'normal_contained_in': ['24.a1.a1', '24.d1.a1', '36.e1.a1', '36.h1.a1', '36.j1.a1'], 'normal_contains': ['144.d1.a1', '216.b1.a1', '216.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '72.d1.a1', 'projective_image': '648.731', 'quotient_action_image': '4.2', 'quotient_action_kernel': '18.3', 'quotient_action_kernel_order': 18, 'quotient_fusion': None, 'short_label': '72.d1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 71060233
    {'ambient': '1296.3190', 'aut_centralizer_order': 864, 'aut_label': '72.e1', 'aut_quo_index': 24, 'aut_stab_index': 1, 'aut_weyl_group': '4.2', 'aut_weyl_index': 864, 'centralizer': '4.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['24.b1.a1', '24.d1.a1', '24.m1.a1', '36.b1.a1', '36.k1.a1', '36.l1.a1', '36.ba1.a1', '36.bn1.a1', '36.bw1.a1', '36.ck1.a1'], 'contains': ['144.e1.a1', '216.b1.a1', '216.d1.a1', '216.j1.a1'], 'core': '72.e1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4866, 5507, 7207, 4801, 3821, 4557, 6113, 4876], 'generators': [216, 12, 432], 'label': '1296.3190.72.e1.a1', 'mobius_quo': -1, 'mobius_sub': -24, 'normal_closure': '72.e1.a1', 'normal_contained_in': ['24.b1.a1', '24.d1.a1', '36.b1.a1', '36.k1.a1', '36.l1.a1'], 'normal_contains': ['144.e1.a1', '216.b1.a1', '216.d1.a1'], 'normalizer': '1.a1.a1', 'old_label': '72.e1.a1', 'projective_image': '648.731', 'quotient_action_image': '4.2', 'quotient_action_kernel': '18.3', 'quotient_action_kernel_order': 18, 'quotient_fusion': None, 'short_label': '72.e1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 71060234
    {'ambient': '1296.3190', 'aut_centralizer_order': 864, 'aut_label': '72.f1', 'aut_quo_index': 24, 'aut_stab_index': 1, 'aut_weyl_group': '4.2', 'aut_weyl_index': 864, 'centralizer': '4.f1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['24.c1.a1', '24.d1.a1', '24.o1.a1', '36.c1.a1', '36.f1.a1', '36.g1.a1', '36.by1.a1', '36.cm1.a1', '36.dd1.a1', '36.de1.a1'], 'contains': ['144.f1.a1', '216.c1.a1', '216.d1.a1', '216.k1.a1'], 'core': '72.f1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4499, 6900, 6454, 4089, 4025, 3980, 5837, 4185], 'generators': [216, 12, 144], 'label': '1296.3190.72.f1.a1', 'mobius_quo': -1, 'mobius_sub': -24, 'normal_closure': '72.f1.a1', 'normal_contained_in': ['24.c1.a1', '24.d1.a1', '36.c1.a1', '36.f1.a1', '36.g1.a1'], 'normal_contains': ['144.f1.a1', '216.c1.a1', '216.d1.a1'], 'normalizer': '1.a1.a1', 'old_label': '72.f1.a1', 'projective_image': '648.731', 'quotient_action_image': '4.2', 'quotient_action_kernel': '18.3', 'quotient_action_kernel_order': 18, 'quotient_fusion': None, 'short_label': '72.f1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 71060235
    {'ambient': '1296.3190', 'aut_centralizer_order': 144, 'aut_label': '72.g1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '12.4', 'aut_weyl_index': 288, 'centralizer': '6.f1.a1', 'complements': ['18.c1.a1', '18.bx1.a1', '18.bz1.a1', '18.bl1.a1', '18.bn1.a1', '18.bt1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['24.e1.a1', '24.f1.a1', '24.t1.a1', '36.a1.a1', '36.dt1.a1', '36.dx1.a1'], 'contains': ['144.c1.a1', '216.e1.a1', '216.q1.a1'], 'core': '72.g1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [9541, 8347, 1211, 2731, 8963, 1607, 2209, 2345], 'generators': [3, 2, 12], 'label': '1296.3190.72.g1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '72.g1.a1', 'normal_contained_in': ['24.f1.a1', '24.e1.a1', '36.a1.a1'], 'normal_contains': ['144.c1.a1', '216.e1.a1'], 'normalizer': '1.a1.a1', 'old_label': '72.g1.a1', 'projective_image': '432.598', 'quotient_action_image': '1.1', 'quotient_action_kernel': '72.23', 'quotient_action_kernel_order': 72, 'quotient_fusion': None, 'short_label': '72.g1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 71060236
    {'ambient': '1296.3190', 'aut_centralizer_order': 144, 'aut_label': '72.g1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '12.4', 'aut_weyl_index': 288, 'centralizer': '6.f1.a1', 'complements': ['18.c1.a1', '18.bx1.a1', '18.bz1.a1', '18.bl1.a1', '18.bn1.a1', '18.bt1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['24.e1.b1', '24.f1.b1', '24.t1.b1', '36.a1.a1', '36.dt1.b1', '36.dx1.b1'], 'contains': ['144.c1.a1', '216.e1.b1', '216.q1.b1'], 'core': '72.g1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [9541, 8347, 1792, 2023, 8963, 1607, 2678, 2002], 'generators': [219, 2, 12], 'label': '1296.3190.72.g1.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '72.g1.b1', 'normal_contained_in': ['24.f1.b1', '24.e1.b1', '36.a1.a1'], 'normal_contains': ['144.c1.a1', '216.e1.b1'], 'normalizer': '1.a1.a1', 'old_label': '72.g1.b1', 'projective_image': '432.598', 'quotient_action_image': '1.1', 'quotient_action_kernel': '72.23', 'quotient_action_kernel_order': 72, 'quotient_fusion': None, 'short_label': '72.g1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 71060237
    {'ambient': '1296.3190', 'aut_centralizer_order': 144, 'aut_label': '72.h1', 'aut_quo_index': 2, 'aut_stab_index': 2, 'aut_weyl_group': '12.4', 'aut_weyl_index': 288, 'centralizer': '12.d1.a1', 'complements': ['18.bh1.a1', '18.bj1.a1', '18.bu1.a1', '18.bw1.a1', '18.bk1.a1', '18.br1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['24.e1.a1', '24.g1.a1', '24.u1.a1', '36.b1.a1', '36.du1.a1', '36.dy1.a1'], 'contains': ['144.e1.a1', '216.e1.a1', '216.r1.a1'], 'core': '72.h1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [9305, 7862, 2210, 2376, 8710, 2654, 1842, 3216], 'generators': [3, 432, 12], 'label': '1296.3190.72.h1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '72.h1.a1', 'normal_contained_in': ['24.e1.a1', '24.g1.a1', '36.b1.a1'], 'normal_contains': ['144.e1.a1', '216.e1.a1'], 'normalizer': '1.a1.a1', 'old_label': '72.h1.a1', 'projective_image': '1296.3190', 'quotient_action_image': '2.1', 'quotient_action_kernel': '36.12', 'quotient_action_kernel_order': 36, 'quotient_fusion': None, 'short_label': '72.h1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 71060238
    {'ambient': '1296.3190', 'aut_centralizer_order': 144, 'aut_label': '72.h1', 'aut_quo_index': 2, 'aut_stab_index': 2, 'aut_weyl_group': '12.4', 'aut_weyl_index': 288, 'centralizer': '12.d1.a1', 'complements': ['18.bh1.a1', '18.bj1.a1', '18.bu1.a1', '18.bw1.a1', '18.bk1.a1', '18.br1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['24.e1.b1', '24.g1.b1', '24.u1.b1', '36.b1.a1', '36.du1.b1', '36.dy1.b1'], 'contains': ['144.e1.a1', '216.e1.b1', '216.r1.b1'], 'core': '72.h1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [9305, 7862, 2627, 1466, 8710, 2654, 2593, 2688], 'generators': [219, 432, 12], 'label': '1296.3190.72.h1.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '72.h1.b1', 'normal_contained_in': ['24.e1.b1', '24.g1.b1', '36.b1.a1'], 'normal_contains': ['144.e1.a1', '216.e1.b1'], 'normalizer': '1.a1.a1', 'old_label': '72.h1.b1', 'projective_image': '1296.3190', 'quotient_action_image': '2.1', 'quotient_action_kernel': '36.12', 'quotient_action_kernel_order': 36, 'quotient_fusion': None, 'short_label': '72.h1.b1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 71060239
    {'ambient': '1296.3190', 'aut_centralizer_order': 144, 'aut_label': '72.i1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '12.4', 'aut_weyl_index': 288, 'centralizer': '12.l1.a1', 'complements': ['18.ba1.a1', '18.bc1.a1', '18.bp1.a1', '18.bd1.a1', '18.bf1.a1', '18.bo1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['24.f1.a1', '24.g1.a1', '24.v1.a1', '36.c1.a1', '36.dw1.a1', '36.dz1.a1'], 'contains': ['144.f1.a1', '216.e1.a1', '216.s1.a1'], 'core': '72.i1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8967, 9348, 1362, 1112, 8760, 2104, 1672, 1660], 'generators': [3, 144, 12], 'label': '1296.3190.72.i1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '72.i1.a1', 'normal_contained_in': ['24.f1.a1', '24.g1.a1', '36.c1.a1'], 'normal_contains': ['144.f1.a1', '216.e1.a1'], 'normalizer': '1.a1.a1', 'old_label': '72.i1.a1', 'projective_image': '1296.3190', 'quotient_action_image': '2.1', 'quotient_action_kernel': '36.6', 'quotient_action_kernel_order': 36, 'quotient_fusion': None, 'short_label': '72.i1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 71060240
    {'ambient': '1296.3190', 'aut_centralizer_order': 144, 'aut_label': '72.i1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '12.4', 'aut_weyl_index': 288, 'centralizer': '12.l1.a1', 'complements': ['18.ba1.a1', '18.bc1.a1', '18.bp1.a1', '18.bd1.a1', '18.bf1.a1', '18.bo1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['24.f1.b1', '24.g1.b1', '24.v1.b1', '36.c1.a1', '36.dw1.b1', '36.dz1.b1'], 'contains': ['144.f1.a1', '216.e1.b1', '216.s1.b1'], 'core': '72.i1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [8967, 9348, 2172, 542, 8760, 2104, 2123, 1317], 'generators': [219, 144, 12], 'label': '1296.3190.72.i1.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '72.i1.b1', 'normal_contained_in': ['24.f1.b1', '24.g1.b1', '36.c1.a1'], 'normal_contains': ['144.f1.a1', '216.e1.b1'], 'normalizer': '1.a1.a1', 'old_label': '72.i1.b1', 'projective_image': '1296.3190', 'quotient_action_image': '2.1', 'quotient_action_kernel': '36.6', 'quotient_action_kernel_order': 36, 'quotient_fusion': None, 'short_label': '72.i1.b1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 71060241
    {'ambient': '1296.3190', 'aut_centralizer_order': 432, 'aut_label': '72.j1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 864, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.a1.a1', '24.j1.a1', '24.k1.a1', '36.o1.a1', '36.bv1.a1', '36.cf1.a1'], 'contains': ['144.g1.a1', '216.a1.a1', '216.i1.a1', '216.l1.a1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [5078, -1, 6661, -1, 4766, -1, 6370, -1], 'generators': [216, 2, 576], 'label': '1296.3190.72.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '72.j1.a1', 'projective_image': '216.162', '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': '2.1'}
  • id: 71060242
    {'ambient': '1296.3190', 'aut_centralizer_order': 12, 'aut_label': '6.w1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '96.230', 'aut_weyl_index': 36, 'centralizer': '72.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.d1.a1', '3.d1.a1'], 'contains': ['12.e1.a1', '12.bf1.a1', '12.br1.a1', '18.z1.a1', '18.bh1.a1', '18.bi1.a1', '18.bj1.a1'], 'core': '12.e1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3349, -1, 6239, -1, 4294, -1, 6971, -1], 'generators': [18, 144, 216, 108, 2, 12], 'label': '1296.3190.6.w1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.d1.a1', 'old_label': '6.w1.a1', 'projective_image': '216.162', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.w1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 71060243
    {'ambient': '1296.3190', 'aut_centralizer_order': 432, 'aut_label': '72.k1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 864, 'centralizer': '4.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.b1.a1', '24.i1.a1', '24.k1.a1', '36.z1.a1', '36.cg1.a1', '36.cv1.a1'], 'contains': ['144.h1.a1', '216.a1.a1', '216.j1.a1', '216.m1.a1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [538, -1, 8199, -1, 2882, -1, 7248, -1], 'generators': [216, 2, 444], 'label': '1296.3190.72.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.e1.a1', 'old_label': '72.k1.a1', 'projective_image': '216.162', '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': '2.1'}
  • id: 71060244
    {'ambient': '1296.3190', 'aut_centralizer_order': 432, 'aut_label': '72.l1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 864, 'centralizer': '4.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.c1.a1', '24.h1.a1', '24.k1.a1', '36.bl1.a1', '36.ch1.a1', '36.cw1.a1'], 'contains': ['144.i1.a1', '216.a1.a1', '216.k1.a1', '216.n1.a1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2643, -1, 9266, -1, 2730, -1, 8063, -1], 'generators': [216, 2, 156], 'label': '1296.3190.72.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.g1.a1', 'old_label': '72.l1.a1', 'projective_image': '216.162', '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': '2.1'}
  • id: 71060245
    {'ambient': '1296.3190', 'aut_centralizer_order': 216, 'aut_label': '72.m1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '4.2', 'aut_weyl_index': 864, 'centralizer': '8.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.h1.a1', '24.i1.a1', '24.j1.a1', '24.k1.a1', '36.ci1.a1'], 'contains': ['144.j1.a1', '216.a1.a1', '216.o1.a1', '216.p1.a1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [1583, -1, 9026, -1, 2781, -1, 7760, -1], 'generators': [216, 2, 588], 'label': '1296.3190.72.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.e1.a1', 'old_label': '72.m1.a1', 'projective_image': '216.162', '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: 71060246
    {'ambient': '1296.3190', 'aut_centralizer_order': 432, 'aut_label': '72.n1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 864, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.a1.a1', '24.m1.a1', '24.n1.a1', '36.q1.a1', '36.cy1.a1', '36.cz1.a1'], 'contains': ['144.k1.a1', '216.b1.a1', '216.g1.a1', '216.l1.a1'], 'core': '216.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2283, -1, 9122, -1, 2170, -1, 7205, -1], 'generators': [216, 146, 432], 'label': '1296.3190.72.n1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '72.n1.a1', 'projective_image': '648.731', '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': '2.1'}
  • id: 71060247
    {'ambient': '1296.3190', 'aut_centralizer_order': 432, 'aut_label': '72.o1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 864, 'centralizer': '4.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.b1.a1', '24.l1.a1', '24.n1.a1', '36.bb1.a1', '36.bx1.a1', '36.da1.a1'], 'contains': ['144.l1.a1', '216.b1.a1', '216.h1.a1', '216.m1.a1'], 'core': '216.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [787, -1, 6939, -1, 3113, -1, 6942, -1], 'generators': [216, 14, 432], 'label': '1296.3190.72.o1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.a1', 'old_label': '72.o1.a1', 'projective_image': '648.731', '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': '2.1'}
  • id: 71060248
    {'ambient': '1296.3190', 'aut_centralizer_order': 432, 'aut_label': '72.p1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 864, 'centralizer': '8.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.d1.a1', '24.h1.a1', '24.n1.a1', '36.bo1.a1', '36.cl1.a1', '36.db1.a1'], 'contains': ['144.m1.a1', '216.b1.a1', '216.k1.a1', '216.o1.a1'], 'core': '216.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2749, -1, 9370, -1, 2679, -1, 8020, -1], 'generators': [216, 156, 432], 'label': '1296.3190.72.p1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.g1.a1', 'old_label': '72.p1.a1', 'projective_image': '648.731', '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': '4.2'}
  • id: 71060249
    {'ambient': '1296.3190', 'aut_centralizer_order': 216, 'aut_label': '72.q1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '4.2', 'aut_weyl_index': 864, 'centralizer': '8.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.h1.a1', '24.l1.a1', '24.m1.a1', '24.n1.a1', '36.dc1.a1'], 'contains': ['144.n1.a1', '216.b1.a1', '216.n1.a1', '216.p1.a1'], 'core': '216.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [2020, -1, 9181, -1, 2119, -1, 7574, -1], 'generators': [216, 158, 432], 'label': '1296.3190.72.q1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.f1.a1', 'old_label': '72.q1.a1', 'projective_image': '648.731', '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: 71060250
    {'ambient': '1296.3190', 'aut_centralizer_order': 432, 'aut_label': '72.r1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 864, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.a1.a1', '24.o1.a1', '24.p1.a1', '36.r1.a1', '36.be1.a1', '36.bp1.a1'], 'contains': ['144.o1.a1', '216.c1.a1', '216.f1.a1', '216.l1.a1'], 'core': '216.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3290, -1, 3273, -1, 4614, -1, 5231, -1], 'generators': [216, 434, 144], 'label': '1296.3190.72.r1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '72.r1.a1', 'projective_image': '648.731', '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': '2.1'}
  • id: 71060251
    {'ambient': '1296.3190', 'aut_centralizer_order': 432, 'aut_label': '72.s1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 864, 'centralizer': '4.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.c1.a1', '24.l1.a1', '24.p1.a1', '36.bf1.a1', '36.bz1.a1', '36.df1.a1'], 'contains': ['144.p1.a1', '216.c1.a1', '216.h1.a1', '216.n1.a1'], 'core': '216.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2087, -1, 6977, -1, 3062, -1, 6651, -1], 'generators': [216, 14, 144], 'label': '1296.3190.72.s1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.a1', 'old_label': '72.s1.a1', 'projective_image': '648.731', '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': '2.1'}
  • id: 71060252
    {'ambient': '1296.3190', 'aut_centralizer_order': 432, 'aut_label': '72.t1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 864, 'centralizer': '8.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.d1.a1', '24.i1.a1', '24.p1.a1', '36.bg1.a1', '36.cn1.a1', '36.dg1.a1'], 'contains': ['144.q1.a1', '216.c1.a1', '216.j1.a1', '216.o1.a1'], 'core': '216.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [709, -1, 8716, -1, 2832, -1, 7955, -1], 'generators': [216, 444, 144], 'label': '1296.3190.72.t1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.e1.a1', 'old_label': '72.t1.a1', 'projective_image': '648.731', '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': '4.2'}
  • id: 71060253
    {'ambient': '1296.3190', 'aut_centralizer_order': 6, 'aut_label': '6.x1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '288.1040', 'aut_weyl_index': 12, 'centralizer': '72.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.d1.a1'], 'contains': ['12.x1.a1', '12.bh1.a1', '12.bu1.a1', '18.c1.a1', '18.bc1.a1', '18.bj1.a1'], 'core': '18.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1567, -1, 6881, -1, 2972, -1, 7319, -1], 'generators': [18, 432, 144, 108, 14, 216], 'label': '1296.3190.6.x1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.a1', 'old_label': '6.x1.a1', 'projective_image': '648.731', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.x1.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 71060254
    {'ambient': '1296.3190', 'aut_centralizer_order': 216, 'aut_label': '72.u1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '4.2', 'aut_weyl_index': 864, 'centralizer': '8.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.i1.a1', '24.l1.a1', '24.o1.a1', '24.p1.a1', '36.bh1.a1'], 'contains': ['144.r1.a1', '216.c1.a1', '216.m1.a1', '216.p1.a1'], 'core': '216.c1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [1982, -1, 7022, -1, 3011, -1, 6586, -1], 'generators': [216, 446, 144], 'label': '1296.3190.72.u1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.a1', 'old_label': '72.u1.a1', 'projective_image': '648.731', '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': '2.1'}
  • id: 71060255
    {'ambient': '1296.3190', 'aut_centralizer_order': 432, 'aut_label': '72.v1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 864, 'centralizer': '4.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.b1.a1', '24.o1.a1', '24.q1.a1', '36.t1.a1', '36.bc1.a1', '36.bq1.a1'], 'contains': ['144.s1.a1', '216.d1.a1', '216.f1.a1', '216.m1.a1'], 'core': '216.d1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [4461, -1, 2913, -1, 4715, -1, 4685, -1], 'generators': [216, 434, 12], 'label': '1296.3190.72.v1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '72.v1.a1', 'projective_image': '648.731', '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': '2.1'}
  • id: 71060256
    {'ambient': '1296.3190', 'aut_centralizer_order': 432, 'aut_label': '72.w1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 864, 'centralizer': '4.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.c1.a1', '24.m1.a1', '24.q1.a1', '36.u1.a1', '36.dh1.a1', '36.di1.a1'], 'contains': ['144.t1.a1', '216.d1.a1', '216.g1.a1', '216.n1.a1'], 'core': '216.d1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3061, -1, 8661, -1, 2323, -1, 6520, -1], 'generators': [216, 146, 12], 'label': '1296.3190.72.w1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '72.w1.a1', 'projective_image': '648.731', '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': '2.1'}
  • id: 71060257
    {'ambient': '1296.3190', 'aut_centralizer_order': 432, 'aut_label': '72.x1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 864, 'centralizer': '8.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.d1.a1', '24.j1.a1', '24.q1.a1', '36.v1.a1', '36.ca1.a1', '36.co1.a1'], 'contains': ['144.u1.a1', '216.d1.a1', '216.i1.a1', '216.o1.a1'], 'core': '216.d1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [5790, -1, 5045, -1, 4817, -1, 6241, -1], 'generators': [216, 12, 576], 'label': '1296.3190.72.x1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '72.x1.a1', 'projective_image': '648.731', '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': '4.2'}
  • id: 71060258
    {'ambient': '1296.3190', 'aut_centralizer_order': 216, 'aut_label': '72.y1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '4.2', 'aut_weyl_index': 864, 'centralizer': '8.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.j1.a1', '24.m1.a1', '24.o1.a1', '24.q1.a1', '36.w1.a1'], 'contains': ['144.v1.a1', '216.d1.a1', '216.l1.a1', '216.p1.a1'], 'core': '216.d1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [3943, -1, 3302, -1, 4563, -1, 5983, -1], 'generators': [216, 578, 12], 'label': '1296.3190.72.y1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '72.y1.a1', 'projective_image': '648.731', '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': '2.1'}
  • id: 71060259
    {'ambient': '1296.3190', 'aut_centralizer_order': 432, 'aut_label': '72.z1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1728, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.a1.a1', '24.q1.a1', '24.r1.a1', '36.s1.a1'], 'contains': ['144.w1.a1', '216.f1.a1', '216.g1.a1', '216.i1.a1', '216.l1.a1'], 'core': '648.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [3202, -1, 5415, -1, 3923, -1, 6199, -1], 'generators': [216, 434, 576], 'label': '1296.3190.72.z1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '72.z1.a1', 'projective_image': '648.731', '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': '1.1'}
  • id: 71060260
    {'ambient': '1296.3190', 'aut_centralizer_order': 432, 'aut_label': '72.ba1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1728, 'centralizer': '4.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.b1.a1', '24.p1.a1', '24.r1.a1', '36.bd1.a1'], 'contains': ['144.x1.a1', '216.f1.a1', '216.h1.a1', '216.j1.a1', '216.m1.a1'], 'core': '648.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [586, -1, 6810, -1, 2933, -1, 6814, -1], 'generators': [216, 434, 444], 'label': '1296.3190.72.ba1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.a1', 'old_label': '72.ba1.a1', 'projective_image': '648.731', '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': '1.1'}
  • id: 71060261
    {'ambient': '1296.3190', 'aut_centralizer_order': 216, 'aut_label': '72.bb1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '4.2', 'aut_weyl_index': 864, 'centralizer': '8.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.h1.a1', '24.o1.a1', '24.r1.a1', '36.br1.a1'], 'contains': ['144.y1.a1', '216.f1.a1', '216.k1.a1', '216.p1.a1'], 'core': '648.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [2245, -1, 6630, -1, 3424, -1, 6856, -1], 'generators': [216, 434, 156], 'label': '1296.3190.72.bb1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1.a1', 'old_label': '72.bb1.a1', 'projective_image': '648.731', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bb1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 71060262
    {'ambient': '1296.3190', 'aut_centralizer_order': 216, 'aut_label': '72.bc1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1728, 'centralizer': '8.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.h1.a1', '24.p1.a1', '24.q1.a1', '24.r1.a1'], 'contains': ['144.z1.a1', '216.f1.a1', '216.n1.a1', '216.o1.a1', '216.p1.a1'], 'core': '648.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [1365, -1, 7123, -1, 2475, -1, 7419, -1], 'generators': [216, 434, 588], 'label': '1296.3190.72.bc1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.a1.a1', 'old_label': '72.bc1.a1', 'projective_image': '648.731', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bc1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 71060263
    {'ambient': '1296.3190', 'aut_centralizer_order': 432, 'aut_label': '72.bd1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1728, 'centralizer': '4.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.c1.a1', '24.n1.a1', '24.r1.a1', '36.dj1.a1'], 'contains': ['144.ba1.a1', '216.g1.a1', '216.h1.a1', '216.k1.a1', '216.n1.a1'], 'core': '648.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [1650, -1, 8128, -1, 2068, -1, 7803, -1], 'generators': [216, 146, 156], 'label': '1296.3190.72.bd1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.f1.a1', 'old_label': '72.bd1.a1', 'projective_image': '648.731', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bd1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 71060264
    {'ambient': '1296.3190', 'aut_centralizer_order': 4, 'aut_label': '6.y1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '288.1040', 'aut_weyl_index': 12, 'centralizer': '108.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.e1.a1', '3.b1.a1'], 'contains': ['12.d1.a1', '12.bi1.a1', '12.bp1.a1', '18.bd1.a1', '18.bk1.a1', '18.bl1.a1'], 'core': '12.d1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3707, -1, 8488, -1, 3365, -1, 7142, -1], 'generators': [111, 432, 144, 18, 2, 216], 'label': '1296.3190.6.y1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '6.y1.a1', 'projective_image': '216.162', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.y1.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 71060265
    {'ambient': '1296.3190', 'aut_centralizer_order': 216, 'aut_label': '72.be1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '4.2', 'aut_weyl_index': 864, 'centralizer': '8.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.i1.a1', '24.m1.a1', '24.r1.a1', '36.dk1.a1'], 'contains': ['144.bb1.a1', '216.g1.a1', '216.j1.a1', '216.p1.a1'], 'core': '648.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [1272, -1, 9152, -1, 2018, -1, 7717, -1], 'generators': [216, 146, 444], 'label': '1296.3190.72.be1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.g1.a1', 'old_label': '72.be1.a1', 'projective_image': '648.731', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.be1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 71060266
    {'ambient': '1296.3190', 'aut_centralizer_order': 216, 'aut_label': '72.bf1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1728, 'centralizer': '8.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.i1.a1', '24.n1.a1', '24.q1.a1', '24.r1.a1'], 'contains': ['144.bc1.a1', '216.g1.a1', '216.m1.a1', '216.o1.a1', '216.p1.a1'], 'core': '648.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [1022, -1, 8553, -1, 2221, -1, 7376, -1], 'generators': [216, 146, 588], 'label': '1296.3190.72.bf1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.a1.a1', 'old_label': '72.bf1.a1', 'projective_image': '648.731', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bf1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 71060267
    {'ambient': '1296.3190', 'aut_centralizer_order': 216, 'aut_label': '72.bg1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '4.2', 'aut_weyl_index': 864, 'centralizer': '8.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.j1.a1', '24.l1.a1', '24.r1.a1', '36.cb1.a1'], 'contains': ['144.bd1.a1', '216.h1.a1', '216.i1.a1', '216.p1.a1'], 'core': '648.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [2124, -1, 6748, -1, 3526, -1, 6899, -1], 'generators': [216, 14, 576], 'label': '1296.3190.72.bg1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.d1.a1', 'old_label': '72.bg1.a1', 'projective_image': '648.731', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bg1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 71060268
    {'ambient': '1296.3190', 'aut_centralizer_order': 216, 'aut_label': '72.bh1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1728, 'centralizer': '8.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.j1.a1', '24.n1.a1', '24.p1.a1', '24.r1.a1'], 'contains': ['144.be1.a1', '216.h1.a1', '216.l1.a1', '216.o1.a1', '216.p1.a1'], 'core': '648.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [1150, -1, 7078, -1, 2526, -1, 7333, -1], 'generators': [216, 578, 588], 'label': '1296.3190.72.bh1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.a1.a1', 'old_label': '72.bh1.a1', 'projective_image': '648.731', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bh1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 71060269
    {'ambient': '1296.3190', 'aut_centralizer_order': 432, 'aut_label': '72.bi1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1728, 'centralizer': '8.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.d1.a1', '24.k1.a1', '24.r1.a1', '36.cp1.a1'], 'contains': ['144.bf1.a1', '216.i1.a1', '216.j1.a1', '216.k1.a1', '216.o1.a1'], 'core': '648.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [1893, -1, 8091, -1, 2628, -1, 8105, -1], 'generators': [216, 444, 576], 'label': '1296.3190.72.bi1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.e1.a1', 'old_label': '72.bi1.a1', 'projective_image': '648.731', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bi1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 71060270
    {'ambient': '1296.3190', 'aut_centralizer_order': 216, 'aut_label': '72.bj1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1728, 'centralizer': '8.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.k1.a1', '24.l1.a1', '24.q1.a1', '24.r1.a1'], 'contains': ['144.bg1.a1', '216.i1.a1', '216.m1.a1', '216.n1.a1', '216.p1.a1'], 'core': '648.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [1328, -1, 7169, -1, 2577, -1, 7290, -1], 'generators': [216, 446, 576], 'label': '1296.3190.72.bj1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.a1.a1', 'old_label': '72.bj1.a1', 'projective_image': '648.731', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bj1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 71060271
    {'ambient': '1296.3190', 'aut_centralizer_order': 216, 'aut_label': '72.bk1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1728, 'centralizer': '8.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.k1.a1', '24.m1.a1', '24.p1.a1', '24.r1.a1'], 'contains': ['144.bh1.a1', '216.j1.a1', '216.l1.a1', '216.n1.a1', '216.p1.a1'], 'core': '648.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [1234, -1, 7385, -1, 2272, -1, 7646, -1], 'generators': [216, 578, 444], 'label': '1296.3190.72.bk1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.a1.a1', 'old_label': '72.bk1.a1', 'projective_image': '648.731', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bk1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 71060272
    {'ambient': '1296.3190', 'aut_centralizer_order': 216, 'aut_label': '72.bl1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1728, 'centralizer': '8.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.k1.a1', '24.n1.a1', '24.o1.a1', '24.r1.a1'], 'contains': ['144.bi1.a1', '216.k1.a1', '216.l1.a1', '216.m1.a1', '216.p1.a1'], 'core': '648.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [1804, -1, 8044, -1, 2425, -1, 7504, -1], 'generators': [216, 578, 156], 'label': '1296.3190.72.bl1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.a1.a1', 'old_label': '72.bl1.a1', 'projective_image': '648.731', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bl1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 71060273
    {'ambient': '1296.3190', 'aut_centralizer_order': 216, 'aut_label': '72.bm1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1728, 'centralizer': '8.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.k1.a1', '24.n1.a1', '24.p1.a1', '24.q1.a1'], 'contains': ['144.bj1.a1', '216.l1.a1', '216.m1.a1', '216.n1.a1', '216.o1.a1'], 'core': '648.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [1187, -1, 7987, -1, 2374, -1, 7461, -1], 'generators': [216, 1010, 588], 'label': '1296.3190.72.bm1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.a1.a1', 'old_label': '72.bm1.a1', 'projective_image': '648.731', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bm1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 71060274
    {'ambient': '1296.3190', 'aut_centralizer_order': 144, 'aut_label': '72.bn1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '4.2', 'aut_weyl_index': 864, 'centralizer': '6.k1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.e1.a1', '24.s1.a1', '36.m1.a1', '36.dl1.a1', '36.dp1.a1'], 'contains': ['144.a1.a1', '216.q1.a1', '216.r1.a1', '216.t1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [9167, -1, 2982, -1, 8317, -1, 1927, -1], 'generators': [3, 2, 432], 'label': '1296.3190.72.bn1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '72.bn1.a1', 'projective_image': '432.598', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bn1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 71060275
    {'ambient': '1296.3190', 'aut_centralizer_order': 4, 'aut_label': '6.z1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '288.1040', 'aut_weyl_index': 12, 'centralizer': '216.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.e1.a1', '3.d1.a1'], 'contains': ['12.e1.a1', '12.bl1.a1', '12.bs1.a1', '18.be1.a1', '18.bk1.a1', '18.bm1.a1'], 'core': '12.e1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3966, -1, 7688, -1, 3646, -1, 6399, -1], 'generators': [111, 144, 12, 18, 2, 216], 'label': '1296.3190.6.z1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.d1.a1', 'old_label': '6.z1.a1', 'projective_image': '216.162', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.z1.a1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 71060276
    {'ambient': '1296.3190', 'aut_centralizer_order': 144, 'aut_label': '72.bn1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '4.2', 'aut_weyl_index': 864, 'centralizer': '6.k1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.e1.b1', '24.s1.b1', '36.m1.a1', '36.dl1.b1', '36.dp1.b1'], 'contains': ['144.a1.a1', '216.q1.b1', '216.r1.b1', '216.t1.b1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [9167, -1, 3988, -1, 8317, -1, 2636, -1], 'generators': [219, 2, 432], 'label': '1296.3190.72.bn1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.e1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '72.bn1.b1', 'projective_image': '432.598', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bn1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 71060277
    {'ambient': '1296.3190', 'aut_centralizer_order': 144, 'aut_label': '72.bo1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '4.2', 'aut_weyl_index': 864, 'centralizer': '6.m1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.f1.a1', '24.s1.a1', '36.n1.a1', '36.dm1.a1', '36.dq1.a1'], 'contains': ['144.b1.a1', '216.q1.a1', '216.s1.a1', '216.u1.a1'], 'core': '144.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8842, -1, 2868, -1, 8216, -1, 2251, -1], 'generators': [3, 2, 144], 'label': '1296.3190.72.bo1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '72.bo1.a1', 'projective_image': '432.598', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bo1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 71060278
    {'ambient': '1296.3190', 'aut_centralizer_order': 144, 'aut_label': '72.bo1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '4.2', 'aut_weyl_index': 864, 'centralizer': '6.m1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.f1.b1', '24.s1.b1', '36.n1.a1', '36.dm1.b1', '36.dq1.b1'], 'contains': ['144.b1.a1', '216.q1.b1', '216.s1.b1', '216.u1.b1'], 'core': '144.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8842, -1, 4017, -1, 8216, -1, 2721, -1], 'generators': [219, 2, 144], 'label': '1296.3190.72.bo1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.f1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '72.bo1.b1', 'projective_image': '432.598', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bo1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 71060279
    {'ambient': '1296.3190', 'aut_centralizer_order': 72, 'aut_label': '72.bp1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '4.2', 'aut_weyl_index': 864, 'centralizer': '12.q1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.s1.a1', '24.t1.a1', '36.o1.a1', '36.dr1.a1', '36.dr1.a2'], 'contains': ['144.g1.a1', '216.q1.a1', '216.v1.a1', '216.w1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [9353, -1, 4339, -1, 8862, -1, 3127, -1], 'generators': [3, 2, 576], 'label': '1296.3190.72.bp1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.l1.a1', 'old_label': '72.bp1.a1', 'projective_image': '432.598', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bp1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 71060280
    {'ambient': '1296.3190', 'aut_centralizer_order': 72, 'aut_label': '72.bp1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '4.2', 'aut_weyl_index': 864, 'centralizer': '12.q1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.s1.b1', '24.t1.b1', '36.o1.a1', '36.dr1.b1', '36.dr1.b2'], 'contains': ['144.g1.a1', '216.q1.b1', '216.v1.b1', '216.w1.b1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [9353, -1, 4754, -1, 8862, -1, 3256, -1], 'generators': [219, 2, 576], 'label': '1296.3190.72.bp1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.l1.a1', 'old_label': '72.bp1.b1', 'projective_image': '432.598', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bp1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 71060281
    {'ambient': '1296.3190', 'aut_centralizer_order': 144, 'aut_label': '72.bq1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '4.2', 'aut_weyl_index': 864, 'centralizer': '12.q1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.g1.a1', '24.s1.a1', '36.p1.a1', '36.dn1.a1', '36.ds1.a1'], 'contains': ['144.d1.a1', '216.r1.a1', '216.s1.a1', '216.v1.a1'], 'core': '144.d1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [9046, -1, 3011, -1, 8267, -1, 2294, -1], 'generators': [3, 144, 432], 'label': '1296.3190.72.bq1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '72.bq1.a1', 'projective_image': '1296.3190', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bq1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 71060282
    {'ambient': '1296.3190', 'aut_centralizer_order': 144, 'aut_label': '72.bq1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '4.2', 'aut_weyl_index': 864, 'centralizer': '12.q1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.g1.b1', '24.s1.b1', '36.p1.a1', '36.dn1.b1', '36.ds1.b1'], 'contains': ['144.d1.a1', '216.r1.b1', '216.s1.b1', '216.v1.b1'], 'core': '144.d1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [9046, -1, 4055, -1, 8267, -1, 2849, -1], 'generators': [219, 144, 432], 'label': '1296.3190.72.bq1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.g1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '72.bq1.b1', 'projective_image': '1296.3190', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bq1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 71060283
    {'ambient': '1296.3190', 'aut_centralizer_order': 72, 'aut_label': '72.br1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '4.2', 'aut_weyl_index': 864, 'centralizer': '12.q1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.s1.a1', '24.u1.a1', '36.q1.a1'], 'contains': ['144.k1.a1', '216.r1.a1', '216.u1.a1', '216.w1.a1'], 'core': '432.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [8330, -1, 2943, -1, 8165, -1, 1885, -1], 'generators': [3, 146, 432], 'label': '1296.3190.72.br1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.m1.a1', 'old_label': '72.br1.a1', 'projective_image': '1296.3190', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.br1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 71060285
    {'ambient': '1296.3190', 'aut_centralizer_order': 72, 'aut_label': '72.bs1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '4.2', 'aut_weyl_index': 864, 'centralizer': '12.q1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.s1.a1', '24.v1.a1', '36.r1.a1', '36.do1.a1', '36.do1.b1'], 'contains': ['144.o1.a1', '216.s1.a1', '216.t1.a1', '216.w1.a1'], 'core': '432.c1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [8578, -1, 1149, -1, 8368, -1, 741, -1], 'generators': [3, 434, 144], 'label': '1296.3190.72.bs1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.k1.a1', 'old_label': '72.bs1.a1', 'projective_image': '1296.3190', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bs1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 71060286
    {'ambient': '1296.3190', 'aut_centralizer_order': 6, 'aut_label': '2.d1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '576.8675', 'aut_weyl_index': 6, 'centralizer': '72.c1.a1', 'complements': ['648.b1.a1', '648.b1.b1', '648.d1.a1', '648.f1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.b1.a1', '4.d1.a1', '4.f1.a1', '6.f1.a1', '6.g1.a1', '6.u1.a1', '6.w1.a1', '6.x1.a1'], 'core': '2.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3400, 2830, 6852, 7586, 4294, 8252, 6971, 8244], 'generators': [18, 144, 216, 108, 432, 2, 12], 'label': '1296.3190.2.d1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.d1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.b1.a1', '4.d1.a1', '4.f1.a1', '6.f1.a1', '6.g1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.d1.a1', 'projective_image': '216.162', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.d1.a1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 71060287
    {'ambient': '1296.3190', 'aut_centralizer_order': 2, 'aut_label': '6.ba1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '288.1040', 'aut_weyl_index': 12, 'centralizer': '216.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.e1.a1'], 'contains': ['12.w1.a1', '12.bm1.a1', '12.bt1.a1', '18.bf1.a1', '18.bk1.a1', '18.bn1.a1'], 'core': '36.d1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [1313, -1, 8303, -1, 2612, -1, 7988, -1], 'generators': [111, 144, 444, 18, 2, 216], 'label': '1296.3190.6.ba1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.ba1.a1', 'old_label': '6.ba1.a1', 'projective_image': '216.162', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.ba1.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 71060288
    {'ambient': '1296.3190', 'aut_centralizer_order': 72, 'aut_label': '72.bs1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '4.2', 'aut_weyl_index': 864, 'centralizer': '12.q1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.s1.b1', '24.v1.b1', '36.r1.a1', '36.do1.c1', '36.do1.d1'], 'contains': ['144.o1.a1', '216.s1.b1', '216.t1.b1', '216.w1.b1'], 'core': '432.c1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [8578, -1, 1884, -1, 8368, -1, 1262, -1], 'generators': [219, 434, 144], 'label': '1296.3190.72.bs1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.k1.a1', 'old_label': '72.bs1.b1', 'projective_image': '1296.3190', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bs1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 71060289
    {'ambient': '1296.3190', 'aut_centralizer_order': 72, 'aut_label': '72.bt1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1728, 'centralizer': '12.q1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.s1.a1', '24.w1.a1', '36.s1.a1'], 'contains': ['144.w1.a1', '216.t1.a1', '216.u1.a1', '216.v1.a1', '216.w1.a1'], 'core': '1296.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [8473, -1, 2725, -1, 8419, -1, 1799, -1], 'generators': [3, 434, 576], 'label': '1296.3190.72.bt1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.q1.a1', 'old_label': '72.bt1.a1', 'projective_image': '1296.3190', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bt1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 71060290
    {'ambient': '1296.3190', 'aut_centralizer_order': 72, 'aut_label': '72.bt1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1728, 'centralizer': '12.q1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.s1.b1', '24.w1.b1', '36.s1.a1'], 'contains': ['144.w1.a1', '216.t1.b1', '216.u1.b1', '216.v1.b1', '216.w1.b1'], 'core': '1296.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [8473, -1, 2813, -1, 8419, -1, 2422, -1], 'generators': [219, 434, 576], 'label': '1296.3190.72.bt1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.q1.a1', 'old_label': '72.bt1.b1', 'projective_image': '1296.3190', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bt1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 71060291
    {'ambient': '1296.3190', 'aut_centralizer_order': 72, 'aut_label': '72.bu1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '12.4', 'aut_weyl_index': 288, 'centralizer': '12.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.e1.a1', '24.v1.a1', '24.w1.a1', '36.t1.a1', '36.dv1.a1', '36.dv1.b1'], 'contains': ['144.s1.a1', '216.e1.a1', '216.t1.a1'], 'core': '216.e1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8805, -1, 185, -1, 8811, -1, 699, -1], 'generators': [3, 434, 12], 'label': '1296.3190.72.bu1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '72.bu1.a1', 'projective_image': '1296.3190', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bu1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 71060292
    {'ambient': '1296.3190', 'aut_centralizer_order': 72, 'aut_label': '72.bu1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '12.4', 'aut_weyl_index': 288, 'centralizer': '12.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.e1.b1', '24.v1.b1', '24.w1.b1', '36.t1.a1', '36.dv1.c1', '36.dv1.d1'], 'contains': ['144.s1.a1', '216.e1.b1', '216.t1.b1'], 'core': '216.e1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [8805, -1, 285, -1, 8811, -1, 921, -1], 'generators': [219, 434, 12], 'label': '1296.3190.72.bu1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.e1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '72.bu1.b1', 'projective_image': '1296.3190', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bu1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 71060293
    {'ambient': '1296.3190', 'aut_centralizer_order': 72, 'aut_label': '72.bv1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '12.4', 'aut_weyl_index': 288, 'centralizer': '12.l1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.f1.a1', '24.u1.a1', '24.w1.a1', '36.u1.a1'], 'contains': ['144.t1.a1', '216.e1.a1', '216.u1.a1'], 'core': '216.e1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8398, -1, 1822, -1, 8659, -1, 1757, -1], 'generators': [3, 146, 12], 'label': '1296.3190.72.bv1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '72.bv1.a1', 'projective_image': '1296.3190', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bv1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 71060294
    {'ambient': '1296.3190', 'aut_centralizer_order': 72, 'aut_label': '72.bv1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '12.4', 'aut_weyl_index': 288, 'centralizer': '12.l1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.f1.b1', '24.u1.b1', '24.w1.b1', '36.u1.a1'], 'contains': ['144.t1.a1', '216.e1.b1', '216.u1.b1'], 'core': '216.e1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [8398, -1, 2320, -1, 8659, -1, 2508, -1], 'generators': [219, 146, 12], 'label': '1296.3190.72.bv1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.f1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '72.bv1.b1', 'projective_image': '1296.3190', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bv1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 71060295
    {'ambient': '1296.3190', 'aut_centralizer_order': 72, 'aut_label': '72.bw1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '12.4', 'aut_weyl_index': 288, 'centralizer': '24.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.g1.a1', '24.t1.a1', '24.w1.a1', '36.v1.a1', '36.ea1.a1', '36.ea1.a2'], 'contains': ['144.u1.a1', '216.e1.a1', '216.v1.a1'], 'core': '216.e1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [9824, -1, 3152, -1, 9243, -1, 3170, -1], 'generators': [3, 576, 12], 'label': '1296.3190.72.bw1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '72.bw1.a1', 'projective_image': '1296.3190', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bw1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 71060296
    {'ambient': '1296.3190', 'aut_centralizer_order': 72, 'aut_label': '72.bw1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '12.4', 'aut_weyl_index': 288, 'centralizer': '24.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.g1.b1', '24.t1.b1', '24.w1.b1', '36.v1.a1', '36.ea1.b1', '36.ea1.b2'], 'contains': ['144.u1.a1', '216.e1.b1', '216.v1.b1'], 'core': '216.e1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [9824, -1, 3106, -1, 9243, -1, 3298, -1], 'generators': [219, 576, 12], 'label': '1296.3190.72.bw1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.g1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '72.bw1.b1', 'projective_image': '1296.3190', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bw1.b1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 71060297
    {'ambient': '1296.3190', 'aut_centralizer_order': 36, 'aut_label': '72.bx1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '12.4', 'aut_weyl_index': 288, 'centralizer': '24.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.t1.a1', '24.u1.a1', '24.v1.a1', '24.w1.a1', '36.w1.a1'], 'contains': ['144.v1.a1', '216.e1.a1', '216.w1.a1'], 'core': '216.e1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [8435, -1, 419, -1, 9014, -1, 1714, -1], 'generators': [3, 578, 12], 'label': '1296.3190.72.bx1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '72.bx1.a1', 'projective_image': '1296.3190', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bx1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 71060298
    {'ambient': '1296.3190', 'aut_centralizer_order': 4, 'aut_label': '6.bb1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '288.1040', 'aut_weyl_index': 12, 'centralizer': '216.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.f1.a1', '3.c1.a1'], 'contains': ['12.n1.a1', '12.bb1.a1', '12.be1.a1', '18.bo1.a1', '18.bq1.a1', '18.bs1.a1'], 'core': '12.n1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5162, -1, 5657, -1, 5567, -1, 6042, -1], 'generators': [111, 432, 12, 54, 2, 216], 'label': '1296.3190.6.bb1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1.a1', 'old_label': '6.bb1.a1', 'projective_image': '216.162', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.bb1.a1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 71060299
    {'ambient': '1296.3190', 'aut_centralizer_order': 36, 'aut_label': '72.bx1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '12.4', 'aut_weyl_index': 288, 'centralizer': '24.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.t1.b1', '24.u1.b1', '24.v1.b1', '24.w1.b1', '36.w1.a1'], 'contains': ['144.v1.a1', '216.e1.b1', '216.w1.b1'], 'core': '216.e1.b1', 'coset_action_label': None, 'count': 4, 'diagramx': [8435, -1, 473, -1, 9014, -1, 2081, -1], 'generators': [219, 578, 12], 'label': '1296.3190.72.bx1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '72.bx1.b1', 'projective_image': '1296.3190', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bx1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 71060300
    {'ambient': '1296.3190', 'aut_centralizer_order': 144, 'aut_label': '72.by1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '4.2', 'aut_weyl_index': 864, 'centralizer': '6.n1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.x1.a1', '24.y1.a1', '36.x1.a1', '36.dl1.a1', '36.dl1.b1'], 'contains': ['144.a1.a1', '216.x1.a1', '216.y1.a1', '216.ba1.a1', '216.ba1.b1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [7169, -1, 1332, -1, 5516, -1, 1518, -1], 'generators': [18, 2, 432], 'label': '1296.3190.72.by1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.n1.a1', 'old_label': '72.by1.a1', 'projective_image': '432.598', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.by1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 71060301
    {'ambient': '1296.3190', 'aut_centralizer_order': 144, 'aut_label': '72.bz1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '4.2', 'aut_weyl_index': 864, 'centralizer': '12.v1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.x1.a1', '24.z1.a1', '36.y1.a1', '36.dt1.a1', '36.dt1.b1'], 'contains': ['144.c1.a1', '216.x1.a1', '216.z1.a1', '216.bb1.a1'], 'core': '144.c1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [7449, -1, 502, -1, 5618, -1, 2166, -1], 'generators': [18, 2, 12], 'label': '1296.3190.72.bz1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.n1.a1', 'old_label': '72.bz1.a1', 'projective_image': '432.598', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bz1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 71060302
    {'ambient': '1296.3190', 'aut_centralizer_order': 72, 'aut_label': '72.ca1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '4.2', 'aut_weyl_index': 864, 'centralizer': '12.v1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.x1.a1', '24.ba1.a1', '36.z1.a1'], 'contains': ['144.h1.a1', '216.x1.a1', '216.bc1.a1', '216.bd1.a1', '216.bd1.b1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [1441, -1, 3643, -1, 4180, -1, 3639, -1], 'generators': [18, 2, 444], 'label': '1296.3190.72.ca1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.v1.a1', 'old_label': '72.ca1.a1', 'projective_image': '432.598', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ca1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 71060303
    {'ambient': '1296.3190', 'aut_centralizer_order': 144, 'aut_label': '72.cb1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '4.2', 'aut_weyl_index': 864, 'centralizer': '12.v1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.x1.a1', '24.bb1.a1', '36.ba1.a1', '36.du1.a1', '36.du1.b1'], 'contains': ['144.e1.a1', '216.y1.a1', '216.z1.a1', '216.bc1.a1'], 'core': '144.e1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [7411, -1, 802, -1, 5415, -1, 1970, -1], 'generators': [18, 12, 432], 'label': '1296.3190.72.cb1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.n1.a1', 'old_label': '72.cb1.a1', 'projective_image': '1296.3190', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.cb1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 71060304
    {'ambient': '1296.3190', 'aut_centralizer_order': 72, 'aut_label': '72.cc1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '4.2', 'aut_weyl_index': 864, 'centralizer': '12.v1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.x1.a1', '24.bc1.a1', '36.bb1.a1'], 'contains': ['144.l1.a1', '216.y1.a1', '216.bb1.a1', '216.bd1.a1', '216.bd1.b1'], 'core': '432.b1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [1725, -1, 2589, -1, 4383, -1, 3469, -1], 'generators': [18, 14, 432], 'label': '1296.3190.72.cc1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.v1.a1', 'old_label': '72.cc1.a1', 'projective_image': '1296.3190', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.cc1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 71060305
    {'ambient': '1296.3190', 'aut_centralizer_order': 72, 'aut_label': '72.cd1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '4.2', 'aut_weyl_index': 864, 'centralizer': '12.v1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.x1.a1', '24.bd1.a1', '36.bc1.a1', '36.dv1.a1', '36.dv1.c1'], 'contains': ['144.s1.a1', '216.z1.a1', '216.ba1.a1', '216.bd1.a1'], 'core': '432.d1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [7302, -1, 147, -1, 5669, -1, 878, -1], 'generators': [18, 434, 12], 'label': '1296.3190.72.cd1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.n1.a1', 'old_label': '72.cd1.a1', 'projective_image': '1296.3190', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.cd1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 71060306
    {'ambient': '1296.3190', 'aut_centralizer_order': 72, 'aut_label': '72.cd1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '4.2', 'aut_weyl_index': 864, 'centralizer': '12.v1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.x1.a1', '24.bd1.b1', '36.bc1.a1', '36.dv1.b1', '36.dv1.d1'], 'contains': ['144.s1.a1', '216.z1.a1', '216.ba1.b1', '216.bd1.b1'], 'core': '432.d1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [7302, -1, 30, -1, 5669, -1, 836, -1], 'generators': [18, 866, 12], 'label': '1296.3190.72.cd1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.n1.a1', 'old_label': '72.cd1.b1', 'projective_image': '1296.3190', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.cd1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 71060307
    {'ambient': '1296.3190', 'aut_centralizer_order': 72, 'aut_label': '72.ce1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1728, 'centralizer': '12.v1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.x1.a1', '24.be1.a1', '36.bd1.a1'], 'contains': ['144.x1.a1', '216.ba1.a1', '216.bb1.a1', '216.bc1.a1', '216.bd1.b1'], 'core': '1296.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [1687, -1, 1930, -1, 4231, -1, 3597, -1], 'generators': [18, 434, 444], 'label': '1296.3190.72.ce1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.v1.a1', 'old_label': '72.ce1.a1', 'projective_image': '1296.3190', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ce1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 71060308
    {'ambient': '1296.3190', 'aut_centralizer_order': 72, 'aut_label': '72.ce1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1728, 'centralizer': '12.v1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.x1.a1', '24.be1.b1', '36.bd1.a1'], 'contains': ['144.x1.a1', '216.ba1.b1', '216.bb1.a1', '216.bc1.a1', '216.bd1.a1'], 'core': '1296.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [1687, -1, 2283, -1, 4231, -1, 3426, -1], 'generators': [18, 866, 444], 'label': '1296.3190.72.ce1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.v1.a1', 'old_label': '72.ce1.b1', 'projective_image': '1296.3190', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ce1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 71060309
    {'ambient': '1296.3190', 'aut_centralizer_order': 4, 'aut_label': '6.bc1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '288.1040', 'aut_weyl_index': 12, 'centralizer': '108.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.f1.a1', '3.b1.a1'], 'contains': ['12.i1.a1', '12.ba1.a1', '12.bp1.a1', '18.bo1.a1', '18.br1.a1', '18.bt1.a1'], 'core': '12.i1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4516, -1, 7812, -1, 5360, -1, 6517, -1], 'generators': [111, 432, 144, 54, 2, 216], 'label': '1296.3190.6.bc1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '6.bc1.a1', 'projective_image': '216.162', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.bc1.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 71060310
    {'ambient': '1296.3190', 'aut_centralizer_order': 144, 'aut_label': '72.cf1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '12.4', 'aut_weyl_index': 288, 'centralizer': '12.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.y1.a1', '24.z1.a1', '24.ba1.a1', '36.d1.a1', '36.dm1.a1', '36.dm1.b1'], 'contains': ['144.b1.a1', '216.x1.a1', '216.be1.a1'], 'core': '144.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7063, -1, 1634, -1, 5466, -1, 2337, -1], 'generators': [18, 2, 144], 'label': '1296.3190.72.cf1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '72.cf1.a1', 'projective_image': '432.598', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.cf1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 71060311
    {'ambient': '1296.3190', 'aut_centralizer_order': 144, 'aut_label': '72.cg1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '12.4', 'aut_weyl_index': 288, 'centralizer': '12.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.y1.a1', '24.bb1.a1', '24.bc1.a1', '36.e1.a1', '36.dn1.a1', '36.dn1.b1'], 'contains': ['144.d1.a1', '216.y1.a1', '216.be1.a1'], 'core': '144.d1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7120, -1, 1542, -1, 5364, -1, 2039, -1], 'generators': [18, 432, 144], 'label': '1296.3190.72.cg1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '72.cg1.a1', 'projective_image': '1296.3190', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.cg1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 71060312
    {'ambient': '1296.3190', 'aut_centralizer_order': 144, 'aut_label': '72.ch1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '12.4', 'aut_weyl_index': 288, 'centralizer': '24.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.z1.a1', '24.bb1.a1', '24.bd1.a1', '24.bd1.b1', '36.f1.a1', '36.dw1.a1', '36.dw1.b1'], 'contains': ['144.f1.a1', '216.z1.a1', '216.be1.a1'], 'core': '144.f1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7486, -1, 532, -1, 5720, -1, 1304, -1], 'generators': [18, 12, 144], 'label': '1296.3190.72.ch1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '72.ch1.a1', 'projective_image': '1296.3190', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ch1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 71060313
    {'ambient': '1296.3190', 'aut_centralizer_order': 72, 'aut_label': '72.ci1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '12.4', 'aut_weyl_index': 288, 'centralizer': '12.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.y1.a1', '24.bd1.a1', '24.be1.a1', '36.be1.a1', '36.do1.a1', '36.do1.c1'], 'contains': ['144.o1.a1', '216.ba1.a1', '216.be1.a1'], 'core': '432.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [6526, -1, 1416, -1, 5567, -1, 1219, -1], 'generators': [18, 434, 144], 'label': '1296.3190.72.ci1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '72.ci1.a1', 'projective_image': '1296.3190', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ci1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 71060314
    {'ambient': '1296.3190', 'aut_centralizer_order': 72, 'aut_label': '72.ci1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '12.4', 'aut_weyl_index': 288, 'centralizer': '12.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.y1.a1', '24.bd1.b1', '24.be1.b1', '36.be1.a1', '36.do1.b1', '36.do1.d1'], 'contains': ['144.o1.a1', '216.ba1.b1', '216.be1.a1'], 'core': '432.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [6526, -1, 1445, -1, 5567, -1, 1177, -1], 'generators': [18, 866, 144], 'label': '1296.3190.72.ci1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '72.ci1.b1', 'projective_image': '1296.3190', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ci1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 71060315
    {'ambient': '1296.3190', 'aut_centralizer_order': 72, 'aut_label': '72.cj1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '12.4', 'aut_weyl_index': 288, 'centralizer': '24.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.z1.a1', '24.bc1.a1', '24.be1.a1', '24.be1.b1', '36.bf1.a1'], 'contains': ['144.p1.a1', '216.bb1.a1', '216.be1.a1'], 'core': '432.c1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [3863, -1, 2351, -1, 4332, -1, 3512, -1], 'generators': [18, 14, 144], 'label': '1296.3190.72.cj1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.a1', 'old_label': '72.cj1.a1', 'projective_image': '1296.3190', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.cj1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 71060316
    {'ambient': '1296.3190', 'aut_centralizer_order': 72, 'aut_label': '72.ck1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '12.4', 'aut_weyl_index': 288, 'centralizer': '24.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.ba1.a1', '24.bb1.a1', '24.be1.a1', '24.be1.b1', '36.bg1.a1'], 'contains': ['144.q1.a1', '216.bc1.a1', '216.be1.a1'], 'core': '432.c1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [2351, -1, 2380, -1, 4129, -1, 3734, -1], 'generators': [18, 444, 144], 'label': '1296.3190.72.ck1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.a1', 'old_label': '72.ck1.a1', 'projective_image': '1296.3190', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ck1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 71060317
    {'ambient': '1296.3190', 'aut_centralizer_order': 36, 'aut_label': '72.cl1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '12.4', 'aut_weyl_index': 288, 'centralizer': '24.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.ba1.a1', '24.bc1.a1', '24.bd1.a1', '24.be1.b1', '36.bh1.a1'], 'contains': ['144.r1.a1', '216.bd1.a1', '216.be1.a1'], 'core': '432.c1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [2533, -1, 2685, -1, 4282, -1, 3384, -1], 'generators': [18, 446, 144], 'label': '1296.3190.72.cl1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.a1', 'old_label': '72.cl1.a1', 'projective_image': '1296.3190', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.cl1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 71060318
    {'ambient': '1296.3190', 'aut_centralizer_order': 36, 'aut_label': '72.cl1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '12.4', 'aut_weyl_index': 288, 'centralizer': '24.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.ba1.a1', '24.bc1.a1', '24.bd1.b1', '24.be1.a1', '36.bh1.a1'], 'contains': ['144.r1.a1', '216.bd1.b1', '216.be1.a1'], 'core': '432.c1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [2533, -1, 2656, -1, 4282, -1, 3554, -1], 'generators': [18, 878, 144], 'label': '1296.3190.72.cl1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.a1', 'old_label': '72.cl1.b1', 'projective_image': '1296.3190', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.cl1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 71060319
    {'ambient': '1296.3190', 'aut_centralizer_order': 48, 'aut_label': '72.cm1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '4.2', 'aut_weyl_index': 864, 'centralizer': '18.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bf1.a1', '24.bg1.a1', '24.bh1.a1', '36.bi1.a1', '36.dl1.a1', '36.dl1.b1'], 'contains': ['144.a1.a1', '216.bf1.a1', '216.bg1.a1', '216.bh1.a1', '216.bh1.b1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [8736, -1, 1743, -1, 7520, -1, 964, -1], 'generators': [9, 2, 432], 'label': '1296.3190.72.cm1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.d1.a1', 'old_label': '72.cm1.a1', 'projective_image': '432.598', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.cm1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 71060320
    {'ambient': '1296.3190', 'aut_centralizer_order': 4, 'aut_label': '6.bd1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '288.1040', 'aut_weyl_index': 12, 'centralizer': '108.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.g1.a1', '3.b1.a1'], 'contains': ['12.l1.a1', '12.ba1.a1', '12.bi1.a1', '18.bp1.a1', '18.bu1.a1', '18.bx1.a1'], 'core': '12.l1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3451, -1, 8613, -1, 3143, -1, 7201, -1], 'generators': [9, 432, 144, 108, 2, 216], 'label': '1296.3190.6.bd1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '6.bd1.a1', 'projective_image': '216.162', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.bd1.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 71060321
    {'ambient': '1296.3190', 'aut_centralizer_order': 48, 'aut_label': '72.cn1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '12.4', 'aut_weyl_index': 288, 'centralizer': '36.m1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bf1.a1', '24.bi1.a1', '36.bj1.a1', '36.dm1.a1', '36.dm1.b1'], 'contains': ['144.b1.a1', '216.bf1.a1', '216.bi1.a1'], 'core': '144.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [8652, -1, 1676, -1, 7671, -1, 1561, -1], 'generators': [9, 2, 144], 'label': '1296.3190.72.cn1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.k1.a1', 'old_label': '72.cn1.a1', 'projective_image': '432.598', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.cn1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 71060322
    {'ambient': '1296.3190', 'aut_centralizer_order': 48, 'aut_label': '72.co1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '12.4', 'aut_weyl_index': 288, 'centralizer': '36.x1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bg1.a1', '24.bi1.a1', '36.bk1.a1', '36.dt1.a1', '36.dt1.b1'], 'contains': ['144.c1.a1', '216.bf1.a1', '216.bj1.a1'], 'core': '144.c1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [9260, -1, 562, -1, 7857, -1, 1475, -1], 'generators': [9, 2, 12], 'label': '1296.3190.72.co1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.n1.a1', 'old_label': '72.co1.a1', 'projective_image': '432.598', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.co1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 71060323
    {'ambient': '1296.3190', 'aut_centralizer_order': 24, 'aut_label': '72.cp1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '12.4', 'aut_weyl_index': 288, 'centralizer': '72.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bh1.a1', '24.bi1.a1', '36.bl1.a1'], 'contains': ['144.i1.a1', '216.bf1.a1', '216.bk1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [8106, -1, 4261, -1, 6631, -1, 2934, -1], 'generators': [9, 2, 156], 'label': '1296.3190.72.cp1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bc1.a1', 'old_label': '72.cp1.a1', 'projective_image': '432.598', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.cp1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 71060324
    {'ambient': '1296.3190', 'aut_centralizer_order': 48, 'aut_label': '72.cq1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '12.4', 'aut_weyl_index': 288, 'centralizer': '36.m1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bf1.a1', '24.bj1.a1', '36.bm1.a1', '36.dn1.a1', '36.dn1.b1'], 'contains': ['144.d1.a1', '216.bg1.a1', '216.bi1.a1'], 'core': '144.d1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [8689, -1, 1571, -1, 7621, -1, 1134, -1], 'generators': [9, 432, 144], 'label': '1296.3190.72.cq1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.h1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.k1.a1', 'old_label': '72.cq1.a1', 'projective_image': '1296.3190', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.cq1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 71060325
    {'ambient': '1296.3190', 'aut_centralizer_order': 48, 'aut_label': '72.cr1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '12.4', 'aut_weyl_index': 288, 'centralizer': '36.x1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bg1.a1', '24.bj1.a1', '36.bn1.a1', '36.du1.a1', '36.du1.b1'], 'contains': ['144.e1.a1', '216.bg1.a1', '216.bj1.a1'], 'core': '144.e1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [8899, -1, 881, -1, 7722, -1, 1092, -1], 'generators': [9, 432, 12], 'label': '1296.3190.72.cr1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.h1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.n1.a1', 'old_label': '72.cr1.a1', 'projective_image': '1296.3190', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.cr1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 71060326
    {'ambient': '1296.3190', 'aut_centralizer_order': 24, 'aut_label': '72.cs1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '12.4', 'aut_weyl_index': 288, 'centralizer': '72.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bh1.a1', '24.bj1.a1', '36.bo1.a1'], 'contains': ['144.m1.a1', '216.bg1.a1', '216.bk1.a1'], 'core': '432.b1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [8143, -1, 4223, -1, 6581, -1, 2892, -1], 'generators': [9, 432, 156], 'label': '1296.3190.72.cs1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.h1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bc1.a1', 'old_label': '72.cs1.a1', 'projective_image': '1296.3190', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.cs1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 71060327
    {'ambient': '1296.3190', 'aut_centralizer_order': 24, 'aut_label': '72.ct1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '12.4', 'aut_weyl_index': 288, 'centralizer': '36.m1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bf1.a1', '24.bk1.a1', '36.bp1.a1', '36.do1.b1', '36.do1.c1'], 'contains': ['144.o1.a1', '216.bh1.a1', '216.bi1.a1'], 'core': '432.c1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [8541, -1, 1483, -1, 7772, -1, 588, -1], 'generators': [9, 866, 144], 'label': '1296.3190.72.ct1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.k1.a1', 'old_label': '72.ct1.a1', 'projective_image': '1296.3190', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ct1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 71060328
    {'ambient': '1296.3190', 'aut_centralizer_order': 24, 'aut_label': '72.ct1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '12.4', 'aut_weyl_index': 288, 'centralizer': '36.m1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bf1.a1', '24.bk1.b1', '36.bp1.a1', '36.do1.a1', '36.do1.d1'], 'contains': ['144.o1.a1', '216.bh1.b1', '216.bi1.a1'], 'core': '432.c1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [8541, -1, 1512, -1, 7772, -1, 546, -1], 'generators': [9, 434, 144], 'label': '1296.3190.72.ct1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.k1.a1', 'old_label': '72.ct1.b1', 'projective_image': '1296.3190', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ct1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 71060329
    {'ambient': '1296.3190', 'aut_centralizer_order': 24, 'aut_label': '72.cu1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '12.4', 'aut_weyl_index': 288, 'centralizer': '36.x1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bg1.a1', '24.bk1.a1', '36.bq1.a1', '36.dv1.b1', '36.dv1.c1'], 'contains': ['144.s1.a1', '216.bh1.a1', '216.bj1.a1'], 'core': '432.d1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [8616, -1, 118, -1, 7908, -1, 503, -1], 'generators': [9, 866, 12], 'label': '1296.3190.72.cu1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.n1.a1', 'old_label': '72.cu1.a1', 'projective_image': '1296.3190', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.cu1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 71060330
    {'ambient': '1296.3190', 'aut_centralizer_order': 24, 'aut_label': '72.cu1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '12.4', 'aut_weyl_index': 288, 'centralizer': '36.x1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bg1.a1', '24.bk1.b1', '36.bq1.a1', '36.dv1.a1', '36.dv1.d1'], 'contains': ['144.s1.a1', '216.bh1.b1', '216.bj1.a1'], 'core': '432.d1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [8616, -1, 239, -1, 7908, -1, 461, -1], 'generators': [9, 434, 12], 'label': '1296.3190.72.cu1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.n1.a1', 'old_label': '72.cu1.b1', 'projective_image': '1296.3190', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.cu1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 71060331
    {'ambient': '1296.3190', 'aut_centralizer_order': 4, 'aut_label': '6.be1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '288.1040', 'aut_weyl_index': 12, 'centralizer': '216.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.g1.a1', '3.c1.a1'], 'contains': ['12.m1.a1', '12.bb1.a1', '12.bj1.a1', '18.bp1.a1', '18.bv1.a1', '18.by1.a1'], 'core': '12.m1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4637, -1, 7762, -1, 3571, -1, 6458, -1], 'generators': [9, 432, 12, 108, 2, 216], 'label': '1296.3190.6.be1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1.a1', 'old_label': '6.be1.a1', 'projective_image': '216.162', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.be1.a1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 71060332
    {'ambient': '1296.3190', 'aut_centralizer_order': 12, 'aut_label': '72.cv1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '12.4', 'aut_weyl_index': 288, 'centralizer': '72.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bh1.a1', '24.bk1.a1', '36.br1.a1'], 'contains': ['144.y1.a1', '216.bh1.a1', '216.bk1.a1'], 'core': '1296.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [8070, -1, 4168, -1, 6682, -1, 2806, -1], 'generators': [9, 866, 156], 'label': '1296.3190.72.cv1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bc1.a1', 'old_label': '72.cv1.a1', 'projective_image': '1296.3190', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.cv1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 71060333
    {'ambient': '1296.3190', 'aut_centralizer_order': 12, 'aut_label': '72.cv1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '12.4', 'aut_weyl_index': 288, 'centralizer': '72.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bh1.a1', '24.bk1.b1', '36.br1.a1'], 'contains': ['144.y1.a1', '216.bh1.b1', '216.bk1.a1'], 'core': '1296.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [8070, -1, 4130, -1, 6682, -1, 2764, -1], 'generators': [9, 434, 156], 'label': '1296.3190.72.cv1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bc1.a1', 'old_label': '72.cv1.b1', 'projective_image': '1296.3190', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.cv1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 71060334
    {'ambient': '1296.3190', 'aut_centralizer_order': 48, 'aut_label': '72.cw1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '36.10', 'aut_weyl_index': 96, 'centralizer': '72.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bi1.a1', '24.bj1.a1', '24.bk1.a1', '24.bk1.b1', '36.g1.a1', '36.dw1.a1', '36.dw1.b1'], 'contains': ['144.f1.a1', '216.bi1.a1', '216.bj1.a1', '216.bk1.a1'], 'core': '144.f1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8298, -1, 595, -1, 7815, -1, 800, -1], 'generators': [9, 12, 144], 'label': '1296.3190.72.cw1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '72.cw1.a1', 'projective_image': '1296.3190', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.cw1.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 71060335
    {'ambient': '1296.3190', 'aut_centralizer_order': 48, 'aut_label': '72.cx1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '4.2', 'aut_weyl_index': 864, 'centralizer': '36.bs1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bl1.a1', '24.bm1.a1', '24.bn1.a1', '24.bn1.a2', '36.bs1.a1', '36.dx1.a1', '36.dx1.b1'], 'contains': ['144.c1.a1', '216.bl1.a1', '216.bm1.a1', '216.bn1.a1'], 'core': '144.c1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [9589, -1, 1993, -1, 9294, -1, 4089, -1], 'generators': [54, 2, 12], 'label': '1296.3190.72.cx1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.s1.a1', 'old_label': '72.cx1.a1', 'projective_image': '432.598', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.cx1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 71060336
    {'ambient': '1296.3190', 'aut_centralizer_order': 48, 'aut_label': '72.cy1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '12.4', 'aut_weyl_index': 288, 'centralizer': '36.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bl1.a1', '24.bo1.a1', '36.bt1.a1', '36.dp1.a1', '36.dp1.b1'], 'contains': ['144.a1.a1', '216.bl1.a1', '216.bo1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [9436, -1, 4567, -1, 8609, -1, 4132, -1], 'generators': [54, 2, 432], 'label': '1296.3190.72.cy1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.i1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.p1.a1', 'old_label': '72.cy1.a1', 'projective_image': '432.598', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.cy1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 71060337
    {'ambient': '1296.3190', 'aut_centralizer_order': 48, 'aut_label': '72.cz1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '12.4', 'aut_weyl_index': 288, 'centralizer': '36.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bm1.a1', '24.bo1.a1', '36.bu1.a1', '36.dq1.a1', '36.dq1.b1'], 'contains': ['144.b1.a1', '216.bl1.a1', '216.bp1.a1'], 'core': '144.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [9083, -1, 4521, -1, 8497, -1, 4046, -1], 'generators': [54, 2, 144], 'label': '1296.3190.72.cz1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.i1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.q1.a1', 'old_label': '72.cz1.a1', 'projective_image': '432.598', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.cz1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 71060338
    {'ambient': '1296.3190', 'aut_centralizer_order': 24, 'aut_label': '72.da1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '12.4', 'aut_weyl_index': 288, 'centralizer': '36.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bn1.a1', '24.bo1.a1', '36.bv1.a1', '36.dr1.a1', '36.dr1.b1'], 'contains': ['144.g1.a1', '216.bl1.a1', '216.bq1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [9647, -1, 4692, -1, 9193, -1, 4336, -1], 'generators': [54, 2, 576], 'label': '1296.3190.72.da1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.i1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.r1.a1', 'old_label': '72.da1.a1', 'projective_image': '432.598', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.da1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 71060339
    {'ambient': '1296.3190', 'aut_centralizer_order': 24, 'aut_label': '72.da1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '12.4', 'aut_weyl_index': 288, 'centralizer': '36.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bn1.a2', '24.bo1.a1', '36.bv1.a1', '36.dr1.a2', '36.dr1.b2'], 'contains': ['144.g1.a1', '216.bl1.a1', '216.bq1.a2'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [9647, -1, 4663, -1, 9193, -1, 4379, -1], 'generators': [54, 2, 1008], 'label': '1296.3190.72.da1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.i1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.r1.a1', 'old_label': '72.da1.a2', 'projective_image': '432.598', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.da1.a2', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 71060340
    {'ambient': '1296.3190', 'aut_centralizer_order': 48, 'aut_label': '72.db1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '12.4', 'aut_weyl_index': 288, 'centralizer': '72.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bl1.a1', '24.bp1.a1', '36.bw1.a1', '36.dy1.a1', '36.dy1.b1'], 'contains': ['144.e1.a1', '216.bm1.a1', '216.bo1.a1'], 'core': '144.e1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [9505, -1, 3411, -1, 9115, -1, 3955, -1], 'generators': [54, 12, 432], 'label': '1296.3190.72.db1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.j1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.p1.a1', 'old_label': '72.db1.a1', 'projective_image': '1296.3190', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.db1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 71060341
    {'ambient': '1296.3190', 'aut_centralizer_order': 24, 'aut_label': '72.dc1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '12.4', 'aut_weyl_index': 288, 'centralizer': '72.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bl1.a1', '24.bq1.a1', '36.bx1.a1'], 'contains': ['144.l1.a1', '216.bn1.a1', '216.bo1.a1'], 'core': '432.b1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [7570, -1, 3871, -1, 7469, -1, 5078, -1], 'generators': [54, 14, 432], 'label': '1296.3190.72.dc1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.be1.a1', 'old_label': '72.dc1.a1', 'projective_image': '1296.3190', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.dc1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 71060342
    {'ambient': '1296.3190', 'aut_centralizer_order': 2, 'aut_label': '6.bf1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '288.1040', 'aut_weyl_index': 12, 'centralizer': '216.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.g1.a1'], 'contains': ['12.bc1.a1', '12.bk1.a1', '12.bq1.a1', '18.bp1.a1', '18.bw1.a1', '18.bz1.a1'], 'core': '36.i1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [3285, -1, 9297, -1, 2488, -1, 8426, -1], 'generators': [9, 432, 156, 108, 2, 216], 'label': '1296.3190.6.bf1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.bf1.a1', 'old_label': '6.bf1.a1', 'projective_image': '216.162', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.bf1.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 71060343
    {'ambient': '1296.3190', 'aut_centralizer_order': 48, 'aut_label': '72.dd1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '12.4', 'aut_weyl_index': 288, 'centralizer': '72.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bm1.a1', '24.bp1.a1', '36.by1.a1', '36.dz1.a1', '36.dz1.b1'], 'contains': ['144.f1.a1', '216.bm1.a1', '216.bp1.a1'], 'core': '144.f1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [9120, -1, 3382, -1, 9064, -1, 3847, -1], 'generators': [54, 12, 144], 'label': '1296.3190.72.dd1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.j1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.q1.a1', 'old_label': '72.dd1.a1', 'projective_image': '1296.3190', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.dd1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 71060344
    {'ambient': '1296.3190', 'aut_centralizer_order': 24, 'aut_label': '72.de1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '12.4', 'aut_weyl_index': 288, 'centralizer': '72.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bm1.a1', '24.bq1.a1', '36.bz1.a1'], 'contains': ['144.p1.a1', '216.bn1.a1', '216.bp1.a1'], 'core': '432.c1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [7523, -1, 3802, -1, 7418, -1, 4978, -1], 'generators': [54, 14, 144], 'label': '1296.3190.72.de1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bf1.a1', 'old_label': '72.de1.a1', 'projective_image': '1296.3190', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.de1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 71060345
    {'ambient': '1296.3190', 'aut_centralizer_order': 24, 'aut_label': '72.df1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '12.4', 'aut_weyl_index': 288, 'centralizer': '72.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bn1.a1', '24.bp1.a1', '36.ca1.a1', '36.ea1.a1', '36.ea1.b1'], 'contains': ['144.u1.a1', '216.bm1.a1', '216.bq1.a1'], 'core': '432.d1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [9860, -1, 3441, -1, 9372, -1, 4467, -1], 'generators': [54, 12, 576], 'label': '1296.3190.72.df1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.j1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.r1.a1', 'old_label': '72.df1.a1', 'projective_image': '1296.3190', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.df1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 71060346
    {'ambient': '1296.3190', 'aut_centralizer_order': 24, 'aut_label': '72.df1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '12.4', 'aut_weyl_index': 288, 'centralizer': '72.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bn1.a2', '24.bp1.a1', '36.ca1.a1', '36.ea1.a2', '36.ea1.b2'], 'contains': ['144.u1.a1', '216.bm1.a1', '216.bq1.a2'], 'core': '432.d1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [9860, -1, 3470, -1, 9372, -1, 4509, -1], 'generators': [54, 12, 1008], 'label': '1296.3190.72.df1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.j1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.r1.a1', 'old_label': '72.df1.a2', 'projective_image': '1296.3190', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.df1.a2', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 71060347
    {'ambient': '1296.3190', 'aut_centralizer_order': 12, 'aut_label': '72.dg1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '12.4', 'aut_weyl_index': 288, 'centralizer': '72.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bn1.a1', '24.bq1.a1', '36.cb1.a1'], 'contains': ['144.bd1.a1', '216.bn1.a1', '216.bq1.a1'], 'core': '1296.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [7608, -1, 3768, -1, 7570, -1, 5120, -1], 'generators': [54, 14, 576], 'label': '1296.3190.72.dg1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bg1.a1', 'old_label': '72.dg1.a1', 'projective_image': '1296.3190', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.dg1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 71060348
    {'ambient': '1296.3190', 'aut_centralizer_order': 12, 'aut_label': '72.dg1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '12.4', 'aut_weyl_index': 288, 'centralizer': '72.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bn1.a2', '24.bq1.a1', '36.cb1.a1'], 'contains': ['144.bd1.a1', '216.bn1.a1', '216.bq1.a2'], 'core': '1296.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [7608, -1, 3842, -1, 7570, -1, 5163, -1], 'generators': [54, 14, 1008], 'label': '1296.3190.72.dg1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bg1.a1', 'old_label': '72.dg1.a2', 'projective_image': '1296.3190', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.dg1.a2', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 71060349
    {'ambient': '1296.3190', 'aut_centralizer_order': 48, 'aut_label': '72.dh1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '36.10', 'aut_weyl_index': 96, 'centralizer': '36.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bo1.a1', '24.bp1.a1', '24.bq1.a1', '36.h1.a1', '36.ds1.a1', '36.ds1.b1'], 'contains': ['144.d1.a1', '216.bo1.a1', '216.bp1.a1', '216.bq1.a1', '216.bq1.a2'], 'core': '144.d1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [9384, -1, 4463, -1, 8567, -1, 4301, -1], 'generators': [54, 144, 432], 'label': '1296.3190.72.dh1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.h1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '72.dh1.a1', 'projective_image': '1296.3190', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.dh1.a1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 71060350
    {'ambient': '1296.3190', 'aut_centralizer_order': 16, 'aut_label': '72.di1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '12.4', 'aut_weyl_index': 288, 'centralizer': '108.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.br1.a1', '24.bs1.a1', '24.bt1.a1', '36.cc1.a1', '36.dp1.a1', '36.dp1.b1'], 'contains': ['144.a1.a1', '216.br1.a1', '216.bs1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [7811, -1, 4966, -1, 5848, -1, 5339, -1], 'generators': [45, 2, 432], 'label': '1296.3190.72.di1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.h1.a1', 'old_label': '72.di1.a1', 'projective_image': '432.598', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.di1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 71060351
    {'ambient': '1296.3190', 'aut_centralizer_order': 16, 'aut_label': '72.dj1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '12.4', 'aut_weyl_index': 288, 'centralizer': '108.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.br1.a1', '24.bu1.a1', '24.bv1.a1', '36.cd1.a1', '36.dq1.a1', '36.dq1.b1'], 'contains': ['144.b1.a1', '216.br1.a1', '216.bt1.a1'], 'core': '144.b1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [7676, -1, 4810, -1, 5798, -1, 5274, -1], 'generators': [45, 2, 144], 'label': '1296.3190.72.dj1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.i1.a1', 'old_label': '72.dj1.a1', 'projective_image': '432.598', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.dj1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 71060352
    {'ambient': '1296.3190', 'aut_centralizer_order': 16, 'aut_label': '72.dk1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '12.4', 'aut_weyl_index': 288, 'centralizer': '108.x1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bs1.a1', '24.bu1.a1', '24.bw1.a1', '24.bw1.a2', '36.ce1.a1', '36.dx1.a1', '36.dx1.b1'], 'contains': ['144.c1.a1', '216.br1.a1', '216.bu1.a1'], 'core': '144.c1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [8268, -1, 2072, -1, 6266, -1, 4936, -1], 'generators': [45, 2, 12], 'label': '1296.3190.72.dk1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.s1.a1', 'old_label': '72.dk1.a1', 'projective_image': '432.598', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.dk1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 71060353
    {'ambient': '1296.3190', 'aut_centralizer_order': 4, 'aut_label': '6.bg1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '288.1040', 'aut_weyl_index': 12, 'centralizer': '216.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.f1.a1', '3.d1.a1'], 'contains': ['12.g1.a1', '12.bf1.a1', '12.bs1.a1', '18.bq1.a1', '18.br1.a1', '18.ca1.a1'], 'core': '12.g1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4879, -1, 6040, -1, 5500, -1, 5986, -1], 'generators': [111, 144, 12, 54, 2, 216], 'label': '1296.3190.6.bg1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.d1.a1', 'old_label': '6.bg1.a1', 'projective_image': '216.162', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.bg1.a1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 71060354
    {'ambient': '1296.3190', 'aut_centralizer_order': 8, 'aut_label': '72.dl1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '12.4', 'aut_weyl_index': 288, 'centralizer': '108.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.br1.a1', '24.bw1.a1', '24.bx1.a1', '36.cf1.a1', '36.dr1.a1', '36.dr1.b2'], 'contains': ['144.g1.a1', '216.br1.a1', '216.bv1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [8011, -1, 5140, -1, 5933, -1, 5452, -1], 'generators': [45, 2, 576], 'label': '1296.3190.72.dl1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.j1.a1', 'old_label': '72.dl1.a1', 'projective_image': '432.598', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.dl1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 71060355
    {'ambient': '1296.3190', 'aut_centralizer_order': 8, 'aut_label': '72.dl1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '12.4', 'aut_weyl_index': 288, 'centralizer': '108.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.br1.a1', '24.bw1.a2', '24.bx1.a2', '36.cf1.a1', '36.dr1.a2', '36.dr1.b1'], 'contains': ['144.g1.a1', '216.br1.a1', '216.bv1.a2'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [8011, -1, 5170, -1, 5933, -1, 5410, -1], 'generators': [45, 2, 1008], 'label': '1296.3190.72.dl1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.j1.a1', 'old_label': '72.dl1.a2', 'projective_image': '432.598', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.dl1.a2', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 71060356
    {'ambient': '1296.3190', 'aut_centralizer_order': 8, 'aut_label': '72.dm1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '12.4', 'aut_weyl_index': 288, 'centralizer': '216.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bs1.a1', '24.bv1.a1', '24.bx1.a1', '24.bx1.a2', '36.cg1.a1'], 'contains': ['144.h1.a1', '216.br1.a1', '216.bw1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [2691, -1, 6321, -1, 5102, -1, 6745, -1], 'generators': [45, 2, 444], 'label': '1296.3190.72.dm1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.cg1.a1', 'old_label': '72.dm1.a1', 'projective_image': '432.598', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.dm1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 71060357
    {'ambient': '1296.3190', 'aut_centralizer_order': 8, 'aut_label': '72.dn1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '12.4', 'aut_weyl_index': 288, 'centralizer': '216.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bt1.a1', '24.bu1.a1', '24.bx1.a1', '24.bx1.a2', '36.ch1.a1'], 'contains': ['144.i1.a1', '216.br1.a1', '216.bx1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [5514, -1, 6520, -1, 5052, -1, 7055, -1], 'generators': [45, 2, 156], 'label': '1296.3190.72.dn1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.ch1.a1', 'old_label': '72.dn1.a1', 'projective_image': '432.598', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.dn1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 71060358
    {'ambient': '1296.3190', 'aut_centralizer_order': 4, 'aut_label': '72.do1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '12.4', 'aut_weyl_index': 288, 'centralizer': '216.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bt1.a1', '24.bv1.a1', '24.bw1.a1', '24.bx1.a2', '36.ci1.a1'], 'contains': ['144.j1.a1', '216.br1.a1', '216.by1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [3349, -1, 6416, -1, 5001, -1, 6984, -1], 'generators': [45, 2, 588], 'label': '1296.3190.72.do1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.ci1.a1', 'old_label': '72.do1.a1', 'projective_image': '432.598', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.do1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 71060359
    {'ambient': '1296.3190', 'aut_centralizer_order': 4, 'aut_label': '72.do1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '12.4', 'aut_weyl_index': 288, 'centralizer': '216.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bt1.a1', '24.bv1.a1', '24.bw1.a2', '24.bx1.a1', '36.ci1.a1'], 'contains': ['144.j1.a1', '216.br1.a1', '216.by1.a2'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [3349, -1, 6549, -1, 5001, -1, 7097, -1], 'generators': [45, 2, 1020], 'label': '1296.3190.72.do1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.ci1.a1', 'old_label': '72.do1.a2', 'projective_image': '432.598', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.do1.a2', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 71060360
    {'ambient': '1296.3190', 'aut_centralizer_order': 16, 'aut_label': '72.dp1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '36.10', 'aut_weyl_index': 96, 'centralizer': '108.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.br1.a1', '24.by1.a1', '36.cj1.a1', '36.ds1.a1', '36.ds1.b1'], 'contains': ['144.d1.a1', '216.bs1.a1', '216.bt1.a1', '216.bv1.a1', '216.bv1.a2'], 'core': '144.d1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [7778, -1, 4941, -1, 5890, -1, 5374, -1], 'generators': [45, 144, 432], 'label': '1296.3190.72.dp1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.k1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.l1.a1', 'old_label': '72.dp1.a1', 'projective_image': '1296.3190', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.dp1.a1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 71060361
    {'ambient': '1296.3190', 'aut_centralizer_order': 16, 'aut_label': '72.dq1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '36.10', 'aut_weyl_index': 96, 'centralizer': '216.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bs1.a1', '24.by1.a1', '36.ck1.a1', '36.dy1.a1', '36.dy1.b1'], 'contains': ['144.e1.a1', '216.bs1.a1', '216.bu1.a1', '216.bw1.a1'], 'core': '144.e1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [7980, -1, 3610, -1, 6111, -1, 5042, -1], 'generators': [45, 12, 432], 'label': '1296.3190.72.dq1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.k1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.p1.a1', 'old_label': '72.dq1.a1', 'projective_image': '1296.3190', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.dq1.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 71060362
    {'ambient': '1296.3190', 'aut_centralizer_order': 8, 'aut_label': '72.dr1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '36.10', 'aut_weyl_index': 96, 'centralizer': '216.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bt1.a1', '24.by1.a1', '36.cl1.a1'], 'contains': ['144.m1.a1', '216.bs1.a1', '216.bx1.a1', '216.by1.a1', '216.by1.a2'], 'core': '432.b1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [5380, -1, 6604, -1, 4894, -1, 7919, -1], 'generators': [45, 156, 432], 'label': '1296.3190.72.dr1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.k1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bk1.a1', 'old_label': '72.dr1.a1', 'projective_image': '1296.3190', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.dr1.a1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 71060363
    {'ambient': '1296.3190', 'aut_centralizer_order': 16, 'aut_label': '72.ds1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '36.10', 'aut_weyl_index': 96, 'centralizer': '216.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bu1.a1', '24.by1.a1', '36.cm1.a1', '36.dz1.a1', '36.dz1.b1'], 'contains': ['144.f1.a1', '216.bt1.a1', '216.bu1.a1', '216.bx1.a1'], 'core': '144.f1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [7876, -1, 3582, -1, 6077, -1, 5014, -1], 'generators': [45, 12, 144], 'label': '1296.3190.72.ds1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.k1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.q1.a1', 'old_label': '72.ds1.a1', 'projective_image': '1296.3190', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ds1.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 71060364
    {'ambient': '1296.3190', 'aut_centralizer_order': 4, 'aut_label': '6.bh1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '288.1040', 'aut_weyl_index': 12, 'centralizer': '216.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.g1.a1', '3.d1.a1'], 'contains': ['12.g1.a1', '12.bl1.a1', '12.br1.a1', '18.bu1.a1', '18.bv1.a1', '18.bw1.a1', '18.cb1.a1'], 'core': '12.g1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3801, -1, 8053, -1, 3293, -1, 6742, -1], 'generators': [9, 144, 12, 108, 2, 216], 'label': '1296.3190.6.bh1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.d1.a1', 'old_label': '6.bh1.a1', 'projective_image': '216.162', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.bh1.a1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 71060365
    {'ambient': '1296.3190', 'aut_centralizer_order': 8, 'aut_label': '72.dt1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '36.10', 'aut_weyl_index': 96, 'centralizer': '216.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bv1.a1', '24.by1.a1', '36.cn1.a1'], 'contains': ['144.q1.a1', '216.bt1.a1', '216.bw1.a1', '216.by1.a1', '216.by1.a2'], 'core': '432.c1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [2884, -1, 6001, -1, 4860, -1, 7610, -1], 'generators': [45, 444, 144], 'label': '1296.3190.72.dt1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.k1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bm1.a1', 'old_label': '72.dt1.a1', 'projective_image': '1296.3190', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.dt1.a1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 71060366
    {'ambient': '1296.3190', 'aut_centralizer_order': 8, 'aut_label': '72.du1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '36.10', 'aut_weyl_index': 96, 'centralizer': '216.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bw1.a1', '24.by1.a1', '36.co1.a1', '36.ea1.a1', '36.ea1.b2'], 'contains': ['144.u1.a1', '216.bu1.a1', '216.bv1.a1', '216.by1.a1'], 'core': '432.d1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [8226, -1, 3682, -1, 6145, -1, 5707, -1], 'generators': [45, 12, 576], 'label': '1296.3190.72.du1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.k1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.r1.a1', 'old_label': '72.du1.a1', 'projective_image': '1296.3190', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.du1.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 71060367
    {'ambient': '1296.3190', 'aut_centralizer_order': 8, 'aut_label': '72.du1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '36.10', 'aut_weyl_index': 96, 'centralizer': '216.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bw1.a2', '24.by1.a1', '36.co1.a1', '36.ea1.a2', '36.ea1.b1'], 'contains': ['144.u1.a1', '216.bu1.a1', '216.bv1.a2', '216.by1.a2'], 'core': '432.d1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [8226, -1, 3702, -1, 6145, -1, 5736, -1], 'generators': [45, 12, 1008], 'label': '1296.3190.72.du1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.k1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.r1.a1', 'old_label': '72.du1.a2', 'projective_image': '1296.3190', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.du1.a2', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 71060368
    {'ambient': '1296.3190', 'aut_centralizer_order': 8, 'aut_label': '72.dv1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '18.4', 'aut_weyl_index': 192, 'centralizer': '216.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bx1.a1', '24.by1.a1', '36.cp1.a1'], 'contains': ['144.bf1.a1', '216.bv1.a1', '216.bw1.a1', '216.bx1.a1', '216.by1.a2'], 'core': '1296.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [3463, -1, 6574, -1, 4928, -1, 7867, -1], 'generators': [45, 444, 576], 'label': '1296.3190.72.dv1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.k1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bo1.a1', 'old_label': '72.dv1.a1', 'projective_image': '1296.3190', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.dv1.a1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 71060369
    {'ambient': '1296.3190', 'aut_centralizer_order': 8, 'aut_label': '72.dv1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '18.4', 'aut_weyl_index': 192, 'centralizer': '216.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bx1.a2', '24.by1.a1', '36.cp1.a1'], 'contains': ['144.bf1.a1', '216.bv1.a2', '216.bw1.a1', '216.bx1.a1', '216.by1.a1'], 'core': '1296.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [3463, -1, 6496, -1, 4928, -1, 7839, -1], 'generators': [45, 444, 1008], 'label': '1296.3190.72.dv1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.k1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bo1.a1', 'old_label': '72.dv1.a2', 'projective_image': '1296.3190', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.dv1.a2', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 71060370
    {'ambient': '1296.3190', 'aut_centralizer_order': 16, 'aut_label': '81.a1', 'aut_quo_index': None, 'aut_stab_index': 27, 'aut_weyl_group': '8.5', 'aut_weyl_index': 432, 'centralizer': '108.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['27.a1.a1', '27.b1.a1', '27.c1.a1', '27.d1.a1'], 'contains': ['162.a1.a1', '162.b1.a1', '162.c1.a1', '162.d1.a1', '162.e1.a1', '162.f1.a1', '162.g1.a1'], 'core': '648.a1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [2656, -1, 7737, -1, 4739, -1, 7999, -1], 'generators': [3, 18, 108], 'label': '1296.3190.81.a1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1.a1', 'old_label': '81.a1.a1', 'projective_image': '648.731', '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: 71060371
    {'ambient': '1296.3190', 'aut_centralizer_order': 288, 'aut_label': '108.a1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '12.4', 'aut_weyl_index': 288, 'centralizer': '6.f1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['36.a1.a1', '36.b1.a1', '36.c1.a1', '36.t1.a1', '36.u1.a1', '36.v1.a1', '36.w1.a1', '54.m1.a1', '54.n1.a1', '54.o1.a1'], 'contains': ['216.d1.a1', '216.e1.a1', '216.e1.b1', '324.a1.a1'], 'core': '108.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6388, 8310, 3952, 1796, 7006, 2379, 2967, 2952], 'generators': [3, 216, 12], 'label': '1296.3190.108.a1.a1', 'mobius_quo': 0, 'mobius_sub': -18, 'normal_closure': '108.a1.a1', 'normal_contained_in': ['36.a1.a1', '36.b1.a1', '36.c1.a1'], 'normal_contains': ['216.d1.a1', '216.e1.a1', '216.e1.b1'], 'normalizer': '1.a1.a1', 'old_label': '108.a1.a1', 'projective_image': '648.731', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.a1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 71060372
    {'ambient': '1296.3190', 'aut_centralizer_order': 288, 'aut_label': '108.b1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '12.4', 'aut_weyl_index': 288, 'centralizer': '12.a1.a1', 'complements': ['12.ce1.a1', '12.cg1.a1', '12.cg1.a2', '12.ce1.b1', '12.cg1.b1', '12.cg1.b2'], 'conjugacy_class_count': 1, 'contained_in': ['36.d1.a1', '36.e1.a1', '36.f1.a1', '36.be1.a1', '36.bf1.a1', '36.bg1.a1', '36.bh1.a1', '54.d1.a1', '54.x1.a1', '54.y1.a1'], 'contains': ['216.c1.a1', '216.be1.a1', '324.b1.a1'], 'core': '108.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3491, 4795, 7916, 5869, 3731, 5408, 5306, 5693], 'generators': [18, 216, 144], 'label': '1296.3190.108.b1.a1', 'mobius_quo': 0, 'mobius_sub': -18, 'normal_closure': '108.b1.a1', 'normal_contained_in': ['36.d1.a1', '36.e1.a1', '36.f1.a1'], 'normal_contains': ['216.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '108.b1.a1', 'projective_image': '648.731', 'quotient_action_image': '2.1', 'quotient_action_kernel': '54.12', 'quotient_action_kernel_order': 54, 'quotient_fusion': None, 'short_label': '108.b1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 71060373
    {'ambient': '1296.3190', 'aut_centralizer_order': 288, 'aut_label': '108.c1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '12.4', 'aut_weyl_index': 288, 'centralizer': '12.b1.a1', 'complements': ['12.cb1.a1', '12.cd1.a1', '12.cd1.b1', '12.cb1.b1', '12.cd1.c1', '12.cd1.d1', '12.cf1.a1', '12.cg1.a1', '12.cg1.a2', '12.cf1.b1', '12.cg1.b1', '12.cg1.b2'], 'conjugacy_class_count': 1, 'contained_in': ['36.i1.a1', '36.j1.a1', '36.k1.a1', '36.cy1.a1', '36.da1.a1', '36.db1.a1', '36.dc1.a1', '54.j1.a1', '54.s1.a1', '54.bc1.a1'], 'contains': ['216.b1.a1', '324.f1.a1'], 'core': '108.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [882, 2544, 9437, 8478, 1014, 6959, 8984, 7289], 'generators': [108, 216, 432], 'label': '1296.3190.108.c1.a1', 'mobius_quo': 0, 'mobius_sub': -18, 'normal_closure': '108.c1.a1', 'normal_contained_in': ['36.i1.a1', '36.j1.a1', '36.k1.a1'], 'normal_contains': ['216.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '108.c1.a1', 'projective_image': '648.731', 'quotient_action_image': '2.1', 'quotient_action_kernel': '54.12', 'quotient_action_kernel_order': 54, 'quotient_fusion': None, 'short_label': '108.c1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 71060374
    {'ambient': '1296.3190', 'aut_centralizer_order': 288, 'aut_label': '108.d1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '4.2', 'aut_weyl_index': 864, 'centralizer': '3.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.a1.a1', '36.m1.a1', '36.n1.a1', '36.o1.a1', '54.a1.a1', '54.e1.a1', '54.i1.a1'], 'contains': ['216.a1.a1', '216.q1.a1', '216.q1.b1', '324.a1.a1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6186, -1, 5561, -1, 6885, -1, 3213, -1], 'generators': [3, 216, 2], 'label': '1296.3190.108.d1.a1', 'mobius_quo': None, 'mobius_sub': -18, 'normal_closure': '36.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '108.d1.a1', 'projective_image': '216.162', '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: 71060375
    {'ambient': '1296.3190', 'aut_centralizer_order': 216, 'aut_label': '8.a1', 'aut_quo_index': 168, 'aut_stab_index': 1, 'aut_weyl_group': '16.14', 'aut_weyl_index': 216, 'centralizer': '8.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '4.b1.a1', '4.c1.a1', '4.d1.a1', '4.e1.a1', '4.f1.a1', '4.g1.a1'], 'contains': ['16.a1.a1', '24.a1.a1', '24.b1.a1', '24.c1.a1', '24.d1.a1', '24.h1.a1', '24.i1.a1', '24.j1.a1', '24.k1.a1', '24.l1.a1', '24.m1.a1', '24.n1.a1', '24.o1.a1', '24.p1.a1', '24.q1.a1', '24.r1.a1'], 'core': '8.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3154, 5834, 7174, 4604, 3452, 5540, 6828, 4817], 'generators': [216, 432, 2, 12, 144], 'label': '1296.3190.8.a1.a1', 'mobius_quo': -1, 'mobius_sub': -8, 'normal_closure': '8.a1.a1', 'normal_contained_in': ['4.a1.a1', '4.b1.a1', '4.d1.a1', '4.c1.a1', '4.e1.a1', '4.f1.a1', '4.g1.a1'], 'normal_contains': ['16.a1.a1', '24.a1.a1', '24.c1.a1', '24.b1.a1', '24.d1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.a1.a1', 'projective_image': '216.162', 'quotient_action_image': '8.5', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '8.a1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 71060376
    {'ambient': '1296.3190', 'aut_centralizer_order': 288, 'aut_label': '108.e1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '4.2', 'aut_weyl_index': 864, 'centralizer': '6.k1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.b1.a1', '36.m1.a1', '36.p1.a1', '36.q1.a1', '54.b1.a1', '54.f1.a1', '54.j1.a1'], 'contains': ['216.b1.a1', '216.r1.a1', '216.r1.b1', '324.a1.a1'], 'core': '216.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6050, -1, 5885, -1, 6732, -1, 3085, -1], 'generators': [3, 216, 432], 'label': '1296.3190.108.e1.a1', 'mobius_quo': None, 'mobius_sub': -6, 'normal_closure': '36.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '108.e1.a1', 'projective_image': '648.731', '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': '2.1'}
  • id: 71060377
    {'ambient': '1296.3190', 'aut_centralizer_order': 288, 'aut_label': '108.f1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '4.2', 'aut_weyl_index': 864, 'centralizer': '6.m1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.c1.a1', '36.n1.a1', '36.p1.a1', '36.r1.a1', '54.d1.a1', '54.g1.a1', '54.k1.a1'], 'contains': ['216.c1.a1', '216.s1.a1', '216.s1.b1', '324.a1.a1'], 'core': '216.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6149, -1, 5590, -1, 6834, -1, 2999, -1], 'generators': [3, 216, 144], 'label': '1296.3190.108.f1.a1', 'mobius_quo': None, 'mobius_sub': -6, 'normal_closure': '36.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '108.f1.a1', 'projective_image': '648.731', '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': '2.1'}
  • id: 71060378
    {'ambient': '1296.3190', 'aut_centralizer_order': 144, 'aut_label': '108.g1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '4.2', 'aut_weyl_index': 864, 'centralizer': '6.k1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.m1.a1', '36.r1.a1', '36.s1.a1', '36.t1.a1', '54.c1.a1'], 'contains': ['216.f1.a1', '216.t1.a1', '216.t1.b1', '324.a1.a1'], 'core': '648.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [6292, -1, 1988, -1, 6966, -1, 1603, -1], 'generators': [3, 216, 434], 'label': '1296.3190.108.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.k1.a1', 'old_label': '108.g1.a1', 'projective_image': '648.731', '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': '1.1'}
  • id: 71060379
    {'ambient': '1296.3190', 'aut_centralizer_order': 144, 'aut_label': '108.h1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '4.2', 'aut_weyl_index': 864, 'centralizer': '6.m1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.n1.a1', '36.q1.a1', '36.s1.a1', '36.u1.a1', '54.l1.a1'], 'contains': ['216.g1.a1', '216.u1.a1', '216.u1.b1', '324.a1.a1'], 'core': '648.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [6104, -1, 5923, -1, 6783, -1, 3042, -1], 'generators': [3, 216, 146], 'label': '1296.3190.108.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.m1.a1', 'old_label': '108.h1.a1', 'projective_image': '648.731', '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': '1.1'}
  • id: 71060380
    {'ambient': '1296.3190', 'aut_centralizer_order': 144, 'aut_label': '108.i1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '4.2', 'aut_weyl_index': 864, 'centralizer': '12.q1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.o1.a1', '36.p1.a1', '36.s1.a1', '36.v1.a1', '54.h1.a1'], 'contains': ['216.i1.a1', '216.v1.a1', '216.v1.b1', '324.a1.a1'], 'core': '648.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [6486, -1, 5325, -1, 7248, -1, 3341, -1], 'generators': [3, 216, 576], 'label': '1296.3190.108.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.l1.a1', 'old_label': '108.i1.a1', 'projective_image': '648.731', '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': '2.1'}
  • id: 71060381
    {'ambient': '1296.3190', 'aut_centralizer_order': 72, 'aut_label': '108.j1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '4.2', 'aut_weyl_index': 864, 'centralizer': '12.q1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.o1.a1', '36.q1.a1', '36.r1.a1', '36.s1.a1', '36.w1.a1'], 'contains': ['216.l1.a1', '216.w1.a1', '216.w1.b1', '324.a1.a1'], 'core': '648.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [6347, -1, 2898, -1, 7198, -1, 2465, -1], 'generators': [3, 216, 578], 'label': '1296.3190.108.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.q1.a1', 'old_label': '108.j1.a1', 'projective_image': '648.731', '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': '1.1'}
  • id: 71060382
    {'ambient': '1296.3190', 'aut_centralizer_order': 288, 'aut_label': '108.k1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '4.2', 'aut_weyl_index': 864, 'centralizer': '6.n1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.d1.a1', '36.x1.a1', '36.y1.a1', '36.z1.a1', '54.a1.a1', '54.p1.a1', '54.t1.a1'], 'contains': ['216.a1.a1', '216.x1.a1', '324.b1.a1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4344, -1, 7462, -1, 3974, -1, 5606, -1], 'generators': [18, 216, 2], 'label': '1296.3190.108.k1.a1', 'mobius_quo': None, 'mobius_sub': -18, 'normal_closure': '36.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1.a1', 'old_label': '108.k1.a1', 'projective_image': '216.162', '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': '2.1'}
  • id: 71060383
    {'ambient': '1296.3190', 'aut_centralizer_order': 288, 'aut_label': '108.l1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '4.2', 'aut_weyl_index': 864, 'centralizer': '6.n1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.e1.a1', '36.x1.a1', '36.ba1.a1', '36.bb1.a1', '54.b1.a1', '54.s1.a1', '54.u1.a1'], 'contains': ['216.b1.a1', '216.y1.a1', '324.b1.a1'], 'core': '216.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4030, -1, 7300, -1, 3872, -1, 5521, -1], 'generators': [18, 216, 432], 'label': '1296.3190.108.l1.a1', 'mobius_quo': None, 'mobius_sub': -6, 'normal_closure': '36.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1.a1', 'old_label': '108.l1.a1', 'projective_image': '648.731', '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: 71060384
    {'ambient': '1296.3190', 'aut_centralizer_order': 288, 'aut_label': '108.m1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '4.2', 'aut_weyl_index': 864, 'centralizer': '12.v1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.f1.a1', '36.y1.a1', '36.ba1.a1', '36.bc1.a1', '54.m1.a1', '54.q1.a1', '54.v1.a1'], 'contains': ['216.d1.a1', '216.z1.a1', '324.b1.a1'], 'core': '216.d1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5467, -1, 5856, -1, 4512, -1, 4617, -1], 'generators': [18, 216, 12], 'label': '1296.3190.108.m1.a1', 'mobius_quo': None, 'mobius_sub': -6, 'normal_closure': '36.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1.a1', 'old_label': '108.m1.a1', 'projective_image': '648.731', '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': '4.2'}
  • id: 71060385
    {'ambient': '1296.3190', 'aut_centralizer_order': 144, 'aut_label': '108.n1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '4.2', 'aut_weyl_index': 864, 'centralizer': '6.n1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.x1.a1', '36.bc1.a1', '36.bd1.a1', '36.be1.a1', '54.c1.a1'], 'contains': ['216.f1.a1', '216.ba1.a1', '216.ba1.b1', '324.b1.a1'], 'core': '648.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [3296, -1, 5172, -1, 4665, -1, 2380, -1], 'generators': [18, 216, 434], 'label': '1296.3190.108.n1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.n1.a1', 'old_label': '108.n1.a1', 'projective_image': '648.731', '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': '1.1'}
  • id: 71060386
    {'ambient': '1296.3190', 'aut_centralizer_order': 36, 'aut_label': '8.b1', 'aut_quo_index': 2, 'aut_stab_index': 2, 'aut_weyl_group': '48.51', 'aut_weyl_index': 72, 'centralizer': '24.a1.a1', 'complements': ['162.d1.a1', '162.g1.a1', '162.e1.a1', '162.f1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '4.h1.a1', '4.i1.a1'], 'contains': ['16.a1.a1', '24.e1.a1', '24.f1.a1', '24.g1.a1', '24.s1.a1', '24.t1.a1', '24.u1.a1', '24.v1.a1', '24.w1.a1'], 'core': '8.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8752, 9207, 1624, 2426, 9194, 737, 2063, 1104], 'generators': [3, 12, 2, 144, 432], 'label': '1296.3190.8.b1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.b1.a1', 'normal_contained_in': ['4.a1.a1'], 'normal_contains': ['16.a1.a1', '24.f1.a1', '24.e1.a1', '24.g1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.b1.a1', 'projective_image': '432.598', 'quotient_action_image': '4.2', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '8.b1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 71060387
    {'ambient': '1296.3190', 'aut_centralizer_order': 144, 'aut_label': '108.o1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '4.2', 'aut_weyl_index': 864, 'centralizer': '12.v1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.y1.a1', '36.bb1.a1', '36.bd1.a1', '36.bf1.a1', '54.r1.a1'], 'contains': ['216.h1.a1', '216.bb1.a1', '324.b1.a1'], 'core': '648.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [424, -1, 6099, -1, 3319, -1, 5563, -1], 'generators': [18, 216, 14], 'label': '1296.3190.108.o1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.u1.a1', 'old_label': '108.o1.a1', 'projective_image': '648.731', '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: 71060388
    {'ambient': '1296.3190', 'aut_centralizer_order': 144, 'aut_label': '108.p1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '4.2', 'aut_weyl_index': 864, 'centralizer': '12.v1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.z1.a1', '36.ba1.a1', '36.bd1.a1', '36.bg1.a1', '54.w1.a1'], 'contains': ['216.j1.a1', '216.bc1.a1', '324.b1.a1'], 'core': '648.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [346, -1, 7492, -1, 3217, -1, 5649, -1], 'generators': [18, 216, 444], 'label': '1296.3190.108.p1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.v1.a1', 'old_label': '108.p1.a1', 'projective_image': '648.731', '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': '2.1'}
  • id: 71060389
    {'ambient': '1296.3190', 'aut_centralizer_order': 72, 'aut_label': '108.q1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '4.2', 'aut_weyl_index': 864, 'centralizer': '12.v1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.z1.a1', '36.bb1.a1', '36.bc1.a1', '36.bd1.a1', '36.bh1.a1'], 'contains': ['216.m1.a1', '216.bd1.a1', '216.bd1.b1', '324.b1.a1'], 'core': '648.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [108, -1, 6302, -1, 3268, -1, 4574, -1], 'generators': [18, 216, 446], 'label': '1296.3190.108.q1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.v1.a1', 'old_label': '108.q1.a1', 'projective_image': '648.731', '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': '1.1'}
  • id: 71060390
    {'ambient': '1296.3190', 'aut_centralizer_order': 96, 'aut_label': '108.r1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '4.2', 'aut_weyl_index': 864, 'centralizer': '18.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.bi1.a1', '36.bj1.a1', '36.bk1.a1', '36.bl1.a1', '54.a1.a1', '54.z1.a1', '54.bb1.a1'], 'contains': ['216.a1.a1', '216.bf1.a1', '324.c1.a1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [4564, -1, 7037, -1, 6034, -1, 4871, -1], 'generators': [9, 216, 2], 'label': '1296.3190.108.r1.a1', 'mobius_quo': None, 'mobius_sub': -6, 'normal_closure': '12.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '108.r1.a1', 'projective_image': '216.162', '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': '2.1'}
  • id: 71060391
    {'ambient': '1296.3190', 'aut_centralizer_order': 96, 'aut_label': '108.s1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '4.2', 'aut_weyl_index': 864, 'centralizer': '18.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.bi1.a1', '36.bm1.a1', '36.bn1.a1', '36.bo1.a1', '54.b1.a1', '54.ba1.a1', '54.bc1.a1'], 'contains': ['216.b1.a1', '216.bg1.a1', '324.c1.a1'], 'core': '216.b1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [4704, -1, 7097, -1, 5984, -1, 4828, -1], 'generators': [9, 216, 432], 'label': '1296.3190.108.s1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '12.h1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '108.s1.a1', 'projective_image': '648.731', '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': '2.1'}
  • id: 71060392
    {'ambient': '1296.3190', 'aut_centralizer_order': 48, 'aut_label': '108.t1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '4.2', 'aut_weyl_index': 864, 'centralizer': '18.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.bi1.a1', '36.bp1.a1', '36.bq1.a1', '36.br1.a1', '54.c1.a1'], 'contains': ['216.f1.a1', '216.bh1.a1', '216.bh1.b1', '324.c1.a1'], 'core': '648.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [5018, -1, 2589, -1, 6479, -1, 1390, -1], 'generators': [9, 216, 434], 'label': '1296.3190.108.t1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.d1.a1', 'old_label': '108.t1.a1', 'projective_image': '648.731', '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': '1.1'}
  • id: 71060393
    {'ambient': '1296.3190', 'aut_centralizer_order': 96, 'aut_label': '108.u1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '12.4', 'aut_weyl_index': 288, 'centralizer': '36.m1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.g1.a1', '36.bj1.a1', '36.bm1.a1', '36.bp1.a1', '54.d1.a1', '54.be1.a1', '54.bf1.a1'], 'contains': ['216.c1.a1', '216.bi1.a1', '324.c1.a1'], 'core': '216.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4804, -1, 6812, -1, 6227, -1, 4770, -1], 'generators': [9, 216, 144], 'label': '1296.3190.108.u1.a1', 'mobius_quo': None, 'mobius_sub': -6, 'normal_closure': '36.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '108.u1.a1', 'projective_image': '648.731', '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': '12.4'}
  • id: 71060394
    {'ambient': '1296.3190', 'aut_centralizer_order': 96, 'aut_label': '108.v1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '12.4', 'aut_weyl_index': 288, 'centralizer': '36.x1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.g1.a1', '36.bk1.a1', '36.bn1.a1', '36.bq1.a1', '54.m1.a1', '54.bd1.a1', '54.bg1.a1'], 'contains': ['216.d1.a1', '216.bj1.a1', '324.c1.a1'], 'core': '216.d1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5626, -1, 5639, -1, 6305, -1, 4542, -1], 'generators': [9, 216, 12], 'label': '1296.3190.108.v1.a1', 'mobius_quo': None, 'mobius_sub': -6, 'normal_closure': '36.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1.a1', 'old_label': '108.v1.a1', 'projective_image': '648.731', '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: 71060395
    {'ambient': '1296.3190', 'aut_centralizer_order': 48, 'aut_label': '108.w1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '12.4', 'aut_weyl_index': 288, 'centralizer': '72.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.g1.a1', '36.bl1.a1', '36.bo1.a1', '36.br1.a1', '54.bh1.a1'], 'contains': ['216.k1.a1', '216.bk1.a1', '324.c1.a1'], 'core': '648.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [4785, -1, 8148, -1, 5264, -1, 4903, -1], 'generators': [9, 216, 156], 'label': '1296.3190.108.w1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.bf1.a1', 'old_label': '108.w1.a1', 'projective_image': '648.731', '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': '12.4'}
  • id: 71060396
    {'ambient': '1296.3190', 'aut_centralizer_order': 96, 'aut_label': '108.x1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '4.2', 'aut_weyl_index': 864, 'centralizer': '18.s1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.bs1.a1', '36.bt1.a1', '36.bu1.a1', '36.bv1.a1', '54.e1.a1', '54.p1.a1', '54.z1.a1'], 'contains': ['216.a1.a1', '216.bl1.a1', '324.d1.a1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [6887, -1, 7220, -1, 6428, -1, 6156, -1], 'generators': [54, 216, 2], 'label': '1296.3190.108.x1.a1', 'mobius_quo': None, 'mobius_sub': -6, 'normal_closure': '12.i1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.d1.a1', 'old_label': '108.x1.a1', 'projective_image': '216.162', '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: 71060397
    {'ambient': '1296.3190', 'aut_centralizer_order': 2, 'aut_label': '2.e1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '1728.47915', 'aut_weyl_index': 2, 'centralizer': '216.a1.a1', 'complements': ['648.e1.a1', '648.b1.a1', '648.b1.b1', '648.d1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.b1.a1', '4.e1.a1', '4.g1.a1', '6.h1.a1', '6.v1.a1', '6.y1.a1', '6.z1.a1', '6.ba1.a1'], 'core': '2.e1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3825, 5079, 7854, 5651, 3501, 5368, 6633, 4878], 'generators': [111, 144, 12, 18, 432, 2, 216], 'label': '1296.3190.2.e1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.e1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.b1.a1', '4.e1.a1', '4.g1.a1', '6.h1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.e1.a1', 'projective_image': '216.162', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.e1.a1', 'subgroup_fusion': None, 'weyl_group': '216.162'}
  • id: 71060398
    {'ambient': '1296.3190', 'aut_centralizer_order': 36, 'aut_label': '8.b1', 'aut_quo_index': 2, 'aut_stab_index': 2, 'aut_weyl_group': '48.51', 'aut_weyl_index': 72, 'centralizer': '24.a1.a1', 'complements': ['162.d1.a1', '162.g1.a1', '162.e1.a1', '162.f1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '4.h1.b1', '4.i1.b1'], 'contains': ['16.a1.a1', '24.e1.b1', '24.f1.b1', '24.g1.b1', '24.s1.b1', '24.t1.b1', '24.u1.b1', '24.v1.b1', '24.w1.b1'], 'core': '8.b1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [8752, 9207, 2432, 225, 9194, 737, 2504, 175], 'generators': [219, 12, 2, 144, 432], 'label': '1296.3190.8.b1.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.b1.b1', 'normal_contained_in': ['4.a1.a1'], 'normal_contains': ['16.a1.a1', '24.f1.b1', '24.e1.b1', '24.g1.b1'], 'normalizer': '1.a1.a1', 'old_label': '8.b1.b1', 'projective_image': '432.598', 'quotient_action_image': '4.2', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '8.b1.b1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 71060399
    {'ambient': '1296.3190', 'aut_centralizer_order': 96, 'aut_label': '108.y1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '4.2', 'aut_weyl_index': 864, 'centralizer': '36.bs1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.bs1.a1', '36.bw1.a1', '36.by1.a1', '36.ca1.a1', '54.n1.a1', '54.q1.a1', '54.bd1.a1'], 'contains': ['216.d1.a1', '216.bm1.a1', '324.d1.a1'], 'core': '216.d1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [6938, -1, 5698, -1, 6530, -1, 5772, -1], 'generators': [54, 216, 12], 'label': '1296.3190.108.y1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '12.j1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.d1.a1', 'old_label': '108.y1.a1', 'projective_image': '648.731', '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': '4.2'}
  • id: 71060400
    {'ambient': '1296.3190', 'aut_centralizer_order': 48, 'aut_label': '108.z1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '4.2', 'aut_weyl_index': 864, 'centralizer': '36.bs1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.bs1.a1', '36.bx1.a1', '36.bz1.a1', '36.cb1.a1', '54.r1.a1'], 'contains': ['216.h1.a1', '216.bn1.a1', '324.d1.a1'], 'core': '648.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [6844, -1, 6044, -1, 6188, -1, 6412, -1], 'generators': [54, 216, 14], 'label': '1296.3190.108.z1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.z1.a1', 'old_label': '108.z1.a1', 'projective_image': '648.731', '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: 71060401
    {'ambient': '1296.3190', 'aut_centralizer_order': 96, 'aut_label': '108.ba1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '12.4', 'aut_weyl_index': 288, 'centralizer': '36.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.h1.a1', '36.bt1.a1', '36.bw1.a1', '36.bx1.a1', '54.f1.a1', '54.s1.a1', '54.ba1.a1'], 'contains': ['216.b1.a1', '216.bo1.a1', '324.d1.a1'], 'core': '216.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6758, -1, 7166, -1, 6358, -1, 6081, -1], 'generators': [54, 216, 432], 'label': '1296.3190.108.ba1.a1', 'mobius_quo': None, 'mobius_sub': -6, 'normal_closure': '36.h1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1.a1', 'old_label': '108.ba1.a1', 'projective_image': '648.731', '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': '12.4'}
  • id: 71060402
    {'ambient': '1296.3190', 'aut_centralizer_order': 96, 'aut_label': '108.bb1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '12.4', 'aut_weyl_index': 288, 'centralizer': '36.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.h1.a1', '36.bu1.a1', '36.by1.a1', '36.bz1.a1', '54.g1.a1', '54.x1.a1', '54.be1.a1'], 'contains': ['216.c1.a1', '216.bp1.a1', '324.d1.a1'], 'core': '216.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6722, -1, 7367, -1, 6331, -1, 6058, -1], 'generators': [54, 216, 144], 'label': '1296.3190.108.bb1.a1', 'mobius_quo': None, 'mobius_sub': -6, 'normal_closure': '36.h1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.d1.a1', 'old_label': '108.bb1.a1', 'projective_image': '648.731', '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': '12.4'}
  • id: 71060403
    {'ambient': '1296.3190', 'aut_centralizer_order': 48, 'aut_label': '108.bc1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '12.4', 'aut_weyl_index': 288, 'centralizer': '36.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.h1.a1', '36.bv1.a1', '36.ca1.a1', '36.cb1.a1', '54.h1.a1'], 'contains': ['216.i1.a1', '216.bq1.a1', '216.bq1.a2', '324.d1.a1'], 'core': '648.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [7003, -1, 5434, -1, 7379, -1, 5682, -1], 'generators': [54, 216, 576], 'label': '1296.3190.108.bc1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.h1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.r1.a1', 'old_label': '108.bc1.a1', 'projective_image': '648.731', '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': '6.1'}
  • id: 71060404
    {'ambient': '1296.3190', 'aut_centralizer_order': 32, 'aut_label': '108.bd1', 'aut_quo_index': None, 'aut_stab_index': 27, 'aut_weyl_group': '4.2', 'aut_weyl_index': 864, 'centralizer': '54.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.cc1.a1', '36.cd1.a1', '36.ce1.a1', '36.cf1.a1', '36.cg1.a1', '36.ch1.a1', '36.ci1.a1', '54.e1.a1', '54.t1.a1', '54.bb1.a1'], 'contains': ['216.a1.a1', '216.br1.a1', '324.e1.a1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [4306, -1, 8365, -1, 3576, -1, 7162, -1], 'generators': [45, 216, 2], 'label': '1296.3190.108.bd1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1.a1', 'old_label': '108.bd1.a1', 'projective_image': '216.162', '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': '2.1'}
  • id: 71060405
    {'ambient': '1296.3190', 'aut_centralizer_order': 32, 'aut_label': '108.be1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '12.4', 'aut_weyl_index': 288, 'centralizer': '108.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.cc1.a1', '36.cj1.a1', '36.ck1.a1', '36.cl1.a1', '54.f1.a1', '54.u1.a1', '54.bc1.a1'], 'contains': ['216.b1.a1', '216.bs1.a1', '324.e1.a1'], 'core': '216.b1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [4129, -1, 8185, -1, 3642, -1, 6712, -1], 'generators': [45, 216, 432], 'label': '1296.3190.108.be1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '12.k1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '108.be1.a1', 'projective_image': '648.731', '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': '12.4'}
  • id: 71060406
    {'ambient': '1296.3190', 'aut_centralizer_order': 32, 'aut_label': '108.bf1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '12.4', 'aut_weyl_index': 288, 'centralizer': '108.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.cd1.a1', '36.cj1.a1', '36.cm1.a1', '36.cn1.a1', '54.g1.a1', '54.y1.a1', '54.bf1.a1'], 'contains': ['216.c1.a1', '216.bt1.a1', '324.e1.a1'], 'core': '216.c1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [3643, -1, 8342, -1, 3615, -1, 6618, -1], 'generators': [45, 216, 144], 'label': '1296.3190.108.bf1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '12.k1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1.a1', 'old_label': '108.bf1.a1', 'projective_image': '648.731', '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': '12.4'}
  • id: 71060407
    {'ambient': '1296.3190', 'aut_centralizer_order': 32, 'aut_label': '108.bg1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '12.4', 'aut_weyl_index': 288, 'centralizer': '108.x1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.ce1.a1', '36.ck1.a1', '36.cm1.a1', '36.co1.a1', '54.n1.a1', '54.v1.a1', '54.bg1.a1'], 'contains': ['216.d1.a1', '216.bu1.a1', '324.e1.a1'], 'core': '216.d1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [5564, -1, 6878, -1, 4422, -1, 5804, -1], 'generators': [45, 216, 12], 'label': '1296.3190.108.bg1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '12.k1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.d1.a1', 'old_label': '108.bg1.a1', 'projective_image': '648.731', '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': '12.4'}
  • id: 71060408
    {'ambient': '1296.3190', 'aut_centralizer_order': 16, 'aut_label': '108.bh1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '12.4', 'aut_weyl_index': 288, 'centralizer': '108.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.cf1.a1', '36.cj1.a1', '36.co1.a1', '36.cp1.a1', '54.h1.a1'], 'contains': ['216.i1.a1', '216.bv1.a1', '216.bv1.a2', '324.e1.a1'], 'core': '648.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [5232, -1, 8960, -1, 4090, -1, 6488, -1], 'generators': [45, 216, 576], 'label': '1296.3190.108.bh1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.k1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.j1.a1', 'old_label': '108.bh1.a1', 'projective_image': '648.731', '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: 71060409
    {'ambient': '1296.3190', 'aut_centralizer_order': 36, 'aut_label': '8.c1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '48.51', 'aut_weyl_index': 72, 'centralizer': '24.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '4.h1.a1', '4.h1.b1'], 'contains': ['16.a1.a1', '24.x1.a1', '24.y1.a1', '24.z1.a1', '24.ba1.a1', '24.bb1.a1', '24.bc1.a1', '24.bd1.a1', '24.bd1.b1', '24.be1.a1', '24.be1.b1'], 'core': '16.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7327, -1, 1522, -1, 5149, -1, 2112, -1], 'generators': [18, 144, 2, 12, 432], 'label': '1296.3190.8.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '8.c1.a1', 'projective_image': '432.598', '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': '12.4'}
  • id: 71060410
    {'ambient': '1296.3190', 'aut_centralizer_order': 16, 'aut_label': '108.bi1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '12.4', 'aut_weyl_index': 288, 'centralizer': '216.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.cg1.a1', '36.ck1.a1', '36.cn1.a1', '36.cp1.a1', '54.w1.a1'], 'contains': ['216.j1.a1', '216.bw1.a1', '324.e1.a1'], 'core': '648.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [2367, -1, 8256, -1, 3178, -1, 8224, -1], 'generators': [45, 216, 444], 'label': '1296.3190.108.bi1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.k1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bf1.a1', 'old_label': '108.bi1.a1', 'projective_image': '648.731', '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': '12.4'}
  • id: 71060411
    {'ambient': '1296.3190', 'aut_centralizer_order': 16, 'aut_label': '108.bj1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '12.4', 'aut_weyl_index': 288, 'centralizer': '216.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.ch1.a1', '36.cl1.a1', '36.cm1.a1', '36.cp1.a1', '54.bh1.a1'], 'contains': ['216.k1.a1', '216.bx1.a1', '324.e1.a1'], 'core': '648.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [2730, -1, 9526, -1, 2972, -1, 8845, -1], 'generators': [45, 216, 156], 'label': '1296.3190.108.bj1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.k1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bw1.a1', 'old_label': '108.bj1.a1', 'projective_image': '648.731', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.bj1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 71060412
    {'ambient': '1296.3190', 'aut_centralizer_order': 8, 'aut_label': '108.bk1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '12.4', 'aut_weyl_index': 288, 'centralizer': '216.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.ci1.a1', '36.cl1.a1', '36.cn1.a1', '36.co1.a1', '36.cp1.a1'], 'contains': ['216.o1.a1', '216.by1.a1', '216.by1.a2', '324.e1.a1'], 'core': '648.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [2668, -1, 9226, -1, 3151, -1, 8247, -1], 'generators': [45, 216, 588], 'label': '1296.3190.108.bk1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.k1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.ci1.a1', 'old_label': '108.bk1.a1', 'projective_image': '648.731', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.bk1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 71060413
    {'ambient': '1296.3190', 'aut_centralizer_order': 288, 'aut_label': '108.bl1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '4.2', 'aut_weyl_index': 864, 'centralizer': '6.s1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.i1.a1', '36.cr1.a1', '36.ct1.a1', '36.cw1.a1', '54.i1.a1', '54.p1.a1', '54.bb1.a1'], 'contains': ['216.a1.a1', '324.f1.a1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [1658, -1, 8479, -1, 1081, -1, 8915, -1], 'generators': [108, 2, 216], 'label': '1296.3190.108.bl1.a1', 'mobius_quo': None, 'mobius_sub': -18, 'normal_closure': '36.i1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.d1.a1', 'old_label': '108.bl1.a1', 'projective_image': '216.162', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.bl1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 71060414
    {'ambient': '1296.3190', 'aut_centralizer_order': 96, 'aut_label': '108.bm1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '4.2', 'aut_weyl_index': 864, 'centralizer': '18.m1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.cq1.a1', '36.cs1.a1', '36.cu1.a1', '36.cv1.a1', '54.i1.a1', '54.t1.a1', '54.z1.a1'], 'contains': ['216.a1.a1', '324.g1.a1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [2040, -1, 7674, -1, 1713, -1, 8199, -1], 'generators': [111, 2, 216], 'label': '1296.3190.108.bm1.a1', 'mobius_quo': None, 'mobius_sub': -6, 'normal_closure': '12.n1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1.a1', 'old_label': '108.bm1.a1', 'projective_image': '216.162', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.bm1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 71060415
    {'ambient': '1296.3190', 'aut_centralizer_order': 96, 'aut_label': '108.bn1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '12.4', 'aut_weyl_index': 288, 'centralizer': '36.n1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.l1.a1', '36.cq1.a1', '36.cx1.a1', '36.cz1.a1', '54.j1.a1', '54.u1.a1', '54.ba1.a1'], 'contains': ['216.b1.a1', '324.g1.a1'], 'core': '216.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [1895, -1, 8875, -1, 1647, -1, 7682, -1], 'generators': [111, 216, 432], 'label': '1296.3190.108.bn1.a1', 'mobius_quo': None, 'mobius_sub': -6, 'normal_closure': '36.l1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '108.bn1.a1', 'projective_image': '648.731', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.bn1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 71060416
    {'ambient': '1296.3190', 'aut_centralizer_order': 288, 'aut_label': '108.bo1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '4.2', 'aut_weyl_index': 864, 'centralizer': '6.s1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.j1.a1', '36.cr1.a1', '36.dd1.a1', '36.df1.a1', '54.k1.a1', '54.x1.a1', '54.bf1.a1'], 'contains': ['216.c1.a1', '324.f1.a1'], 'core': '216.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [738, -1, 8909, -1, 1048, -1, 8709, -1], 'generators': [108, 144, 216], 'label': '1296.3190.108.bo1.a1', 'mobius_quo': None, 'mobius_sub': -6, 'normal_closure': '36.j1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.d1.a1', 'old_label': '108.bo1.a1', 'projective_image': '648.731', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.bo1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 71060417
    {'ambient': '1296.3190', 'aut_centralizer_order': 96, 'aut_label': '108.bp1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '4.2', 'aut_weyl_index': 864, 'centralizer': '18.m1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.cs1.a1', '36.cx1.a1', '36.de1.a1', '36.dg1.a1', '54.k1.a1', '54.y1.a1', '54.be1.a1'], 'contains': ['216.c1.a1', '324.g1.a1'], 'core': '216.c1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [1634, -1, 9057, -1, 1680, -1, 7539, -1], 'generators': [111, 144, 216], 'label': '1296.3190.108.bp1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '12.p1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1.a1', 'old_label': '108.bp1.a1', 'projective_image': '648.731', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.bp1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 71060418
    {'ambient': '1296.3190', 'aut_centralizer_order': 288, 'aut_label': '108.bq1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '4.2', 'aut_weyl_index': 864, 'centralizer': '12.br1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.k1.a1', '36.ct1.a1', '36.dd1.a1', '36.dh1.a1', '54.o1.a1', '54.q1.a1', '54.bg1.a1'], 'contains': ['216.d1.a1', '324.f1.a1'], 'core': '216.d1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [2113, -1, 8801, -1, 1114, -1, 7020, -1], 'generators': [108, 12, 216], 'label': '1296.3190.108.bq1.a1', 'mobius_quo': None, 'mobius_sub': -6, 'normal_closure': '36.k1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.d1.a1', 'old_label': '108.bq1.a1', 'projective_image': '648.731', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.bq1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 71060419
    {'ambient': '1296.3190', 'aut_centralizer_order': 96, 'aut_label': '108.br1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '12.4', 'aut_weyl_index': 288, 'centralizer': '36.cr1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.l1.a1', '36.cu1.a1', '36.de1.a1', '36.di1.a1', '54.o1.a1', '54.v1.a1', '54.bd1.a1'], 'contains': ['216.d1.a1', '324.g1.a1'], 'core': '216.d1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [2389, -1, 8586, -1, 1747, -1, 6687, -1], 'generators': [111, 216, 12], 'label': '1296.3190.108.br1.a1', 'mobius_quo': None, 'mobius_sub': -6, 'normal_closure': '36.l1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.d1.a1', 'old_label': '108.br1.a1', 'projective_image': '648.731', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.br1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 71060420
    {'ambient': '1296.3190', 'aut_centralizer_order': 12, 'aut_label': '8.d1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '144.192', 'aut_weyl_index': 24, 'centralizer': '72.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.c1.a1', '4.h1.a1', '4.h1.b1'], 'contains': ['16.a1.a1', '24.bf1.a1', '24.bg1.a1', '24.bh1.a1', '24.bi1.a1', '24.bj1.a1', '24.bk1.a1', '24.bk1.b1'], 'core': '16.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8328, -1, 1068, -1, 8304, -1, 1231, -1], 'generators': [9, 144, 2, 432, 12], 'label': '1296.3190.8.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '8.d1.a1', 'projective_image': '432.598', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.d1.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 71060421
    {'ambient': '1296.3190', 'aut_centralizer_order': 144, 'aut_label': '108.bs1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '4.2', 'aut_weyl_index': 864, 'centralizer': '6.s1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.cr1.a1', '36.cy1.a1', '36.dh1.a1', '36.dj1.a1', '54.l1.a1'], 'contains': ['216.g1.a1', '324.f1.a1'], 'core': '648.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [465, -1, 9799, -1, 397, -1, 9477, -1], 'generators': [108, 146, 216], 'label': '1296.3190.108.bs1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.l1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.s1.a1', 'old_label': '108.bs1.a1', 'projective_image': '648.731', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.bs1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 71060422
    {'ambient': '1296.3190', 'aut_centralizer_order': 48, 'aut_label': '108.bt1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '4.2', 'aut_weyl_index': 864, 'centralizer': '18.m1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.cs1.a1', '36.cz1.a1', '36.di1.a1', '36.dk1.a1', '54.l1.a1'], 'contains': ['216.g1.a1', '324.g1.a1'], 'core': '648.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [823, -1, 9758, -1, 767, -1, 8787, -1], 'generators': [111, 146, 216], 'label': '1296.3190.108.bt1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.m1.a1', 'old_label': '108.bt1.a1', 'projective_image': '648.731', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.bt1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 71060423
    {'ambient': '1296.3190', 'aut_centralizer_order': 144, 'aut_label': '108.bu1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '4.2', 'aut_weyl_index': 864, 'centralizer': '12.br1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.ct1.a1', '36.da1.a1', '36.df1.a1', '36.dj1.a1', '54.r1.a1'], 'contains': ['216.h1.a1', '324.f1.a1'], 'core': '648.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [10, -1, 8644, -1, 980, -1, 9012, -1], 'generators': [108, 14, 216], 'label': '1296.3190.108.bu1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.m1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.w1.a1', 'old_label': '108.bu1.a1', 'projective_image': '648.731', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.bu1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 71060424
    {'ambient': '1296.3190', 'aut_centralizer_order': 48, 'aut_label': '108.bv1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '12.4', 'aut_weyl_index': 288, 'centralizer': '72.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.l1.a1', '36.cv1.a1', '36.dg1.a1', '36.dk1.a1', '54.w1.a1'], 'contains': ['216.j1.a1', '324.g1.a1'], 'core': '648.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [151, -1, 8842, -1, 1551, -1, 8887, -1], 'generators': [111, 216, 444], 'label': '1296.3190.108.bv1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.l1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.ba1.a1', 'old_label': '108.bv1.a1', 'projective_image': '648.731', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.bv1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 71060425
    {'ambient': '1296.3190', 'aut_centralizer_order': 144, 'aut_label': '108.bw1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '4.2', 'aut_weyl_index': 864, 'centralizer': '12.br1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.cw1.a1', '36.db1.a1', '36.dd1.a1', '36.dj1.a1', '54.bh1.a1'], 'contains': ['216.k1.a1', '324.f1.a1'], 'core': '648.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [582, -1, 9653, -1, 734, -1, 9504, -1], 'generators': [108, 156, 216], 'label': '1296.3190.108.bw1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.o1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.bh1.a1', 'old_label': '108.bw1.a1', 'projective_image': '648.731', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.bw1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 71060426
    {'ambient': '1296.3190', 'aut_centralizer_order': 72, 'aut_label': '108.bx1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '4.2', 'aut_weyl_index': 864, 'centralizer': '12.br1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.cw1.a1', '36.dc1.a1', '36.df1.a1', '36.dh1.a1', '36.dj1.a1'], 'contains': ['216.n1.a1', '324.f1.a1'], 'core': '648.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [234, -1, 9695, -1, 336, -1, 9717, -1], 'generators': [108, 158, 216], 'label': '1296.3190.108.bx1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.br1.a1', 'old_label': '108.bx1.a1', 'projective_image': '648.731', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.bx1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 71060427
    {'ambient': '1296.3190', 'aut_centralizer_order': 48, 'aut_label': '108.by1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1728, 'centralizer': '18.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.dl1.a1', '36.dm1.a1', '36.dt1.a1', '54.a1.a1'], 'contains': ['216.q1.a1', '216.x1.a1', '216.bf1.a1', '324.h1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [9132, -1, 1239, -1, 8036, -1, 1347, -1], 'generators': [3, 18, 2], 'label': '1296.3190.108.by1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.d1.a1', 'old_label': '108.by1.a1', 'projective_image': '432.598', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.by1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 71060428
    {'ambient': '1296.3190', 'aut_centralizer_order': 48, 'aut_label': '108.by1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1728, 'centralizer': '18.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.dl1.b1', '36.dm1.b1', '36.dt1.b1', '54.a1.a1'], 'contains': ['216.q1.b1', '216.x1.a1', '216.bf1.a1', '324.h1.b1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [9132, -1, 2072, -1, 8036, -1, 1433, -1], 'generators': [219, 18, 2], 'label': '1296.3190.108.by1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.d1.a1', 'old_label': '108.by1.b1', 'projective_image': '432.598', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.by1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 71060429
    {'ambient': '1296.3190', 'aut_centralizer_order': 48, 'aut_label': '108.bz1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1728, 'centralizer': '18.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.dl1.a1', '36.dn1.a1', '36.du1.a1', '54.b1.a1'], 'contains': ['216.r1.a1', '216.y1.a1', '216.bg1.a1', '324.h1.a1'], 'core': '432.b1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [8900, -1, 1199, -1, 7958, -1, 1006, -1], 'generators': [3, 18, 432], 'label': '1296.3190.108.bz1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.d1.a1', 'old_label': '108.bz1.a1', 'projective_image': '1296.3190', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.bz1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 71060430
    {'ambient': '1296.3190', 'aut_centralizer_order': 48, 'aut_label': '108.bz1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1728, 'centralizer': '18.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.dl1.b1', '36.dn1.b1', '36.du1.b1', '54.b1.a1'], 'contains': ['216.r1.b1', '216.y1.a1', '216.bg1.a1', '324.h1.b1'], 'core': '432.b1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [8900, -1, 2034, -1, 7958, -1, 1049, -1], 'generators': [219, 18, 432], 'label': '1296.3190.108.bz1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.d1.a1', 'old_label': '108.bz1.b1', 'projective_image': '1296.3190', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.bz1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 71060431
    {'ambient': '1296.3190', 'aut_centralizer_order': 12, 'aut_label': '8.e1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '144.192', 'aut_weyl_index': 24, 'centralizer': '72.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.d1.a1', '4.i1.a1', '4.i1.b1'], 'contains': ['16.a1.a1', '24.bl1.a1', '24.bm1.a1', '24.bn1.a1', '24.bn1.a2', '24.bo1.a1', '24.bp1.a1', '24.bq1.a1'], 'core': '16.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [9214, -1, 3485, -1, 9375, -1, 4257, -1], 'generators': [54, 432, 2, 12, 144], 'label': '1296.3190.8.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '8.e1.a1', 'projective_image': '432.598', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.e1.a1', 'subgroup_fusion': None, 'weyl_group': '36.13'}
  • id: 71060432
    {'ambient': '1296.3190', 'aut_centralizer_order': 24, 'aut_label': '108.ca1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1728, 'centralizer': '18.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.dl1.a1', '36.do1.a1', '36.dv1.a1', '54.c1.a1'], 'contains': ['216.t1.a1', '216.ba1.a1', '216.bh1.b1', '324.h1.a1'], 'core': '1296.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [8577, -1, 674, -1, 8087, -1, 290, -1], 'generators': [3, 18, 434], 'label': '1296.3190.108.ca1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.d1.a1', 'old_label': '108.ca1.a1', 'projective_image': '1296.3190', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.ca1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 71060433
    {'ambient': '1296.3190', 'aut_centralizer_order': 24, 'aut_label': '108.ca1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1728, 'centralizer': '18.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.dl1.a1', '36.do1.b1', '36.dv1.b1', '54.c1.a1'], 'contains': ['216.t1.a1', '216.ba1.b1', '216.bh1.a1', '324.h1.a1'], 'core': '1296.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [8577, -1, 721, -1, 8087, -1, 333, -1], 'generators': [3, 18, 866], 'label': '1296.3190.108.ca1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.d1.a1', 'old_label': '108.ca1.b1', 'projective_image': '1296.3190', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.ca1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 71060434
    {'ambient': '1296.3190', 'aut_centralizer_order': 24, 'aut_label': '108.ca1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1728, 'centralizer': '18.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.dl1.b1', '36.do1.c1', '36.dv1.c1', '54.c1.a1'], 'contains': ['216.t1.b1', '216.ba1.a1', '216.bh1.a1', '324.h1.b1'], 'core': '1296.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [8577, -1, 1794, -1, 8087, -1, 418, -1], 'generators': [219, 18, 434], 'label': '1296.3190.108.ca1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.d1.a1', 'old_label': '108.ca1.c1', 'projective_image': '1296.3190', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.ca1.c1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 71060435
    {'ambient': '1296.3190', 'aut_centralizer_order': 24, 'aut_label': '108.ca1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1728, 'centralizer': '18.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.dl1.b1', '36.do1.d1', '36.dv1.d1', '54.c1.a1'], 'contains': ['216.t1.b1', '216.ba1.b1', '216.bh1.b1', '324.h1.b1'], 'core': '1296.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [8577, -1, 1721, -1, 8087, -1, 376, -1], 'generators': [219, 18, 866], 'label': '1296.3190.108.ca1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.d1.a1', 'old_label': '108.ca1.d1', 'projective_image': '1296.3190', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.ca1.d1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 71060436
    {'ambient': '1296.3190', 'aut_centralizer_order': 48, 'aut_label': '108.cb1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '6.1', 'aut_weyl_index': 576, 'centralizer': '36.m1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.dm1.a1', '36.dn1.a1', '36.do1.a1', '36.do1.b1', '36.dw1.a1', '54.d1.a1'], 'contains': ['216.s1.a1', '216.be1.a1', '216.bi1.a1', '324.h1.a1'], 'core': '432.c1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [8715, -1, 999, -1, 7997, -1, 643, -1], 'generators': [3, 18, 144], 'label': '1296.3190.108.cb1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.k1.a1', 'old_label': '108.cb1.a1', 'projective_image': '1296.3190', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.cb1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 71060437
    {'ambient': '1296.3190', 'aut_centralizer_order': 48, 'aut_label': '108.cb1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '6.1', 'aut_weyl_index': 576, 'centralizer': '36.m1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.dm1.b1', '36.dn1.b1', '36.do1.c1', '36.do1.d1', '36.dw1.b1', '54.d1.a1'], 'contains': ['216.s1.b1', '216.be1.a1', '216.bi1.a1', '324.h1.b1'], 'core': '432.c1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [8715, -1, 1907, -1, 7997, -1, 774, -1], 'generators': [219, 18, 144], 'label': '1296.3190.108.cb1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.k1.a1', 'old_label': '108.cb1.b1', 'projective_image': '1296.3190', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.cb1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 71060438
    {'ambient': '1296.3190', 'aut_centralizer_order': 16, 'aut_label': '108.cc1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1728, 'centralizer': '54.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.dp1.a1', '36.dq1.a1', '36.dr1.a1', '36.dr1.a2', '36.dx1.a1', '54.e1.a1'], 'contains': ['216.q1.a1', '216.bl1.a1', '216.br1.a1', '324.i1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 54, 'diagramx': [9387, -1, 4488, -1, 8913, -1, 3913, -1], 'generators': [3, 54, 2], 'label': '1296.3190.108.cc1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.e1.a1', 'old_label': '108.cc1.a1', 'projective_image': '432.598', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.cc1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 71060439
    {'ambient': '1296.3190', 'aut_centralizer_order': 16, 'aut_label': '108.cc1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1728, 'centralizer': '54.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.dp1.b1', '36.dq1.b1', '36.dr1.b1', '36.dr1.b2', '36.dx1.b1', '54.e1.a1'], 'contains': ['216.q1.b1', '216.bl1.a1', '216.br1.a1', '324.i1.b1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 54, 'diagramx': [9387, -1, 5095, -1, 8913, -1, 4220, -1], 'generators': [219, 54, 2], 'label': '1296.3190.108.cc1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.e1.a1', 'old_label': '108.cc1.b1', 'projective_image': '432.598', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.cc1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 71060440
    {'ambient': '1296.3190', 'aut_centralizer_order': 16, 'aut_label': '108.cd1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '6.1', 'aut_weyl_index': 576, 'centralizer': '108.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.dp1.a1', '36.ds1.a1', '36.dy1.a1', '54.f1.a1'], 'contains': ['216.r1.a1', '216.bo1.a1', '216.bs1.a1', '324.i1.a1'], 'core': '432.b1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [9255, -1, 4336, -1, 8536, -1, 3880, -1], 'generators': [3, 54, 432], 'label': '1296.3190.108.cd1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.h1.a1', 'old_label': '108.cd1.a1', 'projective_image': '1296.3190', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.cd1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 71060441
    {'ambient': '1296.3190', 'aut_centralizer_order': 16, 'aut_label': '108.cd1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '6.1', 'aut_weyl_index': 576, 'centralizer': '108.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.dp1.b1', '36.ds1.b1', '36.dy1.b1', '54.f1.a1'], 'contains': ['216.r1.b1', '216.bo1.a1', '216.bs1.a1', '324.i1.b1'], 'core': '432.b1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [9255, -1, 4927, -1, 8536, -1, 4187, -1], 'generators': [219, 54, 432], 'label': '1296.3190.108.cd1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.h1.a1', 'old_label': '108.cd1.b1', 'projective_image': '1296.3190', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.cd1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 71060442
    {'ambient': '1296.3190', 'aut_centralizer_order': 4, 'aut_label': '8.f1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '432.759', 'aut_weyl_index': 8, 'centralizer': '216.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.e1.a1', '4.i1.a1', '4.i1.b1'], 'contains': ['16.a1.a1', '24.br1.a1', '24.bs1.a1', '24.bt1.a1', '24.bu1.a1', '24.bv1.a1', '24.bw1.a1', '24.bw1.a2', '24.bx1.a1', '24.bx1.a2', '24.by1.a1'], 'core': '16.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8161, -1, 3946, -1, 5458, -1, 5795, -1], 'generators': [45, 432, 2, 12, 144], 'label': '1296.3190.8.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '8.f1.a1', 'projective_image': '432.598', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.f1.a1', 'subgroup_fusion': None, 'weyl_group': '108.39'}
  • id: 71060443
    {'ambient': '1296.3190', 'aut_centralizer_order': 16, 'aut_label': '108.ce1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '6.1', 'aut_weyl_index': 576, 'centralizer': '108.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.dq1.a1', '36.ds1.a1', '36.dz1.a1', '54.g1.a1'], 'contains': ['216.s1.a1', '216.bp1.a1', '216.bt1.a1', '324.i1.a1'], 'core': '432.c1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [8938, -1, 4286, -1, 8458, -1, 3815, -1], 'generators': [3, 54, 144], 'label': '1296.3190.108.ce1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.i1.a1', 'old_label': '108.ce1.a1', 'projective_image': '1296.3190', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.ce1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 71060444
    {'ambient': '1296.3190', 'aut_centralizer_order': 16, 'aut_label': '108.ce1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '6.1', 'aut_weyl_index': 576, 'centralizer': '108.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.dq1.b1', '36.ds1.b1', '36.dz1.b1', '54.g1.a1'], 'contains': ['216.s1.b1', '216.bp1.a1', '216.bt1.a1', '324.i1.b1'], 'core': '432.c1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [8938, -1, 4894, -1, 8458, -1, 4165, -1], 'generators': [219, 54, 144], 'label': '1296.3190.108.ce1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.i1.a1', 'old_label': '108.ce1.b1', 'projective_image': '1296.3190', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.ce1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 71060445
    {'ambient': '1296.3190', 'aut_centralizer_order': 8, 'aut_label': '108.cf1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '6.1', 'aut_weyl_index': 576, 'centralizer': '108.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.dr1.a1', '36.ds1.a1', '36.ea1.a1', '54.h1.a1'], 'contains': ['216.v1.a1', '216.bq1.a1', '216.bv1.a1', '324.i1.a1'], 'core': '1296.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [9540, -1, 4545, -1, 9154, -1, 4252, -1], 'generators': [3, 54, 576], 'label': '1296.3190.108.cf1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.j1.a1', 'old_label': '108.cf1.a1', 'projective_image': '1296.3190', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.cf1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 71060446
    {'ambient': '1296.3190', 'aut_centralizer_order': 8, 'aut_label': '108.cf1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '6.1', 'aut_weyl_index': 576, 'centralizer': '108.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.dr1.a2', '36.ds1.a1', '36.ea1.a2', '54.h1.a1'], 'contains': ['216.v1.a1', '216.bq1.a2', '216.bv1.a2', '324.i1.a1'], 'core': '1296.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [9540, -1, 4560, -1, 9154, -1, 4275, -1], 'generators': [3, 54, 1008], 'label': '1296.3190.108.cf1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.j1.a1', 'old_label': '108.cf1.a2', 'projective_image': '1296.3190', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.cf1.a2', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 71060447
    {'ambient': '1296.3190', 'aut_centralizer_order': 8, 'aut_label': '108.cf1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '6.1', 'aut_weyl_index': 576, 'centralizer': '108.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.dr1.b1', '36.ds1.b1', '36.ea1.b1', '54.h1.a1'], 'contains': ['216.v1.b1', '216.bq1.a1', '216.bv1.a2', '324.i1.b1'], 'core': '1296.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [9540, -1, 5133, -1, 9154, -1, 4411, -1], 'generators': [219, 54, 576], 'label': '1296.3190.108.cf1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.j1.a1', 'old_label': '108.cf1.b1', 'projective_image': '1296.3190', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.cf1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 71060448
    {'ambient': '1296.3190', 'aut_centralizer_order': 8, 'aut_label': '108.cf1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '6.1', 'aut_weyl_index': 576, 'centralizer': '108.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.dr1.b2', '36.ds1.b1', '36.ea1.b2', '54.h1.a1'], 'contains': ['216.v1.b1', '216.bq1.a2', '216.bv1.a1', '324.i1.b1'], 'core': '1296.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [9540, -1, 5117, -1, 9154, -1, 4434, -1], 'generators': [219, 54, 1008], 'label': '1296.3190.108.cf1.b2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.j1.a1', 'old_label': '108.cf1.b2', 'projective_image': '1296.3190', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.cf1.b2', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 71060449
    {'ambient': '1296.3190', 'aut_centralizer_order': 48, 'aut_label': '108.cg1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '6.1', 'aut_weyl_index': 576, 'centralizer': '36.x1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.dt1.a1', '36.du1.a1', '36.dv1.a1', '36.dv1.b1', '36.dw1.a1', '54.m1.a1'], 'contains': ['216.e1.a1', '216.z1.a1', '216.bj1.a1', '324.h1.a1'], 'core': '216.e1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [9499, -1, 460, -1, 8126, -1, 621, -1], 'generators': [3, 18, 12], 'label': '1296.3190.108.cg1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.n1.a1', 'old_label': '108.cg1.a1', 'projective_image': '1296.3190', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.cg1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 71060450
    {'ambient': '1296.3190', 'aut_centralizer_order': 48, 'aut_label': '108.cg1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '6.1', 'aut_weyl_index': 576, 'centralizer': '36.x1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.dt1.b1', '36.du1.b1', '36.dv1.c1', '36.dv1.d1', '36.dw1.b1', '54.m1.a1'], 'contains': ['216.e1.b1', '216.z1.a1', '216.bj1.a1', '324.h1.b1'], 'core': '216.e1.b1', 'coset_action_label': None, 'count': 6, 'diagramx': [9499, -1, 588, -1, 8126, -1, 666, -1], 'generators': [219, 18, 12], 'label': '1296.3190.108.cg1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.n1.a1', 'old_label': '108.cg1.b1', 'projective_image': '1296.3190', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.cg1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 71060451
    {'ambient': '1296.3190', 'aut_centralizer_order': 16, 'aut_label': '108.ch1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '6.1', 'aut_weyl_index': 576, 'centralizer': '108.x1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.dx1.a1', '36.dy1.a1', '36.dz1.a1', '36.ea1.a1', '36.ea1.a2', '54.n1.a1'], 'contains': ['216.e1.a1', '216.bm1.a1', '216.bu1.a1', '324.i1.a1'], 'core': '216.e1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [9865, -1, 3194, -1, 9333, -1, 3792, -1], 'generators': [3, 54, 12], 'label': '1296.3190.108.ch1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.s1.a1', 'old_label': '108.ch1.a1', 'projective_image': '1296.3190', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.ch1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 71060452
    {'ambient': '1296.3190', 'aut_centralizer_order': 16, 'aut_label': '108.ch1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '6.1', 'aut_weyl_index': 576, 'centralizer': '108.x1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.dx1.b1', '36.dy1.b1', '36.dz1.b1', '36.ea1.b1', '36.ea1.b2', '54.n1.a1'], 'contains': ['216.e1.b1', '216.bm1.a1', '216.bu1.a1', '324.i1.b1'], 'core': '216.e1.b1', 'coset_action_label': None, 'count': 18, 'diagramx': [9865, -1, 3936, -1, 9333, -1, 3988, -1], 'generators': [219, 54, 12], 'label': '1296.3190.108.ch1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.s1.a1', 'old_label': '108.ch1.b1', 'projective_image': '1296.3190', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.ch1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 71060453
    {'ambient': '1296.3190', 'aut_centralizer_order': 4, 'aut_label': '9.a1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '96.230', 'aut_weyl_index': 36, 'centralizer': '108.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.b1.a1', '3.c1.a1'], 'contains': ['18.d1.a1', '18.h1.a1', '18.l1.a1', '18.ba1.a1', '18.bd1.a1', '18.bo1.a1', '18.bp1.a1', '27.a1.a1', '27.b1.a1'], 'core': '36.i1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [3931, -1, 7431, -1, 4632, -1, 7086, -1], 'generators': [3, 432, 216, 18, 108, 2], 'label': '1296.3190.9.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': '216.162', '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: 71060454
    {'ambient': '1296.3190', 'aut_centralizer_order': 864, 'aut_label': '144.a1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '4.2', 'aut_weyl_index': 864, 'centralizer': '2.a1.a1', 'complements': ['9.f1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['48.a1.a1', '48.b1.a1', '48.e1.a1', '72.a1.a1', '72.bn1.a1', '72.bn1.b1', '72.by1.a1', '72.cm1.a1', '72.cy1.a1', '72.di1.a1'], 'contains': ['432.a1.a1', '432.b1.a1', '432.e1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7919, 5057, 3539, 5007, 6906, 4808, 3932, 5152], 'generators': [2, 432], 'label': '1296.3190.144.a1.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '144.a1.a1', 'normal_contained_in': ['48.a1.a1', '48.b1.a1', '72.a1.a1'], 'normal_contains': ['432.a1.a1', '432.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '144.a1.a1', 'projective_image': '432.598', 'quotient_action_image': '2.1', 'quotient_action_kernel': '72.46', 'quotient_action_kernel_order': 72, 'quotient_fusion': None, 'short_label': '144.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 71060455
    {'ambient': '1296.3190', 'aut_centralizer_order': 864, 'aut_label': '144.b1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '4.2', 'aut_weyl_index': 864, 'centralizer': '2.c1.a1', 'complements': ['9.e1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['48.a1.a1', '48.c1.a1', '48.f1.a1', '72.b1.a1', '72.bo1.a1', '72.bo1.b1', '72.cf1.a1', '72.cn1.a1', '72.cz1.a1', '72.dj1.a1'], 'contains': ['432.a1.a1', '432.c1.a1', '432.f1.a1'], 'core': '144.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7783, 5725, 3557, 4793, 6814, 4401, 4035, 4736], 'generators': [2, 144], 'label': '1296.3190.144.b1.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '144.b1.a1', 'normal_contained_in': ['48.a1.a1', '48.c1.a1', '72.b1.a1'], 'normal_contains': ['432.a1.a1', '432.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '144.b1.a1', 'projective_image': '432.598', 'quotient_action_image': '2.1', 'quotient_action_kernel': '72.20', 'quotient_action_kernel_order': 72, 'quotient_fusion': None, 'short_label': '144.b1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 71060456
    {'ambient': '1296.3190', 'aut_centralizer_order': 864, 'aut_label': '144.c1', 'aut_quo_index': 4, 'aut_stab_index': 1, 'aut_weyl_group': '4.2', 'aut_weyl_index': 864, 'centralizer': '2.d1.a1', 'complements': ['9.c1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['48.b1.a1', '48.c1.a1', '48.g1.a1', '72.c1.a1', '72.g1.a1', '72.g1.b1', '72.bz1.a1', '72.co1.a1', '72.cx1.a1', '72.dk1.a1'], 'contains': ['432.a1.a1', '432.d1.a1', '432.g1.a1'], 'core': '144.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8252, 6685, 1375, 3461, 7125, 3484, 3984, 3701], 'generators': [2, 12], 'label': '1296.3190.144.c1.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '144.c1.a1', 'normal_contained_in': ['48.c1.a1', '48.b1.a1', '72.c1.a1', '72.g1.a1', '72.g1.b1'], 'normal_contains': ['432.a1.a1', '432.d1.a1'], 'normalizer': '1.a1.a1', 'old_label': '144.c1.a1', 'projective_image': '432.598', 'quotient_action_image': '2.1', 'quotient_action_kernel': '72.23', 'quotient_action_kernel_order': 72, 'quotient_fusion': None, 'short_label': '144.c1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 71060457
    {'ambient': '1296.3190', 'aut_centralizer_order': 864, 'aut_label': '144.d1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '4.2', 'aut_weyl_index': 864, 'centralizer': '4.a1.a1', 'complements': ['9.d1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['48.a1.a1', '48.d1.a1', '48.i1.a1', '72.d1.a1', '72.bq1.a1', '72.bq1.b1', '72.cg1.a1', '72.cq1.a1', '72.dh1.a1', '72.dp1.a1'], 'contains': ['432.b1.a1', '432.c1.a1', '432.h1.a1'], 'core': '144.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7972, 5285, 3251, 4578, 6875, 5215, 4010, 4944], 'generators': [144, 432], 'label': '1296.3190.144.d1.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '144.d1.a1', 'normal_contained_in': ['48.a1.a1', '48.d1.a1', '72.d1.a1'], 'normal_contains': ['432.b1.a1', '432.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '144.d1.a1', 'projective_image': '1296.3190', 'quotient_action_image': '4.2', 'quotient_action_kernel': '36.12', 'quotient_action_kernel_order': 36, 'quotient_fusion': None, 'short_label': '144.d1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 71060458
    {'ambient': '1296.3190', 'aut_centralizer_order': 864, 'aut_label': '144.e1', 'aut_quo_index': 8, 'aut_stab_index': 1, 'aut_weyl_group': '4.2', 'aut_weyl_index': 864, 'centralizer': '4.b1.a1', 'complements': ['9.b1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['48.b1.a1', '48.d1.a1', '48.j1.a1', '72.e1.a1', '72.h1.a1', '72.h1.b1', '72.cb1.a1', '72.cr1.a1', '72.db1.a1', '72.dq1.a1'], 'contains': ['432.b1.a1', '432.d1.a1', '432.i1.a1'], 'core': '144.e1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8059, 6083, 2433, 3235, 6968, 4184, 3907, 3909], 'generators': [12, 432], 'label': '1296.3190.144.e1.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '144.e1.a1', 'normal_contained_in': ['48.b1.a1', '48.d1.a1', '72.e1.a1', '72.h1.a1', '72.h1.b1'], 'normal_contains': ['432.b1.a1', '432.d1.a1'], 'normalizer': '1.a1.a1', 'old_label': '144.e1.a1', 'projective_image': '1296.3190', 'quotient_action_image': '4.2', 'quotient_action_kernel': '36.12', 'quotient_action_kernel_order': 36, 'quotient_fusion': None, 'short_label': '144.e1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 71060459
    {'ambient': '1296.3190', 'aut_centralizer_order': 864, 'aut_label': '144.f1', 'aut_quo_index': 4, 'aut_stab_index': 1, 'aut_weyl_group': '4.2', 'aut_weyl_index': 864, 'centralizer': '4.f1.a1', 'complements': ['9.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['48.c1.a1', '48.d1.a1', '48.l1.a1', '72.f1.a1', '72.i1.a1', '72.i1.b1', '72.ch1.a1', '72.cw1.a1', '72.dd1.a1', '72.ds1.a1'], 'contains': ['432.c1.a1', '432.d1.a1', '432.j1.a1'], 'core': '144.f1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7836, 6913, 1512, 2963, 6999, 3777, 3059, 3492], 'generators': [12, 144], 'label': '1296.3190.144.f1.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '144.f1.a1', 'normal_contained_in': ['48.c1.a1', '48.d1.a1', '72.f1.a1', '72.i1.a1', '72.i1.b1'], 'normal_contains': ['432.c1.a1', '432.d1.a1'], 'normalizer': '1.a1.a1', 'old_label': '144.f1.a1', 'projective_image': '1296.3190', 'quotient_action_image': '4.2', 'quotient_action_kernel': '36.6', 'quotient_action_kernel_order': 36, 'quotient_fusion': None, 'short_label': '144.f1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 71060460
    {'ambient': '1296.3190', 'aut_centralizer_order': 432, 'aut_label': '144.g1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 864, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.a1.a1', '48.g1.a1', '48.h1.a1', '72.j1.a1', '72.bp1.a1', '72.bp1.b1', '72.da1.a1', '72.da1.a2', '72.dl1.a1', '72.dl1.a2'], 'contains': ['432.a1.a1', '432.h1.a1', '432.k1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8136, -1, 4789, -1, 7030, -1, 4379, -1], 'generators': [2, 576], 'label': '1296.3190.144.g1.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.g1.a1', 'projective_image': '432.598', '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': '2.1'}
  • id: 71060461
    {'ambient': '1296.3190', 'aut_centralizer_order': 432, 'aut_label': '144.h1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 864, 'centralizer': '4.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.b1.a1', '48.f1.a1', '48.h1.a1', '72.k1.a1', '72.ca1.a1', '72.dm1.a1'], 'contains': ['432.a1.a1', '432.i1.a1', '432.l1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1548, -1, 5996, -1, 4974, -1, 5368, -1], 'generators': [2, 444], 'label': '1296.3190.144.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.e1.a1', 'old_label': '144.h1.a1', 'projective_image': '432.598', '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: 71060462
    {'ambient': '1296.3190', 'aut_centralizer_order': 432, 'aut_label': '144.i1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 864, 'centralizer': '4.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.c1.a1', '48.e1.a1', '48.h1.a1', '72.l1.a1', '72.cp1.a1', '72.dn1.a1'], 'contains': ['432.a1.a1', '432.j1.a1', '432.m1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [5365, -1, 6112, -1, 5464, -1, 6016, -1], 'generators': [2, 156], 'label': '1296.3190.144.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.g1.a1', 'old_label': '144.i1.a1', 'projective_image': '432.598', '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: 71060463
    {'ambient': '1296.3190', 'aut_centralizer_order': 216, 'aut_label': '144.j1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '4.2', 'aut_weyl_index': 864, 'centralizer': '8.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.e1.a1', '48.f1.a1', '48.g1.a1', '48.h1.a1', '72.m1.a1', '72.do1.a1', '72.do1.a2'], 'contains': ['432.a1.a1', '432.n1.a1', '432.o1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [3543, -1, 6163, -1, 5219, -1, 6320, -1], 'generators': [2, 588], 'label': '1296.3190.144.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.e1.a1', 'old_label': '144.j1.a1', 'projective_image': '432.598', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.j1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 71060464
    {'ambient': '1296.3190', 'aut_centralizer_order': 4, 'aut_label': '9.b1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '96.230', 'aut_weyl_index': 36, 'centralizer': '108.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.b1.a1', '3.d1.a1'], 'contains': ['18.e1.a1', '18.i1.a1', '18.m1.a1', '18.bh1.a1', '18.bk1.a1', '18.br1.a1', '18.bu1.a1', '27.a1.a1', '27.c1.a1'], 'core': '36.d1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [3521, -1, 7820, -1, 4570, -1, 6916, -1], 'generators': [3, 144, 216, 18, 108, 2], 'label': '1296.3190.9.b1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1.a1', 'old_label': '9.b1.a1', 'projective_image': '216.162', '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': '12.4'}
  • id: 71060465
    {'ambient': '1296.3190', 'aut_centralizer_order': 432, 'aut_label': '144.k1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 864, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.a1.a1', '48.j1.a1', '48.k1.a1', '72.n1.a1', '72.br1.a1', '72.br1.b1'], 'contains': ['432.b1.a1', '432.f1.a1', '432.k1.a1'], 'core': '432.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7338, -1, 3441, -1, 6691, -1, 4087, -1], 'generators': [146, 432], 'label': '1296.3190.144.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '144.k1.a1', 'projective_image': '1296.3190', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.k1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 71060466
    {'ambient': '1296.3190', 'aut_centralizer_order': 432, 'aut_label': '144.l1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 864, 'centralizer': '4.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.b1.a1', '48.i1.a1', '48.k1.a1', '72.o1.a1', '72.cc1.a1', '72.dc1.a1'], 'contains': ['432.b1.a1', '432.g1.a1', '432.l1.a1'], 'core': '432.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2603, -1, 3369, -1, 5583, -1, 5144, -1], 'generators': [14, 432], 'label': '1296.3190.144.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.a1', 'old_label': '144.l1.a1', 'projective_image': '1296.3190', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.l1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 71060467
    {'ambient': '1296.3190', 'aut_centralizer_order': 432, 'aut_label': '144.m1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 864, 'centralizer': '8.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.d1.a1', '48.e1.a1', '48.k1.a1', '72.p1.a1', '72.cs1.a1', '72.dr1.a1'], 'contains': ['432.b1.a1', '432.j1.a1', '432.n1.a1'], 'core': '432.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [5340, -1, 5235, -1, 5434, -1, 5745, -1], 'generators': [156, 432], 'label': '1296.3190.144.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.g1.a1', 'old_label': '144.m1.a1', 'projective_image': '1296.3190', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.m1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 71060468
    {'ambient': '1296.3190', 'aut_centralizer_order': 216, 'aut_label': '144.n1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '4.2', 'aut_weyl_index': 864, 'centralizer': '8.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.e1.a1', '48.i1.a1', '48.j1.a1', '48.k1.a1', '72.q1.a1'], 'contains': ['432.b1.a1', '432.m1.a1', '432.o1.a1'], 'core': '432.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [4085, -1, 4657, -1, 5403, -1, 5394, -1], 'generators': [158, 432], 'label': '1296.3190.144.n1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.f1.a1', 'old_label': '144.n1.a1', 'projective_image': '1296.3190', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.n1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 71060469
    {'ambient': '1296.3190', 'aut_centralizer_order': 432, 'aut_label': '144.o1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 864, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.a1.a1', '48.l1.a1', '48.m1.a1', '72.r1.a1', '72.bs1.a1', '72.bs1.b1', '72.ci1.a1', '72.ci1.b1', '72.ct1.a1', '72.ct1.b1'], 'contains': ['432.c1.a1', '432.e1.a1', '432.k1.a1'], 'core': '432.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7571, -1, 1563, -1, 6783, -1, 1536, -1], 'generators': [434, 144], 'label': '1296.3190.144.o1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '144.o1.a1', 'projective_image': '1296.3190', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.o1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 71060470
    {'ambient': '1296.3190', 'aut_centralizer_order': 432, 'aut_label': '144.p1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 864, 'centralizer': '4.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.c1.a1', '48.i1.a1', '48.m1.a1', '72.s1.a1', '72.cj1.a1', '72.de1.a1'], 'contains': ['432.c1.a1', '432.g1.a1', '432.m1.a1'], 'core': '432.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3865, -1, 2781, -1, 5526, -1, 5073, -1], 'generators': [14, 144], 'label': '1296.3190.144.p1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.a1', 'old_label': '144.p1.a1', 'projective_image': '1296.3190', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.p1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 71060471
    {'ambient': '1296.3190', 'aut_centralizer_order': 432, 'aut_label': '144.q1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 864, 'centralizer': '8.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.d1.a1', '48.f1.a1', '48.m1.a1', '72.t1.a1', '72.ck1.a1', '72.dt1.a1'], 'contains': ['432.c1.a1', '432.i1.a1', '432.n1.a1'], 'core': '432.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2539, -1, 3057, -1, 4862, -1, 5590, -1], 'generators': [444, 144], 'label': '1296.3190.144.q1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.e1.a1', 'old_label': '144.q1.a1', 'projective_image': '1296.3190', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.q1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 71060472
    {'ambient': '1296.3190', 'aut_centralizer_order': 216, 'aut_label': '144.r1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '4.2', 'aut_weyl_index': 864, 'centralizer': '8.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.f1.a1', '48.i1.a1', '48.l1.a1', '48.m1.a1', '72.u1.a1', '72.cl1.a1', '72.cl1.b1'], 'contains': ['432.c1.a1', '432.l1.a1', '432.o1.a1'], 'core': '432.c1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [3205, -1, 2817, -1, 5097, -1, 4996, -1], 'generators': [446, 144], 'label': '1296.3190.144.r1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.a1', 'old_label': '144.r1.a1', 'projective_image': '1296.3190', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.r1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 71060473
    {'ambient': '1296.3190', 'aut_centralizer_order': 432, 'aut_label': '144.s1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 864, 'centralizer': '4.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.b1.a1', '48.l1.a1', '48.n1.a1', '72.v1.a1', '72.bu1.a1', '72.bu1.b1', '72.cd1.a1', '72.cd1.b1', '72.cu1.a1', '72.cu1.b1'], 'contains': ['432.d1.a1', '432.e1.a1', '432.l1.a1'], 'core': '432.d1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7646, -1, 271, -1, 6938, -1, 1488, -1], 'generators': [434, 12], 'label': '1296.3190.144.s1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '144.s1.a1', 'projective_image': '1296.3190', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.s1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 71060474
    {'ambient': '1296.3190', 'aut_centralizer_order': 432, 'aut_label': '144.t1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 864, 'centralizer': '4.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.c1.a1', '48.j1.a1', '48.n1.a1', '72.w1.a1', '72.bv1.a1', '72.bv1.b1'], 'contains': ['432.d1.a1', '432.f1.a1', '432.m1.a1'], 'core': '432.d1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7392, -1, 2191, -1, 6722, -1, 4061, -1], 'generators': [146, 12], 'label': '1296.3190.144.t1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '144.t1.a1', 'projective_image': '1296.3190', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.t1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 71060475
    {'ambient': '1296.3190', 'aut_centralizer_order': 4, 'aut_label': '9.c1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '288.1040', 'aut_weyl_index': 12, 'centralizer': '108.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1.a1', '3.b1.a1'], 'contains': ['18.c1.a1', '18.f1.a1', '18.k1.a1', '18.n1.a1', '18.bl1.a1', '18.bt1.a1', '18.bx1.a1', '27.b1.a1', '27.c1.a1'], 'core': '18.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3676, -1, 8305, -1, 4504, -1, 6861, -1], 'generators': [3, 432, 144, 18, 108, 216], 'label': '1296.3190.9.c1.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.c1.a1', 'projective_image': '648.731', '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': '36.10'}
  • id: 71060476
    {'ambient': '1296.3190', 'aut_centralizer_order': 432, 'aut_label': '144.u1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '4.2', 'aut_weyl_index': 864, 'centralizer': '8.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.d1.a1', '48.g1.a1', '48.n1.a1', '72.x1.a1', '72.bw1.a1', '72.bw1.b1', '72.df1.a1', '72.df1.a2', '72.du1.a1', '72.du1.a2'], 'contains': ['432.d1.a1', '432.h1.a1', '432.n1.a1'], 'core': '432.d1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8796, -1, 3310, -1, 7063, -1, 4651, -1], 'generators': [12, 576], 'label': '1296.3190.144.u1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '144.u1.a1', 'projective_image': '1296.3190', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.u1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 71060477
    {'ambient': '1296.3190', 'aut_centralizer_order': 216, 'aut_label': '144.v1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '4.2', 'aut_weyl_index': 864, 'centralizer': '8.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.g1.a1', '48.j1.a1', '48.l1.a1', '48.n1.a1', '72.y1.a1', '72.bx1.a1', '72.bx1.b1'], 'contains': ['432.d1.a1', '432.k1.a1', '432.o1.a1'], 'core': '432.d1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [7242, -1, 608, -1, 6844, -1, 3958, -1], 'generators': [578, 12], 'label': '1296.3190.144.v1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '144.v1.a1', 'projective_image': '1296.3190', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.v1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 71060478
    {'ambient': '1296.3190', 'aut_centralizer_order': 432, 'aut_label': '144.w1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1728, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.a1.a1', '48.n1.a1', '48.o1.a1', '72.z1.a1', '72.bt1.a1', '72.bt1.b1'], 'contains': ['432.e1.a1', '432.f1.a1', '432.h1.a1', '432.k1.a1'], 'core': '1296.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [7370, -1, 3176, -1, 6753, -1, 4113, -1], 'generators': [434, 576], 'label': '1296.3190.144.w1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '144.w1.a1', 'projective_image': '1296.3190', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.w1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 71060479
    {'ambient': '1296.3190', 'aut_centralizer_order': 432, 'aut_label': '144.x1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1728, 'centralizer': '4.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.b1.a1', '48.m1.a1', '48.o1.a1', '72.ba1.a1', '72.ce1.a1', '72.ce1.b1'], 'contains': ['432.e1.a1', '432.g1.a1', '432.i1.a1', '432.l1.a1'], 'core': '1296.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [1456, -1, 2299, -1, 5035, -1, 5048, -1], 'generators': [434, 444], 'label': '1296.3190.144.x1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.a1', 'old_label': '144.x1.a1', 'projective_image': '1296.3190', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.x1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 71060480
    {'ambient': '1296.3190', 'aut_centralizer_order': 216, 'aut_label': '144.y1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '4.2', 'aut_weyl_index': 864, 'centralizer': '8.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.e1.a1', '48.l1.a1', '48.o1.a1', '72.bb1.a1', '72.cv1.a1', '72.cv1.b1'], 'contains': ['432.e1.a1', '432.j1.a1', '432.o1.a1'], 'core': '1296.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [5856, -1, 4178, -1, 5495, -1, 5022, -1], 'generators': [434, 156], 'label': '1296.3190.144.y1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1.a1', 'old_label': '144.y1.a1', 'projective_image': '1296.3190', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.y1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 71060481
    {'ambient': '1296.3190', 'aut_centralizer_order': 216, 'aut_label': '144.z1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1728, 'centralizer': '8.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.e1.a1', '48.m1.a1', '48.n1.a1', '48.o1.a1', '72.bc1.a1'], 'contains': ['432.e1.a1', '432.m1.a1', '432.n1.a1', '432.o1.a1'], 'core': '1296.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [3715, -1, 3595, -1, 5280, -1, 5719, -1], 'generators': [434, 588], 'label': '1296.3190.144.z1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.a1.a1', 'old_label': '144.z1.a1', 'projective_image': '1296.3190', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.z1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 71060482
    {'ambient': '1296.3190', 'aut_centralizer_order': 432, 'aut_label': '144.ba1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1728, 'centralizer': '4.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.c1.a1', '48.k1.a1', '48.o1.a1', '72.bd1.a1'], 'contains': ['432.f1.a1', '432.g1.a1', '432.j1.a1', '432.m1.a1'], 'core': '1296.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [4245, -1, 4197, -1, 5373, -1, 5693, -1], 'generators': [146, 156], 'label': '1296.3190.144.ba1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.f1.a1', 'old_label': '144.ba1.a1', 'projective_image': '1296.3190', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.ba1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 71060483
    {'ambient': '1296.3190', 'aut_centralizer_order': 216, 'aut_label': '144.bb1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '4.2', 'aut_weyl_index': 864, 'centralizer': '8.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.f1.a1', '48.j1.a1', '48.o1.a1', '72.be1.a1'], 'contains': ['432.f1.a1', '432.i1.a1', '432.o1.a1'], 'core': '1296.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [3434, -1, 3913, -1, 5004, -1, 5539, -1], 'generators': [146, 444], 'label': '1296.3190.144.bb1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.g1.a1', 'old_label': '144.bb1.a1', 'projective_image': '1296.3190', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.bb1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 71060484
    {'ambient': '1296.3190', 'aut_centralizer_order': 216, 'aut_label': '144.bc1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1728, 'centralizer': '8.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.f1.a1', '48.k1.a1', '48.n1.a1', '48.o1.a1', '72.bf1.a1'], 'contains': ['432.f1.a1', '432.l1.a1', '432.n1.a1', '432.o1.a1'], 'core': '1296.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [2920, -1, 4698, -1, 5066, -1, 5513, -1], 'generators': [146, 588], 'label': '1296.3190.144.bc1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.a1.a1', 'old_label': '144.bc1.a1', 'projective_image': '1296.3190', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.bc1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 71060485
    {'ambient': '1296.3190', 'aut_centralizer_order': 216, 'aut_label': '144.bd1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '4.2', 'aut_weyl_index': 864, 'centralizer': '8.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.g1.a1', '48.i1.a1', '48.o1.a1', '72.bg1.a1', '72.dg1.a1', '72.dg1.a2'], 'contains': ['432.g1.a1', '432.h1.a1', '432.o1.a1'], 'core': '1296.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [3922, -1, 3688, -1, 5722, -1, 5320, -1], 'generators': [14, 576], 'label': '1296.3190.144.bd1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.d1.a1', 'old_label': '144.bd1.a1', 'projective_image': '1296.3190', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.bd1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 71060486
    {'ambient': '1296.3190', 'aut_centralizer_order': 4, 'aut_label': '9.d1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '96.230', 'aut_weyl_index': 36, 'centralizer': '216.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.c1.a1', '3.d1.a1'], 'contains': ['18.p1.a1', '18.s1.a1', '18.w1.a1', '18.z1.a1', '18.be1.a1', '18.bq1.a1', '18.bv1.a1', '27.a1.a1', '27.d1.a1'], 'core': '36.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [5129, -1, 5636, -1, 4826, -1, 6277, -1], 'generators': [3, 12, 216, 18, 108, 2], 'label': '1296.3190.9.d1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.d1.a1', 'old_label': '9.d1.a1', 'projective_image': '216.162', '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': '24.14'}
  • id: 71060487
    {'ambient': '1296.3190', 'aut_centralizer_order': 216, 'aut_label': '144.be1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1728, 'centralizer': '8.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.g1.a1', '48.k1.a1', '48.m1.a1', '48.o1.a1', '72.bh1.a1'], 'contains': ['432.g1.a1', '432.k1.a1', '432.n1.a1', '432.o1.a1'], 'core': '1296.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [3024, -1, 3619, -1, 5311, -1, 5487, -1], 'generators': [578, 588], 'label': '1296.3190.144.be1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.a1.a1', 'old_label': '144.be1.a1', 'projective_image': '1296.3190', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.be1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 71060488
    {'ambient': '1296.3190', 'aut_centralizer_order': 432, 'aut_label': '144.bf1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1728, 'centralizer': '8.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.d1.a1', '48.h1.a1', '48.o1.a1', '72.bi1.a1', '72.dv1.a1', '72.dv1.a2'], 'contains': ['432.h1.a1', '432.i1.a1', '432.j1.a1', '432.n1.a1'], 'core': '1296.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [3606, -1, 6214, -1, 5188, -1, 6923, -1], 'generators': [444, 576], 'label': '1296.3190.144.bf1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.e1.a1', 'old_label': '144.bf1.a1', 'projective_image': '1296.3190', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.bf1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 71060489
    {'ambient': '1296.3190', 'aut_centralizer_order': 216, 'aut_label': '144.bg1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1728, 'centralizer': '8.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.h1.a1', '48.i1.a1', '48.n1.a1', '48.o1.a1', '72.bj1.a1'], 'contains': ['432.h1.a1', '432.l1.a1', '432.m1.a1', '432.o1.a1'], 'core': '1296.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [3781, -1, 3636, -1, 5342, -1, 5565, -1], 'generators': [446, 576], 'label': '1296.3190.144.bg1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.a1.a1', 'old_label': '144.bg1.a1', 'projective_image': '1296.3190', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.bg1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 71060490
    {'ambient': '1296.3190', 'aut_centralizer_order': 216, 'aut_label': '144.bh1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1728, 'centralizer': '8.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.h1.a1', '48.j1.a1', '48.m1.a1', '48.o1.a1', '72.bk1.a1'], 'contains': ['432.i1.a1', '432.k1.a1', '432.m1.a1', '432.o1.a1'], 'core': '1296.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [3737, -1, 3654, -1, 5127, -1, 5667, -1], 'generators': [578, 444], 'label': '1296.3190.144.bh1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.a1.a1', 'old_label': '144.bh1.a1', 'projective_image': '1296.3190', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.bh1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 71060491
    {'ambient': '1296.3190', 'aut_centralizer_order': 216, 'aut_label': '144.bi1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1728, 'centralizer': '8.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.h1.a1', '48.k1.a1', '48.l1.a1', '48.o1.a1', '72.bl1.a1'], 'contains': ['432.j1.a1', '432.k1.a1', '432.l1.a1', '432.o1.a1'], 'core': '1296.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [4010, -1, 4678, -1, 5250, -1, 5642, -1], 'generators': [578, 156], 'label': '1296.3190.144.bi1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.a1.a1', 'old_label': '144.bi1.a1', 'projective_image': '1296.3190', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.bi1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 71060492
    {'ambient': '1296.3190', 'aut_centralizer_order': 216, 'aut_label': '144.bj1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1728, 'centralizer': '8.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.h1.a1', '48.k1.a1', '48.m1.a1', '48.n1.a1', '72.bm1.a1'], 'contains': ['432.k1.a1', '432.l1.a1', '432.m1.a1', '432.n1.a1'], 'core': '1296.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [3490, -1, 4621, -1, 5158, -1, 5616, -1], 'generators': [1010, 588], 'label': '1296.3190.144.bj1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.a1.a1', 'old_label': '144.bj1.a1', 'projective_image': '1296.3190', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.bj1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 71060493
    {'ambient': '1296.3190', 'aut_centralizer_order': 96, 'aut_label': '162.a1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '4.2', 'aut_weyl_index': 864, 'centralizer': '18.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['54.a1.a1', '54.b1.a1', '54.c1.a1', '54.d1.a1', '54.m1.a1', '81.a1.a1'], 'contains': ['324.a1.a1', '324.b1.a1', '324.c1.a1', '324.h1.a1', '324.h1.b1'], 'core': '648.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [5751, -1, 5371, -1, 6387, -1, 1638, -1], 'generators': [3, 18, 216], 'label': '1296.3190.162.a1.a1', 'mobius_quo': None, 'mobius_sub': -3, 'normal_closure': '18.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '162.a1.a1', 'projective_image': '648.731', '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: 71060494
    {'ambient': '1296.3190', 'aut_centralizer_order': 32, 'aut_label': '162.b1', 'aut_quo_index': None, 'aut_stab_index': 27, 'aut_weyl_group': '4.2', 'aut_weyl_index': 864, 'centralizer': '54.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['54.e1.a1', '54.f1.a1', '54.g1.a1', '54.h1.a1', '54.n1.a1', '81.a1.a1'], 'contains': ['324.a1.a1', '324.d1.a1', '324.e1.a1', '324.i1.a1', '324.i1.b1'], 'core': '648.a1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [6649, -1, 5958, -1, 6926, -1, 4794, -1], 'generators': [3, 54, 216], 'label': '1296.3190.162.b1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '6.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1.a1', 'old_label': '162.b1.a1', 'projective_image': '648.731', '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: 71060495
    {'ambient': '1296.3190', 'aut_centralizer_order': 96, 'aut_label': '162.c1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '4.2', 'aut_weyl_index': 864, 'centralizer': '18.m1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['54.i1.a1', '54.j1.a1', '54.k1.a1', '54.l1.a1', '54.o1.a1', '81.a1.a1'], 'contains': ['324.a1.a1', '324.f1.a1', '324.g1.a1'], 'core': '648.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [916, -1, 9283, -1, 1263, -1, 8744, -1], 'generators': [3, 108], 'label': '1296.3190.162.c1.a1', 'mobius_quo': None, 'mobius_sub': -3, 'normal_closure': '18.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1.a1', 'old_label': '162.c1.a1', 'projective_image': '648.731', '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': '2.1'}
  • id: 71060496
    {'ambient': '1296.3190', 'aut_centralizer_order': 96, 'aut_label': '162.d1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '4.2', 'aut_weyl_index': 864, 'centralizer': '36.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['54.p1.a1', '54.q1.a1', '54.r1.a1', '54.s1.a1', '54.x1.a1', '81.a1.a1'], 'contains': ['324.b1.a1', '324.d1.a1', '324.f1.a1'], 'core': '648.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [976, -1, 7432, -1, 4064, -1, 7130, -1], 'generators': [18, 108], 'label': '1296.3190.162.d1.a1', 'mobius_quo': None, 'mobius_sub': -3, 'normal_closure': '18.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.d1.a1', 'old_label': '162.d1.a1', 'projective_image': '648.731', '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: 71060497
    {'ambient': '1296.3190', 'aut_centralizer_order': 4, 'aut_label': '9.e1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '288.1040', 'aut_weyl_index': 12, 'centralizer': '216.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1.a1', '3.c1.a1'], 'contains': ['18.b1.a1', '18.q1.a1', '18.t1.a1', '18.bb1.a1', '18.bg1.a1', '18.bs1.a1', '18.by1.a1', '27.b1.a1', '27.d1.a1'], 'core': '18.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4932, -1, 6076, -1, 4755, -1, 6217, -1], 'generators': [3, 432, 12, 18, 108, 216], 'label': '1296.3190.9.e1.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.e1.a1', 'projective_image': '648.731', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '9.e1.a1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 71060498
    {'ambient': '1296.3190', 'aut_centralizer_order': 32, 'aut_label': '162.e1', 'aut_quo_index': None, 'aut_stab_index': 27, 'aut_weyl_group': '4.2', 'aut_weyl_index': 864, 'centralizer': '108.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['54.t1.a1', '54.u1.a1', '54.v1.a1', '54.w1.a1', '54.y1.a1', '81.a1.a1'], 'contains': ['324.b1.a1', '324.e1.a1', '324.g1.a1'], 'core': '648.a1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [1082, -1, 7764, -1, 3385, -1, 7893, -1], 'generators': [111, 18], 'label': '1296.3190.162.e1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '6.h1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1.a1', 'old_label': '162.e1.a1', 'projective_image': '648.731', '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': '4.2'}
  • id: 71060499
    {'ambient': '1296.3190', 'aut_centralizer_order': 32, 'aut_label': '162.f1', 'aut_quo_index': None, 'aut_stab_index': 27, 'aut_weyl_group': '4.2', 'aut_weyl_index': 864, 'centralizer': '108.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['54.z1.a1', '54.ba1.a1', '54.bd1.a1', '54.be1.a1', '81.a1.a1'], 'contains': ['324.c1.a1', '324.d1.a1', '324.g1.a1'], 'core': '648.a1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [4278, -1, 7375, -1, 5759, -1, 6553, -1], 'generators': [111, 54], 'label': '1296.3190.162.f1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '6.i1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1.a1', 'old_label': '162.f1.a1', 'projective_image': '648.731', '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: 71060500
    {'ambient': '1296.3190', 'aut_centralizer_order': 32, 'aut_label': '162.g1', 'aut_quo_index': None, 'aut_stab_index': 27, 'aut_weyl_group': '4.2', 'aut_weyl_index': 864, 'centralizer': '108.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['54.bb1.a1', '54.bc1.a1', '54.bf1.a1', '54.bg1.a1', '54.bh1.a1', '81.a1.a1'], 'contains': ['324.c1.a1', '324.e1.a1', '324.f1.a1'], 'core': '648.a1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [2942, -1, 8541, -1, 3358, -1, 7987, -1], 'generators': [9, 108], 'label': '1296.3190.162.g1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '6.j1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1.a1', 'old_label': '162.g1.a1', 'projective_image': '648.731', '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: 71060501
    {'ambient': '1296.3190', 'aut_centralizer_order': 1728, 'aut_label': '216.a1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1728, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['72.a1.a1', '72.b1.a1', '72.c1.a1', '72.j1.a1', '72.k1.a1', '72.l1.a1', '72.m1.a1', '108.d1.a1', '108.k1.a1', '108.r1.a1', '108.x1.a1', '108.bd1.a1', '108.bl1.a1', '108.bm1.a1'], 'contains': ['432.a1.a1', '648.a1.a1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4123, 4672, 7495, 5413, 3739, 4604, 6415, 5530], 'generators': [216, 2], 'label': '1296.3190.216.a1.a1', 'mobius_quo': 1, 'mobius_sub': 216, 'normal_closure': '216.a1.a1', 'normal_contained_in': ['72.b1.a1', '72.a1.a1', '72.c1.a1'], 'normal_contains': ['432.a1.a1', '648.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '216.a1.a1', 'projective_image': '216.162', 'quotient_action_image': '1.1', 'quotient_action_kernel': '216.162', 'quotient_action_kernel_order': 216, 'quotient_fusion': None, 'short_label': '216.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 71060502
    {'ambient': '1296.3190', 'aut_centralizer_order': 1728, 'aut_label': '216.b1', 'aut_quo_index': 8, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1728, 'centralizer': '2.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['72.a1.a1', '72.d1.a1', '72.e1.a1', '72.n1.a1', '72.o1.a1', '72.p1.a1', '72.q1.a1', '108.c1.a1', '108.e1.a1', '108.l1.a1', '108.s1.a1', '108.ba1.a1', '108.be1.a1', '108.bn1.a1'], 'contains': ['432.b1.a1', '648.a1.a1'], 'core': '216.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3948, 4033, 7515, 6355, 3589, 5550, 6392, 5835], 'generators': [216, 432], 'label': '1296.3190.216.b1.a1', 'mobius_quo': 1, 'mobius_sub': 72, 'normal_closure': '216.b1.a1', 'normal_contained_in': ['72.a1.a1', '72.d1.a1', '72.e1.a1', '108.c1.a1'], 'normal_contains': ['432.b1.a1', '648.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '216.b1.a1', 'projective_image': '648.731', 'quotient_action_image': '2.1', 'quotient_action_kernel': '108.38', 'quotient_action_kernel_order': 108, 'quotient_fusion': None, 'short_label': '216.b1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 71060503
    {'ambient': '1296.3190', 'aut_centralizer_order': 1728, 'aut_label': '216.c1', 'aut_quo_index': 8, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1728, 'centralizer': '2.c1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['72.b1.a1', '72.d1.a1', '72.f1.a1', '72.r1.a1', '72.s1.a1', '72.t1.a1', '72.u1.a1', '108.b1.a1', '108.f1.a1', '108.u1.a1', '108.bb1.a1', '108.bf1.a1', '108.bo1.a1', '108.bp1.a1'], 'contains': ['432.c1.a1', '648.a1.a1'], 'core': '216.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3668, 4873, 7448, 5224, 3678, 5011, 6273, 5348], 'generators': [216, 144], 'label': '1296.3190.216.c1.a1', 'mobius_quo': 1, 'mobius_sub': 72, 'normal_closure': '216.c1.a1', 'normal_contained_in': ['72.b1.a1', '72.d1.a1', '72.f1.a1', '108.b1.a1'], 'normal_contains': ['432.c1.a1', '648.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '216.c1.a1', 'projective_image': '648.731', 'quotient_action_image': '2.1', 'quotient_action_kernel': '108.38', 'quotient_action_kernel_order': 108, 'quotient_fusion': None, 'short_label': '216.c1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 71060504
    {'ambient': '1296.3190', 'aut_centralizer_order': 1728, 'aut_label': '216.d1', 'aut_quo_index': 8, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1728, 'centralizer': '2.d1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['72.c1.a1', '72.e1.a1', '72.f1.a1', '72.v1.a1', '72.w1.a1', '72.x1.a1', '72.y1.a1', '108.a1.a1', '108.m1.a1', '108.v1.a1', '108.y1.a1', '108.bg1.a1', '108.bq1.a1', '108.br1.a1'], 'contains': ['432.d1.a1', '648.a1.a1'], 'core': '216.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5407, 6471, 5934, 4110, 4486, 3980, 5344, 4358], 'generators': [216, 12], 'label': '1296.3190.216.d1.a1', 'mobius_quo': 1, 'mobius_sub': 72, 'normal_closure': '216.d1.a1', 'normal_contained_in': ['72.c1.a1', '72.e1.a1', '72.f1.a1', '108.a1.a1'], 'normal_contains': ['432.d1.a1', '648.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '216.d1.a1', 'projective_image': '648.731', 'quotient_action_image': '2.1', 'quotient_action_kernel': '108.38', 'quotient_action_kernel_order': 108, 'quotient_fusion': None, 'short_label': '216.d1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 71060569
    {'ambient': '1296.3190', 'aut_centralizer_order': 16, 'aut_label': '216.bw1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '6.1', 'aut_weyl_index': 576, 'centralizer': '216.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.dm1.a1', '72.dq1.a1', '72.dt1.a1', '72.dv1.a1', '72.dv1.a2', '108.bi1.a1'], 'contains': ['432.i1.a1', '648.f1.a1'], 'core': '1296.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [3169, -1, 6080, -1, 4945, -1, 7313, -1], 'generators': [45, 444], 'label': '1296.3190.216.bw1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.k1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.cg1.a1', 'old_label': '216.bw1.a1', 'projective_image': '1296.3190', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.bw1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 71060505
    {'ambient': '1296.3190', 'aut_centralizer_order': 288, 'aut_label': '216.e1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '6.1', 'aut_weyl_index': 576, 'centralizer': '6.f1.a1', 'complements': ['6.f1.a1', '6.x1.a1', '6.bd1.a1', '6.bf1.a1', '6.y1.a1', '6.ba1.a1', '6.bc1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['72.g1.a1', '72.h1.a1', '72.i1.a1', '72.bu1.a1', '72.bv1.a1', '72.bw1.a1', '72.bx1.a1', '108.a1.a1', '108.cg1.a1', '108.ch1.a1'], 'contains': ['432.d1.a1', '648.b1.a1'], 'core': '216.e1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [9545, 8158, 1478, 2267, 8685, 2379, 2006, 2952], 'generators': [3, 12], 'label': '1296.3190.216.e1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '216.e1.a1', 'normal_contained_in': ['72.g1.a1', '72.h1.a1', '72.i1.a1', '108.a1.a1'], 'normal_contains': ['432.d1.a1'], 'normalizer': '1.a1.a1', 'old_label': '216.e1.a1', 'projective_image': '1296.3190', 'quotient_action_image': '1.1', 'quotient_action_kernel': '216.122', 'quotient_action_kernel_order': 216, 'quotient_fusion': None, 'short_label': '216.e1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 71060506
    {'ambient': '1296.3190', 'aut_centralizer_order': 288, 'aut_label': '216.e1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '6.1', 'aut_weyl_index': 576, 'centralizer': '6.f1.a1', 'complements': ['6.f1.a1', '6.x1.a1', '6.bd1.a1', '6.bf1.a1', '6.y1.a1', '6.ba1.a1', '6.bc1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['72.g1.b1', '72.h1.b1', '72.i1.b1', '72.bu1.b1', '72.bv1.b1', '72.bw1.b1', '72.bx1.b1', '108.a1.a1', '108.cg1.b1', '108.ch1.b1'], 'contains': ['432.d1.a1', '648.b1.b1'], 'core': '216.e1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [9545, 8158, 2272, 1796, 8685, 2379, 2589, 2688], 'generators': [219, 12], 'label': '1296.3190.216.e1.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '216.e1.b1', 'normal_contained_in': ['72.g1.b1', '72.h1.b1', '72.i1.b1', '108.a1.a1'], 'normal_contains': ['432.d1.a1'], 'normalizer': '1.a1.a1', 'old_label': '216.e1.b1', 'projective_image': '1296.3190', 'quotient_action_image': '1.1', 'quotient_action_kernel': '216.122', 'quotient_action_kernel_order': 216, 'quotient_fusion': None, 'short_label': '216.e1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 71060507
    {'ambient': '1296.3190', 'aut_centralizer_order': 864, 'aut_label': '216.f1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1728, 'centralizer': '2.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.a1.a1', '72.r1.a1', '72.v1.a1', '72.z1.a1', '72.ba1.a1', '72.bb1.a1', '72.bc1.a1', '108.g1.a1', '108.n1.a1', '108.t1.a1'], 'contains': ['432.e1.a1', '648.a1.a1'], 'core': '648.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3320, -1, 5278, -1, 3993, -1, 5250, -1], 'generators': [216, 434], 'label': '1296.3190.216.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '72.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '216.f1.a1', 'projective_image': '648.731', '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': '1.1'}
  • id: 71060508
    {'ambient': '1296.3190', 'aut_centralizer_order': 2, 'aut_label': '2.f1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '1728.47915', 'aut_weyl_index': 2, 'centralizer': '216.a1.a1', 'complements': ['648.c1.a1', '648.b1.a1', '648.b1.b1', '648.f1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.c1.a1', '4.d1.a1', '4.g1.a1', '6.i1.a1', '6.bb1.a1', '6.bc1.a1', '6.bg1.a1'], 'core': '2.f1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4835, 4430, 6347, 5042, 5470, 4752, 6014, 5949], 'generators': [111, 144, 12, 54, 432, 2, 216], 'label': '1296.3190.2.f1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.f1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.d1.a1', '4.c1.a1', '4.g1.a1', '6.i1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.f1.a1', 'projective_image': '216.162', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.f1.a1', 'subgroup_fusion': None, 'weyl_group': '216.162'}
  • id: 71060509
    {'ambient': '1296.3190', 'aut_centralizer_order': 4, 'aut_label': '9.f1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '288.1040', 'aut_weyl_index': 12, 'centralizer': '216.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1.a1', '3.d1.a1'], 'contains': ['18.a1.a1', '18.u1.a1', '18.x1.a1', '18.bi1.a1', '18.bm1.a1', '18.ca1.a1', '18.cb1.a1', '27.c1.a1', '27.d1.a1'], 'core': '18.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4457, -1, 6285, -1, 4694, -1, 6166, -1], 'generators': [3, 144, 12, 18, 108, 216], 'label': '1296.3190.9.f1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.d1.a1', 'old_label': '9.f1.a1', 'projective_image': '648.731', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '9.f1.a1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 71060510
    {'ambient': '1296.3190', 'aut_centralizer_order': 864, 'aut_label': '216.g1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1728, 'centralizer': '2.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.b1.a1', '72.n1.a1', '72.w1.a1', '72.z1.a1', '72.bd1.a1', '72.be1.a1', '72.bf1.a1', '108.h1.a1', '108.bs1.a1', '108.bt1.a1'], 'contains': ['432.f1.a1', '648.a1.a1'], 'core': '648.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2367, -1, 8992, -1, 2272, -1, 6866, -1], 'generators': [216, 146], 'label': '1296.3190.216.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '72.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '216.g1.a1', 'projective_image': '648.731', '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: 71060511
    {'ambient': '1296.3190', 'aut_centralizer_order': 864, 'aut_label': '216.h1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1728, 'centralizer': '2.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.c1.a1', '72.o1.a1', '72.s1.a1', '72.ba1.a1', '72.bd1.a1', '72.bg1.a1', '72.bh1.a1', '108.o1.a1', '108.z1.a1', '108.bu1.a1'], 'contains': ['432.g1.a1', '648.a1.a1'], 'core': '648.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1303, -1, 6784, -1, 3216, -1, 6731, -1], 'generators': [216, 14], 'label': '1296.3190.216.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '72.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.a1', 'old_label': '216.h1.a1', 'projective_image': '648.731', '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: 71060512
    {'ambient': '1296.3190', 'aut_centralizer_order': 864, 'aut_label': '216.i1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1728, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.d1.a1', '72.j1.a1', '72.x1.a1', '72.z1.a1', '72.bg1.a1', '72.bi1.a1', '72.bj1.a1', '108.i1.a1', '108.bc1.a1', '108.bh1.a1'], 'contains': ['432.h1.a1', '648.a1.a1'], 'core': '648.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [4728, -1, 6663, -1, 4055, -1, 6295, -1], 'generators': [216, 576], 'label': '1296.3190.216.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '72.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '216.i1.a1', 'projective_image': '648.731', '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: 71060513
    {'ambient': '1296.3190', 'aut_centralizer_order': 864, 'aut_label': '216.j1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1728, 'centralizer': '4.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.e1.a1', '72.k1.a1', '72.t1.a1', '72.ba1.a1', '72.be1.a1', '72.bi1.a1', '72.bk1.a1', '108.p1.a1', '108.bi1.a1', '108.bv1.a1'], 'contains': ['432.i1.a1', '648.a1.a1'], 'core': '648.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1117, -1, 7866, -1, 2908, -1, 7438, -1], 'generators': [216, 444], 'label': '1296.3190.216.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '72.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.e1.a1', 'old_label': '216.j1.a1', 'projective_image': '648.731', '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': '2.1'}
  • id: 71060514
    {'ambient': '1296.3190', 'aut_centralizer_order': 864, 'aut_label': '216.k1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1728, 'centralizer': '4.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.f1.a1', '72.l1.a1', '72.p1.a1', '72.bb1.a1', '72.bd1.a1', '72.bi1.a1', '72.bl1.a1', '108.w1.a1', '108.bj1.a1', '108.bw1.a1'], 'contains': ['432.j1.a1', '648.a1.a1'], 'core': '648.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2751, -1, 8344, -1, 2947, -1, 7582, -1], 'generators': [216, 156], 'label': '1296.3190.216.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '72.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.g1.a1', 'old_label': '216.k1.a1', 'projective_image': '648.731', '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: 71060515
    {'ambient': '1296.3190', 'aut_centralizer_order': 432, 'aut_label': '216.l1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1728, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.j1.a1', '72.n1.a1', '72.r1.a1', '72.y1.a1', '72.z1.a1', '72.bh1.a1', '72.bk1.a1', '72.bl1.a1', '72.bm1.a1', '108.j1.a1'], 'contains': ['432.k1.a1', '648.a1.a1'], 'core': '648.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [2791, -1, 6647, -1, 3616, -1, 6370, -1], 'generators': [216, 578], 'label': '1296.3190.216.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '216.l1.a1', 'projective_image': '648.731', '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: 71060516
    {'ambient': '1296.3190', 'aut_centralizer_order': 432, 'aut_label': '216.m1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1728, 'centralizer': '4.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.k1.a1', '72.o1.a1', '72.u1.a1', '72.v1.a1', '72.ba1.a1', '72.bf1.a1', '72.bj1.a1', '72.bl1.a1', '72.bm1.a1', '108.q1.a1'], 'contains': ['432.l1.a1', '648.a1.a1'], 'core': '648.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [1097, -1, 6976, -1, 2986, -1, 6834, -1], 'generators': [216, 446], 'label': '1296.3190.216.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.a1', 'old_label': '216.m1.a1', 'projective_image': '648.731', '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: 71060517
    {'ambient': '1296.3190', 'aut_centralizer_order': 432, 'aut_label': '216.n1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1728, 'centralizer': '4.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.l1.a1', '72.q1.a1', '72.s1.a1', '72.w1.a1', '72.bc1.a1', '72.bd1.a1', '72.bj1.a1', '72.bk1.a1', '72.bm1.a1', '108.bx1.a1'], 'contains': ['432.m1.a1', '648.a1.a1'], 'core': '648.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [1645, -1, 8006, -1, 2425, -1, 7290, -1], 'generators': [216, 158], 'label': '1296.3190.216.n1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.f1.a1', 'old_label': '216.n1.a1', 'projective_image': '648.731', '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': '1.1'}
  • id: 71060518
    {'ambient': '1296.3190', 'aut_centralizer_order': 432, 'aut_label': '216.o1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1728, 'centralizer': '8.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.m1.a1', '72.p1.a1', '72.t1.a1', '72.x1.a1', '72.bc1.a1', '72.bf1.a1', '72.bh1.a1', '72.bi1.a1', '72.bm1.a1', '108.bk1.a1'], 'contains': ['432.n1.a1', '648.a1.a1'], 'core': '648.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [1345, -1, 8329, -1, 2730, -1, 7461, -1], 'generators': [216, 588], 'label': '1296.3190.216.o1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.e1.a1', 'old_label': '216.o1.a1', 'projective_image': '648.731', '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: 71060519
    {'ambient': '1296.3190', 'aut_centralizer_order': 216, 'aut_label': '216.p1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1728, 'centralizer': '8.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.m1.a1', '72.q1.a1', '72.u1.a1', '72.y1.a1', '72.bb1.a1', '72.bc1.a1', '72.be1.a1', '72.bf1.a1', '72.bg1.a1', '72.bh1.a1', '72.bj1.a1', '72.bk1.a1', '72.bl1.a1'], 'contains': ['432.o1.a1', '648.a1.a1'], 'core': '648.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [1519, -1, 7150, -1, 2577, -1, 6899, -1], 'generators': [216, 590], 'label': '1296.3190.216.p1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.a1.a1', 'old_label': '216.p1.a1', 'projective_image': '648.731', '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: 71060520
    {'ambient': '1296.3190', 'aut_centralizer_order': 72, 'aut_label': '12.a1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '48.51', 'aut_weyl_index': 72, 'centralizer': '12.d1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '6.d1.a1', '6.n1.a1', '6.p1.a1'], 'contains': ['24.b1.a1', '24.e1.a1', '24.e1.b1', '36.a1.a1', '36.b1.a1', '36.m1.a1', '36.t1.a1'], 'core': '12.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6109, 8171, 3264, 1858, 7587, 1221, 2654, 2102], 'generators': [3, 12, 216, 2, 432], 'label': '1296.3190.12.a1.a1', 'mobius_quo': 0, 'mobius_sub': -6, 'normal_closure': '12.a1.a1', 'normal_contained_in': ['4.a1.a1', '6.d1.a1'], 'normal_contains': ['24.b1.a1', '24.e1.a1', '24.e1.b1', '36.a1.a1', '36.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '12.a1.a1', 'projective_image': '216.162', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.a1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 71060521
    {'ambient': '1296.3190', 'aut_centralizer_order': 288, 'aut_label': '216.q1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1728, 'centralizer': '3.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.g1.a1', '72.bn1.a1', '72.bo1.a1', '72.bp1.a1', '108.d1.a1', '108.by1.a1', '108.cc1.a1'], 'contains': ['432.a1.a1', '648.b1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [9052, -1, 3098, -1, 8341, -1, 2657, -1], 'generators': [3, 2], 'label': '1296.3190.216.q1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '72.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '216.q1.a1', 'projective_image': '432.598', '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: 71060522
    {'ambient': '1296.3190', 'aut_centralizer_order': 288, 'aut_label': '216.q1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1728, 'centralizer': '3.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.g1.b1', '72.bn1.b1', '72.bo1.b1', '72.bp1.b1', '108.d1.a1', '108.by1.b1', '108.cc1.b1'], 'contains': ['432.a1.a1', '648.b1.b1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [9052, -1, 4050, -1, 8341, -1, 2725, -1], 'generators': [219, 2], 'label': '1296.3190.216.q1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '72.g1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '216.q1.b1', 'projective_image': '432.598', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.q1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 71060523
    {'ambient': '1296.3190', 'aut_centralizer_order': 288, 'aut_label': '216.r1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1728, 'centralizer': '6.k1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.h1.a1', '72.bn1.a1', '72.bq1.a1', '72.br1.a1', '108.e1.a1', '108.bz1.a1', '108.cd1.a1'], 'contains': ['432.b1.a1', '648.b1.a1'], 'core': '432.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [9000, -1, 2992, -1, 8234, -1, 2284, -1], 'generators': [3, 432], 'label': '1296.3190.216.r1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '72.h1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '216.r1.a1', 'projective_image': '1296.3190', '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': '2.1'}
  • id: 71060524
    {'ambient': '1296.3190', 'aut_centralizer_order': 288, 'aut_label': '216.r1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1728, 'centralizer': '6.k1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.h1.b1', '72.bn1.b1', '72.bq1.b1', '72.br1.b1', '108.e1.a1', '108.bz1.b1', '108.cd1.b1'], 'contains': ['432.b1.a1', '648.b1.b1'], 'core': '432.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [9000, -1, 3975, -1, 8234, -1, 2702, -1], 'generators': [219, 432], 'label': '1296.3190.216.r1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '72.h1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '216.r1.b1', 'projective_image': '1296.3190', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.r1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 71060525
    {'ambient': '1296.3190', 'aut_centralizer_order': 288, 'aut_label': '216.s1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1728, 'centralizer': '6.m1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.i1.a1', '72.bo1.a1', '72.bq1.a1', '72.bs1.a1', '108.f1.a1', '108.cb1.a1', '108.ce1.a1'], 'contains': ['432.c1.a1', '648.b1.a1'], 'core': '432.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8725, -1, 2865, -1, 8261, -1, 2194, -1], 'generators': [3, 144], 'label': '1296.3190.216.s1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '72.i1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '216.s1.a1', 'projective_image': '1296.3190', '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': '2.1'}
  • id: 71060526
    {'ambient': '1296.3190', 'aut_centralizer_order': 288, 'aut_label': '216.s1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1728, 'centralizer': '6.m1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.i1.b1', '72.bo1.b1', '72.bq1.b1', '72.bs1.b1', '108.f1.a1', '108.cb1.b1', '108.ce1.b1'], 'contains': ['432.c1.a1', '648.b1.b1'], 'core': '432.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8725, -1, 3807, -1, 8261, -1, 2612, -1], 'generators': [219, 144], 'label': '1296.3190.216.s1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '72.i1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '216.s1.b1', 'projective_image': '1296.3190', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.s1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 71060527
    {'ambient': '1296.3190', 'aut_centralizer_order': 144, 'aut_label': '216.t1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1728, 'centralizer': '6.k1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.bn1.a1', '72.bs1.a1', '72.bt1.a1', '72.bu1.a1', '108.g1.a1', '108.ca1.a1', '108.ca1.b1'], 'contains': ['432.e1.a1', '648.b1.a1'], 'core': '1296.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [8553, -1, 1302, -1, 8288, -1, 1110, -1], 'generators': [3, 434], 'label': '1296.3190.216.t1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.k1.a1', 'old_label': '216.t1.a1', 'projective_image': '1296.3190', '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': '1.1'}
  • id: 71060528
    {'ambient': '1296.3190', 'aut_centralizer_order': 144, 'aut_label': '216.t1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1728, 'centralizer': '6.k1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.bn1.b1', '72.bs1.b1', '72.bt1.b1', '72.bu1.b1', '108.g1.a1', '108.ca1.c1', '108.ca1.d1'], 'contains': ['432.e1.a1', '648.b1.b1'], 'core': '1296.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [8553, -1, 2017, -1, 8288, -1, 1441, -1], 'generators': [219, 434], 'label': '1296.3190.216.t1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.e1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.k1.a1', 'old_label': '216.t1.b1', 'projective_image': '1296.3190', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.t1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 71060529
    {'ambient': '1296.3190', 'aut_centralizer_order': 144, 'aut_label': '216.u1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1728, 'centralizer': '6.m1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.bo1.a1', '72.br1.a1', '72.bt1.a1', '72.bv1.a1', '108.h1.a1'], 'contains': ['432.f1.a1', '648.b1.a1'], 'core': '1296.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [8366, -1, 2945, -1, 8207, -1, 2261, -1], 'generators': [3, 146], 'label': '1296.3190.216.u1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.m1.a1', 'old_label': '216.u1.a1', 'projective_image': '1296.3190', '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': '1.1'}
  • id: 71060530
    {'ambient': '1296.3190', 'aut_centralizer_order': 144, 'aut_label': '216.u1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1728, 'centralizer': '6.m1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.bo1.b1', '72.br1.b1', '72.bt1.b1', '72.bv1.b1', '108.h1.a1'], 'contains': ['432.f1.a1', '648.b1.b1'], 'core': '1296.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [8366, -1, 3888, -1, 8207, -1, 2680, -1], 'generators': [219, 146], 'label': '1296.3190.216.u1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.f1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.m1.a1', 'old_label': '216.u1.b1', 'projective_image': '1296.3190', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.u1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 71060531
    {'ambient': '1296.3190', 'aut_centralizer_order': 72, 'aut_label': '12.b1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '48.51', 'aut_weyl_index': 72, 'centralizer': '12.l1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '6.a1.a1', '6.q1.a1', '6.s1.a1'], 'contains': ['24.c1.a1', '24.f1.a1', '24.f1.b1', '36.a1.a1', '36.c1.a1', '36.n1.a1', '36.u1.a1'], 'core': '12.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6166, 9763, 4612, 1309, 7351, 254, 2786, 640], 'generators': [3, 12, 216, 2, 144], 'label': '1296.3190.12.b1.a1', 'mobius_quo': 0, 'mobius_sub': -6, 'normal_closure': '12.b1.a1', 'normal_contained_in': ['4.a1.a1', '6.a1.a1'], 'normal_contains': ['24.c1.a1', '24.f1.a1', '24.f1.b1', '36.a1.a1', '36.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '12.b1.a1', 'projective_image': '216.162', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.b1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 71060532
    {'ambient': '1296.3190', 'aut_centralizer_order': 144, 'aut_label': '216.v1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1728, 'centralizer': '12.q1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.bp1.a1', '72.bq1.a1', '72.bt1.a1', '72.bw1.a1', '108.i1.a1', '108.cf1.a1', '108.cf1.a2'], 'contains': ['432.h1.a1', '648.b1.a1'], 'core': '1296.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [9286, -1, 4441, -1, 8422, -1, 3170, -1], 'generators': [3, 576], 'label': '1296.3190.216.v1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.l1.a1', 'old_label': '216.v1.a1', 'projective_image': '1296.3190', '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': '2.1'}
  • id: 71060533
    {'ambient': '1296.3190', 'aut_centralizer_order': 144, 'aut_label': '216.v1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1728, 'centralizer': '12.q1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.bp1.b1', '72.bq1.b1', '72.bt1.b1', '72.bw1.b1', '108.i1.a1', '108.cf1.b1', '108.cf1.b2'], 'contains': ['432.h1.a1', '648.b1.b1'], 'core': '1296.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [9286, -1, 4840, -1, 8422, -1, 3298, -1], 'generators': [219, 576], 'label': '1296.3190.216.v1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.g1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.l1.a1', 'old_label': '216.v1.b1', 'projective_image': '1296.3190', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.v1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 71060534
    {'ambient': '1296.3190', 'aut_centralizer_order': 72, 'aut_label': '216.w1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1728, 'centralizer': '12.q1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.bp1.a1', '72.br1.a1', '72.bs1.a1', '72.bt1.a1', '72.bx1.a1', '108.j1.a1'], 'contains': ['432.k1.a1', '648.b1.a1'], 'core': '1296.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [8330, -1, 2834, -1, 8368, -1, 2216, -1], 'generators': [3, 578], 'label': '1296.3190.216.w1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.q1.a1', 'old_label': '216.w1.a1', 'projective_image': '1296.3190', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.w1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 71060535
    {'ambient': '1296.3190', 'aut_centralizer_order': 72, 'aut_label': '216.w1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1728, 'centralizer': '12.q1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.bp1.b1', '72.br1.b1', '72.bs1.b1', '72.bt1.b1', '72.bx1.b1', '108.j1.a1'], 'contains': ['432.k1.a1', '648.b1.b1'], 'core': '1296.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [8330, -1, 2849, -1, 8368, -1, 2508, -1], 'generators': [219, 578], 'label': '1296.3190.216.w1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.q1.a1', 'old_label': '216.w1.b1', 'projective_image': '1296.3190', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.w1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 71060536
    {'ambient': '1296.3190', 'aut_centralizer_order': 288, 'aut_label': '216.x1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1728, 'centralizer': '6.n1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.by1.a1', '72.bz1.a1', '72.ca1.a1', '72.cf1.a1', '108.k1.a1', '108.by1.a1', '108.by1.b1'], 'contains': ['432.a1.a1', '648.c1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [7198, -1, 1533, -1, 5639, -1, 2634, -1], 'generators': [18, 2], 'label': '1296.3190.216.x1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.n1.a1', 'old_label': '216.x1.a1', 'projective_image': '432.598', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.x1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 71060537
    {'ambient': '1296.3190', 'aut_centralizer_order': 288, 'aut_label': '216.y1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1728, 'centralizer': '6.n1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.by1.a1', '72.cb1.a1', '72.cc1.a1', '72.cg1.a1', '108.l1.a1', '108.bz1.a1', '108.bz1.b1'], 'contains': ['432.b1.a1', '648.c1.a1'], 'core': '432.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [7175, -1, 1500, -1, 5612, -1, 2239, -1], 'generators': [18, 432], 'label': '1296.3190.216.y1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.n1.a1', 'old_label': '216.y1.a1', 'projective_image': '1296.3190', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.y1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 71060538
    {'ambient': '1296.3190', 'aut_centralizer_order': 288, 'aut_label': '216.z1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1728, 'centralizer': '12.v1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.bz1.a1', '72.cb1.a1', '72.cd1.a1', '72.cd1.b1', '72.ch1.a1', '108.m1.a1', '108.cg1.a1', '108.cg1.b1'], 'contains': ['432.d1.a1', '648.c1.a1'], 'core': '432.d1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [7488, -1, 481, -1, 5751, -1, 1464, -1], 'generators': [18, 12], 'label': '1296.3190.216.z1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.n1.a1', 'old_label': '216.z1.a1', 'projective_image': '1296.3190', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.z1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 71060539
    {'ambient': '1296.3190', 'aut_centralizer_order': 144, 'aut_label': '216.ba1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1728, 'centralizer': '6.n1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.by1.a1', '72.cd1.a1', '72.ce1.a1', '72.ci1.a1', '108.n1.a1', '108.ca1.a1', '108.ca1.c1'], 'contains': ['432.e1.a1', '648.c1.a1'], 'core': '1296.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [6411, -1, 1368, -1, 5666, -1, 1419, -1], 'generators': [18, 434], 'label': '1296.3190.216.ba1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.n1.a1', 'old_label': '216.ba1.a1', 'projective_image': '1296.3190', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.ba1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 71060540
    {'ambient': '1296.3190', 'aut_centralizer_order': 144, 'aut_label': '216.ba1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1728, 'centralizer': '6.n1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.by1.a1', '72.cd1.b1', '72.ce1.b1', '72.ci1.b1', '108.n1.a1', '108.ca1.b1', '108.ca1.d1'], 'contains': ['432.e1.a1', '648.c1.a1'], 'core': '1296.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [6411, -1, 1343, -1, 5666, -1, 1396, -1], 'generators': [18, 866], 'label': '1296.3190.216.ba1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.n1.a1', 'old_label': '216.ba1.b1', 'projective_image': '1296.3190', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.ba1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 71060541
    {'ambient': '1296.3190', 'aut_centralizer_order': 144, 'aut_label': '216.bb1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1728, 'centralizer': '12.v1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.bz1.a1', '72.cc1.a1', '72.ce1.a1', '72.ce1.b1', '72.cj1.a1', '108.o1.a1'], 'contains': ['432.g1.a1', '648.c1.a1'], 'core': '1296.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [2731, -1, 2555, -1, 4383, -1, 3490, -1], 'generators': [18, 14], 'label': '1296.3190.216.bb1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.v1.a1', 'old_label': '216.bb1.a1', 'projective_image': '1296.3190', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.bb1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 71060542
    {'ambient': '1296.3190', 'aut_centralizer_order': 72, 'aut_label': '12.c1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '48.51', 'aut_weyl_index': 72, 'centralizer': '24.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '6.b1.a1', '6.c1.a1', '6.e1.a1'], 'contains': ['24.d1.a1', '24.g1.a1', '24.g1.b1', '36.b1.a1', '36.c1.a1', '36.p1.a1', '36.v1.a1'], 'core': '12.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6287, 8755, 4772, 759, 7508, 2627, 2902, 1569], 'generators': [3, 12, 216, 144, 432], 'label': '1296.3190.12.c1.a1', 'mobius_quo': 0, 'mobius_sub': -2, 'normal_closure': '12.c1.a1', 'normal_contained_in': ['4.a1.a1', '6.b1.a1', '6.c1.a1', '6.e1.a1'], 'normal_contains': ['24.d1.a1', '24.g1.a1', '24.g1.b1', '36.b1.a1', '36.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '12.c1.a1', 'projective_image': '648.731', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.c1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 71060543
    {'ambient': '1296.3190', 'aut_centralizer_order': 144, 'aut_label': '216.bc1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1728, 'centralizer': '12.v1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.ca1.a1', '72.cb1.a1', '72.ce1.a1', '72.ce1.b1', '72.ck1.a1', '108.p1.a1'], 'contains': ['432.i1.a1', '648.c1.a1'], 'core': '1296.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [2300, -1, 2627, -1, 4231, -1, 3618, -1], 'generators': [18, 444], 'label': '1296.3190.216.bc1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.v1.a1', 'old_label': '216.bc1.a1', 'projective_image': '1296.3190', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.bc1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 71060544
    {'ambient': '1296.3190', 'aut_centralizer_order': 72, 'aut_label': '216.bd1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1728, 'centralizer': '12.v1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.ca1.a1', '72.cc1.a1', '72.cd1.a1', '72.ce1.b1', '72.cl1.a1', '108.q1.a1'], 'contains': ['432.l1.a1', '648.c1.a1'], 'core': '1296.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [1869, -1, 2685, -1, 4319, -1, 3447, -1], 'generators': [18, 446], 'label': '1296.3190.216.bd1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.v1.a1', 'old_label': '216.bd1.a1', 'projective_image': '1296.3190', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.bd1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 71060545
    {'ambient': '1296.3190', 'aut_centralizer_order': 72, 'aut_label': '216.bd1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1728, 'centralizer': '12.v1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.ca1.a1', '72.cc1.a1', '72.cd1.b1', '72.ce1.a1', '72.cl1.b1', '108.q1.a1'], 'contains': ['432.l1.a1', '648.c1.a1'], 'core': '1296.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [1869, -1, 2611, -1, 4319, -1, 3575, -1], 'generators': [18, 878], 'label': '1296.3190.216.bd1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.v1.a1', 'old_label': '216.bd1.b1', 'projective_image': '1296.3190', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.bd1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 71060546
    {'ambient': '1296.3190', 'aut_centralizer_order': 288, 'aut_label': '216.be1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '6.1', 'aut_weyl_index': 576, 'centralizer': '12.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.cf1.a1', '72.cg1.a1', '72.ch1.a1', '72.ci1.a1', '72.ci1.b1', '72.cj1.a1', '72.ck1.a1', '72.cl1.a1', '72.cl1.b1', '108.b1.a1', '108.cb1.a1', '108.cb1.b1'], 'contains': ['432.c1.a1', '648.c1.a1'], 'core': '432.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [6430, -1, 1744, -1, 5555, -1, 2337, -1], 'generators': [18, 144], 'label': '1296.3190.216.be1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '108.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '216.be1.a1', 'projective_image': '1296.3190', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.be1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 71060547
    {'ambient': '1296.3190', 'aut_centralizer_order': 96, 'aut_label': '216.bf1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1728, 'centralizer': '18.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.cm1.a1', '72.cn1.a1', '72.co1.a1', '72.cp1.a1', '108.r1.a1', '108.by1.a1', '108.by1.b1'], 'contains': ['432.a1.a1', '648.d1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [8602, -1, 1864, -1, 7521, -1, 1561, -1], 'generators': [9, 2], 'label': '1296.3190.216.bf1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.d1.a1', 'old_label': '216.bf1.a1', 'projective_image': '432.598', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.bf1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 71060548
    {'ambient': '1296.3190', 'aut_centralizer_order': 96, 'aut_label': '216.bg1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1728, 'centralizer': '18.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.cm1.a1', '72.cq1.a1', '72.cr1.a1', '72.cs1.a1', '108.s1.a1', '108.bz1.a1', '108.bz1.b1'], 'contains': ['432.b1.a1', '648.d1.a1'], 'core': '432.b1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [8573, -1, 1839, -1, 7494, -1, 1512, -1], 'generators': [9, 432], 'label': '1296.3190.216.bg1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.h1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.d1.a1', 'old_label': '216.bg1.a1', 'projective_image': '1296.3190', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.bg1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 71060549
    {'ambient': '1296.3190', 'aut_centralizer_order': 48, 'aut_label': '216.bh1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1728, 'centralizer': '18.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.cm1.a1', '72.ct1.a1', '72.cu1.a1', '72.cv1.a1', '108.t1.a1', '108.ca1.b1', '108.ca1.c1'], 'contains': ['432.e1.a1', '648.d1.a1'], 'core': '1296.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [8397, -1, 1718, -1, 7548, -1, 1031, -1], 'generators': [9, 866], 'label': '1296.3190.216.bh1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.d1.a1', 'old_label': '216.bh1.a1', 'projective_image': '1296.3190', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.bh1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 71060550
    {'ambient': '1296.3190', 'aut_centralizer_order': 48, 'aut_label': '216.bh1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1728, 'centralizer': '18.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.cm1.a1', '72.ct1.b1', '72.cu1.b1', '72.cv1.b1', '108.t1.a1', '108.ca1.a1', '108.ca1.d1'], 'contains': ['432.e1.a1', '648.d1.a1'], 'core': '1296.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [8397, -1, 1686, -1, 7548, -1, 964, -1], 'generators': [9, 434], 'label': '1296.3190.216.bh1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.d1.a1', 'old_label': '216.bh1.b1', 'projective_image': '1296.3190', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.bh1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 71060551
    {'ambient': '1296.3190', 'aut_centralizer_order': 96, 'aut_label': '216.bi1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '6.1', 'aut_weyl_index': 576, 'centralizer': '36.m1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.cn1.a1', '72.cq1.a1', '72.ct1.a1', '72.ct1.b1', '72.cw1.a1', '108.u1.a1', '108.cb1.a1', '108.cb1.b1'], 'contains': ['432.c1.a1', '648.d1.a1'], 'core': '432.c1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [8465, -1, 1608, -1, 7646, -1, 1133, -1], 'generators': [9, 144], 'label': '1296.3190.216.bi1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.k1.a1', 'old_label': '216.bi1.a1', 'projective_image': '1296.3190', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.bi1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 71060552
    {'ambient': '1296.3190', 'aut_centralizer_order': 96, 'aut_label': '216.bj1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '6.1', 'aut_weyl_index': 576, 'centralizer': '36.x1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.co1.a1', '72.cr1.a1', '72.cu1.a1', '72.cu1.b1', '72.cw1.a1', '108.v1.a1', '108.cg1.a1', '108.cg1.b1'], 'contains': ['432.d1.a1', '648.d1.a1'], 'core': '432.d1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [9153, -1, 539, -1, 7768, -1, 1087, -1], 'generators': [9, 12], 'label': '1296.3190.216.bj1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.n1.a1', 'old_label': '216.bj1.a1', 'projective_image': '1296.3190', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.bj1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 71060570
    {'ambient': '1296.3190', 'aut_centralizer_order': 16, 'aut_label': '216.bx1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '6.1', 'aut_weyl_index': 576, 'centralizer': '216.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.dn1.a1', '72.dr1.a1', '72.ds1.a1', '72.dv1.a1', '72.dv1.a2', '108.bj1.a1'], 'contains': ['432.j1.a1', '648.f1.a1'], 'core': '1296.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [5387, -1, 6516, -1, 4918, -1, 7386, -1], 'generators': [45, 156], 'label': '1296.3190.216.bx1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.k1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.ch1.a1', 'old_label': '216.bx1.a1', 'projective_image': '1296.3190', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.bx1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 71060553
    {'ambient': '1296.3190', 'aut_centralizer_order': 72, 'aut_label': '12.d1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '48.51', 'aut_weyl_index': 72, 'centralizer': '12.a1.a1', 'complements': ['108.ch1.a1', '108.ch1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '6.f1.a1', '6.k1.a1', '6.y1.a1'], 'contains': ['24.a1.a1', '24.y1.a1', '36.d1.a1', '36.e1.a1', '36.x1.a1', '36.be1.a1'], 'core': '12.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3608, 1464, 7702, 8172, 4186, 8511, 5364, 8569], 'generators': [18, 144, 216, 2, 432], 'label': '1296.3190.12.d1.a1', 'mobius_quo': 0, 'mobius_sub': -6, 'normal_closure': '12.d1.a1', 'normal_contained_in': ['4.b1.a1', '6.f1.a1'], 'normal_contains': ['24.a1.a1', '36.d1.a1', '36.e1.a1'], 'normalizer': '1.a1.a1', 'old_label': '12.d1.a1', 'projective_image': '216.162', 'quotient_action_image': '2.1', 'quotient_action_kernel': '6.1', 'quotient_action_kernel_order': 6, 'quotient_fusion': None, 'short_label': '12.d1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 71060554
    {'ambient': '1296.3190', 'aut_centralizer_order': 48, 'aut_label': '216.bk1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '6.1', 'aut_weyl_index': 576, 'centralizer': '72.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.cp1.a1', '72.cs1.a1', '72.cv1.a1', '72.cv1.b1', '72.cw1.a1', '108.w1.a1'], 'contains': ['432.j1.a1', '648.d1.a1'], 'core': '1296.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [8065, -1, 4233, -1, 6631, -1, 2849, -1], 'generators': [9, 156], 'label': '1296.3190.216.bk1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bc1.a1', 'old_label': '216.bk1.a1', 'projective_image': '1296.3190', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.bk1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 71060555
    {'ambient': '1296.3190', 'aut_centralizer_order': 96, 'aut_label': '216.bl1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1728, 'centralizer': '18.s1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.cx1.a1', '72.cy1.a1', '72.cz1.a1', '72.da1.a1', '72.da1.a2', '108.x1.a1', '108.cc1.a1', '108.cc1.b1'], 'contains': ['432.a1.a1', '648.e1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [9327, -1, 4575, -1, 8553, -1, 4230, -1], 'generators': [54, 2], 'label': '1296.3190.216.bl1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.i1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.s1.a1', 'old_label': '216.bl1.a1', 'projective_image': '432.598', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.bl1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 71060556
    {'ambient': '1296.3190', 'aut_centralizer_order': 96, 'aut_label': '216.bm1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1728, 'centralizer': '36.bs1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.cx1.a1', '72.db1.a1', '72.dd1.a1', '72.df1.a1', '72.df1.a2', '108.y1.a1', '108.ch1.a1', '108.ch1.b1'], 'contains': ['432.d1.a1', '648.e1.a1'], 'core': '432.d1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [9758, -1, 3298, -1, 9089, -1, 4163, -1], 'generators': [54, 12], 'label': '1296.3190.216.bm1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.j1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.s1.a1', 'old_label': '216.bm1.a1', 'projective_image': '1296.3190', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.bm1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 71060557
    {'ambient': '1296.3190', 'aut_centralizer_order': 48, 'aut_label': '216.bn1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1728, 'centralizer': '36.bs1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.cx1.a1', '72.dc1.a1', '72.de1.a1', '72.dg1.a1', '72.dg1.a2', '108.z1.a1'], 'contains': ['432.g1.a1', '648.e1.a1'], 'core': '1296.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [7545, -1, 3872, -1, 7467, -1, 5120, -1], 'generators': [54, 14], 'label': '1296.3190.216.bn1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.bs1.a1', 'old_label': '216.bn1.a1', 'projective_image': '1296.3190', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.bn1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 71060558
    {'ambient': '1296.3190', 'aut_centralizer_order': 96, 'aut_label': '216.bo1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '6.1', 'aut_weyl_index': 576, 'centralizer': '36.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.cy1.a1', '72.db1.a1', '72.dc1.a1', '72.dh1.a1', '108.ba1.a1', '108.cd1.a1', '108.cd1.b1'], 'contains': ['432.b1.a1', '648.e1.a1'], 'core': '432.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [9213, -1, 4352, -1, 8395, -1, 4208, -1], 'generators': [54, 432], 'label': '1296.3190.216.bo1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.h1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.p1.a1', 'old_label': '216.bo1.a1', 'projective_image': '1296.3190', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.bo1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 71060559
    {'ambient': '1296.3190', 'aut_centralizer_order': 96, 'aut_label': '216.bp1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '6.1', 'aut_weyl_index': 576, 'centralizer': '36.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.cz1.a1', '72.dd1.a1', '72.de1.a1', '72.dh1.a1', '108.bb1.a1', '108.ce1.a1', '108.ce1.b1'], 'contains': ['432.c1.a1', '648.e1.a1'], 'core': '432.c1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [8912, -1, 4286, -1, 8315, -1, 4185, -1], 'generators': [54, 144], 'label': '1296.3190.216.bp1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.h1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.q1.a1', 'old_label': '216.bp1.a1', 'projective_image': '1296.3190', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.bp1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 71060560
    {'ambient': '1296.3190', 'aut_centralizer_order': 48, 'aut_label': '216.bq1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '6.1', 'aut_weyl_index': 576, 'centralizer': '36.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.da1.a1', '72.df1.a1', '72.dg1.a1', '72.dh1.a1', '108.bc1.a1', '108.cf1.a1', '108.cf1.b1'], 'contains': ['432.h1.a1', '648.e1.a1'], 'core': '1296.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [9433, -1, 4521, -1, 8712, -1, 4411, -1], 'generators': [54, 576], 'label': '1296.3190.216.bq1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.h1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.r1.a1', 'old_label': '216.bq1.a1', 'projective_image': '1296.3190', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.bq1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 71060561
    {'ambient': '1296.3190', 'aut_centralizer_order': 48, 'aut_label': '216.bq1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '6.1', 'aut_weyl_index': 576, 'centralizer': '36.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.da1.a2', '72.df1.a2', '72.dg1.a2', '72.dh1.a1', '108.bc1.a1', '108.cf1.a2', '108.cf1.b2'], 'contains': ['432.h1.a1', '648.e1.a1'], 'core': '1296.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [9433, -1, 4560, -1, 8712, -1, 4434, -1], 'generators': [54, 1008], 'label': '1296.3190.216.bq1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.h1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.r1.a1', 'old_label': '216.bq1.a2', 'projective_image': '1296.3190', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.bq1.a2', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 71060562
    {'ambient': '1296.3190', 'aut_centralizer_order': 32, 'aut_label': '216.br1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1728, 'centralizer': '54.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.di1.a1', '72.dj1.a1', '72.dk1.a1', '72.dl1.a1', '72.dl1.a2', '72.dm1.a1', '72.dn1.a1', '72.do1.a1', '72.do1.a2', '108.bd1.a1', '108.cc1.a1', '108.cc1.b1'], 'contains': ['432.a1.a1', '648.f1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 54, 'diagramx': [7749, -1, 5098, -1, 5693, -1, 5463, -1], 'generators': [45, 2], 'label': '1296.3190.216.br1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.e1.a1', 'old_label': '216.br1.a1', 'projective_image': '432.598', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.br1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 71060563
    {'ambient': '1296.3190', 'aut_centralizer_order': 32, 'aut_label': '216.bs1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '6.1', 'aut_weyl_index': 576, 'centralizer': '108.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.di1.a1', '72.dp1.a1', '72.dq1.a1', '72.dr1.a1', '108.be1.a1', '108.cd1.a1', '108.cd1.b1'], 'contains': ['432.b1.a1', '648.f1.a1'], 'core': '432.b1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [7711, -1, 4942, -1, 5890, -1, 5295, -1], 'generators': [45, 432], 'label': '1296.3190.216.bs1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.k1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.h1.a1', 'old_label': '216.bs1.a1', 'projective_image': '1296.3190', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.bs1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 71060564
    {'ambient': '1296.3190', 'aut_centralizer_order': 72, 'aut_label': '12.e1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '48.51', 'aut_weyl_index': 72, 'centralizer': '24.b1.a1', 'complements': ['108.cd1.a1', '108.cf1.a1', '108.cf1.a2', '108.cd1.b1', '108.cf1.b1', '108.cf1.b2'], 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '6.a1.a1', '6.w1.a1', '6.z1.a1'], 'contains': ['24.c1.a1', '24.z1.a1', '36.d1.a1', '36.f1.a1', '36.y1.a1', '36.bf1.a1'], 'core': '12.e1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4045, 5610, 6249, 4864, 4107, 3621, 5298, 3873], 'generators': [18, 144, 216, 2, 12], 'label': '1296.3190.12.e1.a1', 'mobius_quo': 0, 'mobius_sub': -6, 'normal_closure': '12.e1.a1', 'normal_contained_in': ['4.b1.a1', '6.a1.a1'], 'normal_contains': ['24.c1.a1', '36.d1.a1', '36.f1.a1'], 'normalizer': '1.a1.a1', 'old_label': '12.e1.a1', 'projective_image': '216.162', 'quotient_action_image': '4.2', 'quotient_action_kernel': '3.1', 'quotient_action_kernel_order': 3, 'quotient_fusion': None, 'short_label': '12.e1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 71060565
    {'ambient': '1296.3190', 'aut_centralizer_order': 32, 'aut_label': '216.bt1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '6.1', 'aut_weyl_index': 576, 'centralizer': '108.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.dj1.a1', '72.dp1.a1', '72.ds1.a1', '72.dt1.a1', '108.bf1.a1', '108.ce1.a1', '108.ce1.b1'], 'contains': ['432.c1.a1', '648.f1.a1'], 'core': '432.c1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [7675, -1, 4782, -1, 5863, -1, 5273, -1], 'generators': [45, 144], 'label': '1296.3190.216.bt1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.k1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.i1.a1', 'old_label': '216.bt1.a1', 'projective_image': '1296.3190', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.bt1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 71060566
    {'ambient': '1296.3190', 'aut_centralizer_order': 32, 'aut_label': '216.bu1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '6.1', 'aut_weyl_index': 576, 'centralizer': '108.x1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.dk1.a1', '72.dq1.a1', '72.ds1.a1', '72.du1.a1', '72.du1.a2', '108.bg1.a1', '108.ch1.a1', '108.ch1.b1'], 'contains': ['432.d1.a1', '648.f1.a1'], 'core': '432.d1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [8126, -1, 3470, -1, 6128, -1, 5098, -1], 'generators': [45, 12], 'label': '1296.3190.216.bu1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.k1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.s1.a1', 'old_label': '216.bu1.a1', 'projective_image': '1296.3190', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.bu1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 71060567
    {'ambient': '1296.3190', 'aut_centralizer_order': 16, 'aut_label': '216.bv1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '6.1', 'aut_weyl_index': 576, 'centralizer': '108.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.dl1.a1', '72.dp1.a1', '72.du1.a1', '72.dv1.a1', '108.bh1.a1', '108.cf1.a1', '108.cf1.b2'], 'contains': ['432.h1.a1', '648.f1.a1'], 'core': '1296.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [7996, -1, 4992, -1, 5925, -1, 5440, -1], 'generators': [45, 576], 'label': '1296.3190.216.bv1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.k1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.j1.a1', 'old_label': '216.bv1.a1', 'projective_image': '1296.3190', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.bv1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 71060568
    {'ambient': '1296.3190', 'aut_centralizer_order': 16, 'aut_label': '216.bv1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '6.1', 'aut_weyl_index': 576, 'centralizer': '108.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.dl1.a2', '72.dp1.a1', '72.du1.a2', '72.dv1.a2', '108.bh1.a1', '108.cf1.a2', '108.cf1.b1'], 'contains': ['432.h1.a1', '648.f1.a1'], 'core': '1296.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [7996, -1, 5042, -1, 5925, -1, 5418, -1], 'generators': [45, 1008], 'label': '1296.3190.216.bv1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.k1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.j1.a1', 'old_label': '216.bv1.a2', 'projective_image': '1296.3190', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.bv1.a2', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 71060571
    {'ambient': '1296.3190', 'aut_centralizer_order': 8, 'aut_label': '216.by1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '6.1', 'aut_weyl_index': 576, 'centralizer': '216.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.do1.a1', '72.dr1.a1', '72.dt1.a1', '72.du1.a1', '72.dv1.a2', '108.bk1.a1'], 'contains': ['432.n1.a1', '648.f1.a1'], 'core': '1296.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [3462, -1, 6251, -1, 4891, -1, 7364, -1], 'generators': [45, 588], 'label': '1296.3190.216.by1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.k1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.ci1.a1', 'old_label': '216.by1.a1', 'projective_image': '1296.3190', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.by1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 71060572
    {'ambient': '1296.3190', 'aut_centralizer_order': 8, 'aut_label': '216.by1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '6.1', 'aut_weyl_index': 576, 'centralizer': '216.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.do1.a2', '72.dr1.a1', '72.dt1.a1', '72.du1.a2', '72.dv1.a1', '108.bk1.a1'], 'contains': ['432.n1.a1', '648.f1.a1'], 'core': '1296.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [3462, -1, 6534, -1, 4891, -1, 7414, -1], 'generators': [45, 1020], 'label': '1296.3190.216.by1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.k1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.ci1.a1', 'old_label': '216.by1.a2', 'projective_image': '1296.3190', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.by1.a2', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 71060573
    {'ambient': '1296.3190', 'aut_centralizer_order': 576, 'aut_label': '324.a1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1728, 'centralizer': '3.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.a1.a1', '108.d1.a1', '108.e1.a1', '108.f1.a1', '108.g1.a1', '108.h1.a1', '108.i1.a1', '108.j1.a1', '162.a1.a1', '162.b1.a1', '162.c1.a1'], 'contains': ['648.a1.a1', '648.b1.a1', '648.b1.b1'], 'core': '648.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6186, -1, 5387, -1, 6661, -1, 3085, -1], 'generators': [3, 216], 'label': '1296.3190.324.a1.a1', 'mobius_quo': None, 'mobius_sub': 18, 'normal_closure': '108.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '324.a1.a1', 'projective_image': '648.731', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 71060574
    {'ambient': '1296.3190', 'aut_centralizer_order': 576, 'aut_label': '324.b1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1728, 'centralizer': '6.n1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.b1.a1', '108.k1.a1', '108.l1.a1', '108.m1.a1', '108.n1.a1', '108.o1.a1', '108.p1.a1', '108.q1.a1', '162.a1.a1', '162.d1.a1', '162.e1.a1'], 'contains': ['648.a1.a1', '648.c1.a1'], 'core': '648.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [2472, -1, 7181, -1, 3872, -1, 5226, -1], 'generators': [18, 216], 'label': '1296.3190.324.b1.a1', 'mobius_quo': None, 'mobius_sub': 18, 'normal_closure': '108.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1.a1', 'old_label': '324.b1.a1', 'projective_image': '648.731', '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': '2.1'}
  • id: 71060575
    {'ambient': '1296.3190', 'aut_centralizer_order': 72, 'aut_label': '12.f1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '48.51', 'aut_weyl_index': 72, 'centralizer': '24.b1.a1', 'complements': ['108.cc1.a1', '108.cc1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '6.b1.a1', '6.g1.a1', '6.h1.a1'], 'contains': ['24.d1.a1', '24.bb1.a1', '36.e1.a1', '36.f1.a1', '36.ba1.a1', '36.bg1.a1'], 'core': '12.f1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4357, 4397, 7630, 6005, 4029, 6026, 5232, 5284], 'generators': [18, 144, 216, 12, 432], 'label': '1296.3190.12.f1.a1', 'mobius_quo': 0, 'mobius_sub': -2, 'normal_closure': '12.f1.a1', 'normal_contained_in': ['4.b1.a1', '6.b1.a1', '6.g1.a1', '6.h1.a1'], 'normal_contains': ['24.d1.a1', '36.e1.a1', '36.f1.a1'], 'normalizer': '1.a1.a1', 'old_label': '12.f1.a1', 'projective_image': '648.731', 'quotient_action_image': '4.2', 'quotient_action_kernel': '3.1', 'quotient_action_kernel_order': 3, 'quotient_fusion': None, 'short_label': '12.f1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 71060576
    {'ambient': '1296.3190', 'aut_centralizer_order': 192, 'aut_label': '324.c1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1728, 'centralizer': '18.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.r1.a1', '108.s1.a1', '108.t1.a1', '108.u1.a1', '108.v1.a1', '108.w1.a1', '162.a1.a1', '162.f1.a1', '162.g1.a1'], 'contains': ['648.a1.a1', '648.d1.a1'], 'core': '648.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [4651, -1, 6875, -1, 6034, -1, 4828, -1], 'generators': [9, 216], 'label': '1296.3190.324.c1.a1', 'mobius_quo': None, 'mobius_sub': 6, 'normal_closure': '36.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '324.c1.a1', 'projective_image': '648.731', '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: 71060577
    {'ambient': '1296.3190', 'aut_centralizer_order': 192, 'aut_label': '324.d1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1728, 'centralizer': '18.s1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.x1.a1', '108.y1.a1', '108.z1.a1', '108.ba1.a1', '108.bb1.a1', '108.bc1.a1', '162.b1.a1', '162.d1.a1', '162.f1.a1'], 'contains': ['648.a1.a1', '648.e1.a1'], 'core': '648.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [6758, -1, 7162, -1, 6358, -1, 5990, -1], 'generators': [54, 216], 'label': '1296.3190.324.d1.a1', 'mobius_quo': None, 'mobius_sub': 6, 'normal_closure': '36.h1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.d1.a1', 'old_label': '324.d1.a1', 'projective_image': '648.731', '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: 71060578
    {'ambient': '1296.3190', 'aut_centralizer_order': 64, 'aut_label': '324.e1', 'aut_quo_index': None, 'aut_stab_index': 27, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1728, 'centralizer': '54.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.bd1.a1', '108.be1.a1', '108.bf1.a1', '108.bg1.a1', '108.bh1.a1', '108.bi1.a1', '108.bj1.a1', '108.bk1.a1', '162.b1.a1', '162.e1.a1', '162.g1.a1'], 'contains': ['648.a1.a1', '648.f1.a1'], 'core': '648.a1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [3516, -1, 8276, -1, 3645, -1, 7337, -1], 'generators': [45, 216], 'label': '1296.3190.324.e1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '12.k1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1.a1', 'old_label': '324.e1.a1', 'projective_image': '648.731', '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: 71060579
    {'ambient': '1296.3190', 'aut_centralizer_order': 576, 'aut_label': '324.f1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1728, 'centralizer': '6.s1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.c1.a1', '108.bl1.a1', '108.bo1.a1', '108.bq1.a1', '108.bs1.a1', '108.bu1.a1', '108.bw1.a1', '108.bx1.a1', '162.c1.a1', '162.d1.a1', '162.g1.a1'], 'contains': ['648.a1.a1'], 'core': '648.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [717, -1, 9271, -1, 1064, -1, 8833, -1], 'generators': [108], 'label': '1296.3190.324.f1.a1', 'mobius_quo': None, 'mobius_sub': 18, 'normal_closure': '108.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.d1.a1', 'old_label': '324.f1.a1', 'projective_image': '648.731', '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: 71060580
    {'ambient': '1296.3190', 'aut_centralizer_order': 192, 'aut_label': '324.g1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1728, 'centralizer': '18.m1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.bm1.a1', '108.bn1.a1', '108.bp1.a1', '108.br1.a1', '108.bt1.a1', '108.bv1.a1', '162.c1.a1', '162.e1.a1', '162.f1.a1'], 'contains': ['648.a1.a1'], 'core': '648.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [1614, -1, 9014, -1, 1697, -1, 7787, -1], 'generators': [111], 'label': '1296.3190.324.g1.a1', 'mobius_quo': None, 'mobius_sub': 6, 'normal_closure': '36.l1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1.a1', 'old_label': '324.g1.a1', 'projective_image': '648.731', '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: 71060581
    {'ambient': '1296.3190', 'aut_centralizer_order': 96, 'aut_label': '324.h1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '1.1', 'aut_weyl_index': 3456, 'centralizer': '18.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.by1.a1', '108.bz1.a1', '108.ca1.a1', '108.ca1.b1', '108.cb1.a1', '108.cg1.a1', '162.a1.a1'], 'contains': ['648.b1.a1', '648.c1.a1', '648.d1.a1'], 'core': '1296.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [8840, -1, 696, -1, 7997, -1, 1006, -1], 'generators': [3, 18], 'label': '1296.3190.324.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.d1.a1', 'old_label': '324.h1.a1', 'projective_image': '1296.3190', '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: 71060582
    {'ambient': '1296.3190', 'aut_centralizer_order': 96, 'aut_label': '324.h1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '1.1', 'aut_weyl_index': 3456, 'centralizer': '18.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.by1.b1', '108.bz1.b1', '108.ca1.c1', '108.ca1.d1', '108.cb1.b1', '108.cg1.b1', '162.a1.a1'], 'contains': ['648.b1.b1', '648.c1.a1', '648.d1.a1'], 'core': '1296.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [8840, -1, 1937, -1, 7997, -1, 1060, -1], 'generators': [219, 18], 'label': '1296.3190.324.h1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.d1.a1', 'old_label': '324.h1.b1', 'projective_image': '1296.3190', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.h1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 71060583
    {'ambient': '1296.3190', 'aut_centralizer_order': 32, 'aut_label': '324.i1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '1.1', 'aut_weyl_index': 3456, 'centralizer': '54.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.cc1.a1', '108.cd1.a1', '108.ce1.a1', '108.cf1.a1', '108.cf1.a2', '108.ch1.a1', '162.b1.a1'], 'contains': ['648.b1.a1', '648.e1.a1', '648.f1.a1'], 'core': '1296.a1.a1', 'coset_action_label': None, 'count': 54, 'diagramx': [9103, -1, 4406, -1, 8458, -1, 4138, -1], 'generators': [3, 54], 'label': '1296.3190.324.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.e1.a1', 'old_label': '324.i1.a1', 'projective_image': '1296.3190', '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: 71060584
    {'ambient': '1296.3190', 'aut_centralizer_order': 32, 'aut_label': '324.i1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '1.1', 'aut_weyl_index': 3456, 'centralizer': '54.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.cc1.b1', '108.cd1.b1', '108.ce1.b1', '108.cf1.b1', '108.cf1.b2', '108.ch1.b1', '162.b1.a1'], 'contains': ['648.b1.b1', '648.e1.a1', '648.f1.a1'], 'core': '1296.a1.a1', 'coset_action_label': None, 'count': 54, 'diagramx': [9103, -1, 5076, -1, 8458, -1, 4255, -1], 'generators': [219, 54], 'label': '1296.3190.324.i1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.e1.a1', 'old_label': '324.i1.b1', 'projective_image': '1296.3190', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.i1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 71060585
    {'ambient': '1296.3190', 'aut_centralizer_order': 1728, 'aut_label': '432.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1728, 'centralizer': '1.a1.a1', 'complements': ['3.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['144.a1.a1', '144.b1.a1', '144.c1.a1', '144.g1.a1', '144.h1.a1', '144.i1.a1', '144.j1.a1', '216.a1.a1', '216.q1.a1', '216.q1.b1', '216.x1.a1', '216.bf1.a1', '216.bl1.a1', '216.br1.a1'], 'contains': ['1296.a1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7935, 5371, 4112, 4995, 6722, 4401, 4175, 4944], 'generators': [2], 'label': '1296.3190.432.a1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '432.a1.a1', 'normal_contained_in': ['144.b1.a1', '144.a1.a1', '144.c1.a1', '216.a1.a1'], 'normal_contains': ['1296.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '432.a1.a1', 'projective_image': '432.598', 'quotient_action_image': '1.1', 'quotient_action_kernel': '432.598', 'quotient_action_kernel_order': 432, 'quotient_fusion': None, 'short_label': '432.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 71060626
    {'ambient': '1296.3190', 'aut_centralizer_order': 36, 'aut_label': '12.w1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '48.51', 'aut_weyl_index': 72, 'centralizer': '24.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '6.ba1.a1'], 'contains': ['24.i1.a1', '24.ba1.a1', '36.d1.a1', '36.z1.a1', '36.bg1.a1', '36.bh1.a1'], 'core': '36.d1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [1719, -1, 7859, -1, 2683, -1, 5496, -1], 'generators': [18, 144, 216, 2, 444], 'label': '1296.3190.12.w1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.e1.a1', 'old_label': '12.w1.a1', 'projective_image': '216.162', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.w1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 71060586
    {'ambient': '1296.3190', 'aut_centralizer_order': 24, 'aut_label': '12.g1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '144.192', 'aut_weyl_index': 24, 'centralizer': '72.a1.a1', 'complements': ['108.cd1.a1', '108.cf1.a1', '108.cf1.a2', '108.cd1.b1', '108.cf1.b1', '108.cf1.b2'], 'conjugacy_class_count': 1, 'contained_in': ['4.c1.a1', '6.a1.a1', '6.bg1.a1', '6.bh1.a1'], 'contains': ['24.c1.a1', '24.bi1.a1', '36.g1.a1', '36.bj1.a1', '36.bk1.a1', '36.bl1.a1'], 'core': '12.g1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4802, 7436, 5817, 3047, 5867, 1718, 5032, 2975], 'generators': [9, 144, 216, 2, 12], 'label': '1296.3190.12.g1.a1', 'mobius_quo': 0, 'mobius_sub': -6, 'normal_closure': '12.g1.a1', 'normal_contained_in': ['4.c1.a1', '6.a1.a1'], 'normal_contains': ['24.c1.a1', '36.g1.a1'], 'normalizer': '1.a1.a1', 'old_label': '12.g1.a1', 'projective_image': '216.162', 'quotient_action_image': '4.2', 'quotient_action_kernel': '3.1', 'quotient_action_kernel_order': 3, 'quotient_fusion': None, 'short_label': '12.g1.a1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 71060587
    {'ambient': '1296.3190', 'aut_centralizer_order': 1728, 'aut_label': '432.b1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1728, 'centralizer': '2.a1.a1', 'complements': ['3.d1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['144.a1.a1', '144.d1.a1', '144.e1.a1', '144.k1.a1', '144.l1.a1', '144.m1.a1', '144.n1.a1', '216.b1.a1', '216.r1.a1', '216.r1.b1', '216.y1.a1', '216.bg1.a1', '216.bo1.a1', '216.bs1.a1'], 'contains': ['1296.a1.a1'], 'core': '432.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7779, 5172, 3516, 4806, 6691, 4972, 4087, 5127], 'generators': [432], 'label': '1296.3190.432.b1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '432.b1.a1', 'normal_contained_in': ['144.a1.a1', '144.d1.a1', '144.e1.a1', '216.b1.a1'], 'normal_contains': ['1296.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '432.b1.a1', 'projective_image': '1296.3190', 'quotient_action_image': '2.1', 'quotient_action_kernel': '216.170', 'quotient_action_kernel_order': 216, 'quotient_fusion': None, 'short_label': '432.b1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 71060588
    {'ambient': '1296.3190', 'aut_centralizer_order': 1728, 'aut_label': '432.c1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1728, 'centralizer': '2.c1.a1', 'complements': ['3.c1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['144.b1.a1', '144.d1.a1', '144.f1.a1', '144.o1.a1', '144.p1.a1', '144.q1.a1', '144.r1.a1', '216.c1.a1', '216.s1.a1', '216.s1.b1', '216.be1.a1', '216.bi1.a1', '216.bp1.a1', '216.bt1.a1'], 'contains': ['1296.a1.a1'], 'core': '432.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7673, 5572, 2855, 4618, 6664, 4591, 4035, 4762], 'generators': [144], 'label': '1296.3190.432.c1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '432.c1.a1', 'normal_contained_in': ['144.b1.a1', '144.d1.a1', '144.f1.a1', '216.c1.a1'], 'normal_contains': ['1296.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '432.c1.a1', 'projective_image': '1296.3190', 'quotient_action_image': '2.1', 'quotient_action_kernel': '216.119', 'quotient_action_kernel_order': 216, 'quotient_fusion': None, 'short_label': '432.c1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 71060589
    {'ambient': '1296.3190', 'aut_centralizer_order': 1728, 'aut_label': '432.d1', 'aut_quo_index': 4, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1728, 'centralizer': '2.d1.a1', 'complements': ['3.b1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['144.c1.a1', '144.e1.a1', '144.f1.a1', '144.s1.a1', '144.t1.a1', '144.u1.a1', '144.v1.a1', '216.d1.a1', '216.e1.a1', '216.e1.b1', '216.z1.a1', '216.bj1.a1', '216.bm1.a1', '216.bu1.a1'], 'contains': ['1296.a1.a1'], 'core': '432.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8124, 6651, 1514, 3235, 6953, 3880, 3958, 3701], 'generators': [12], 'label': '1296.3190.432.d1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '432.d1.a1', 'normal_contained_in': ['144.c1.a1', '144.e1.a1', '144.f1.a1', '216.d1.a1', '216.e1.a1', '216.e1.b1'], 'normal_contains': ['1296.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '432.d1.a1', 'projective_image': '1296.3190', 'quotient_action_image': '2.1', 'quotient_action_kernel': '216.122', 'quotient_action_kernel_order': 216, 'quotient_fusion': None, 'short_label': '432.d1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 71060590
    {'ambient': '1296.3190', 'aut_centralizer_order': 864, 'aut_label': '432.e1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1728, 'centralizer': '2.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.a1.a1', '144.o1.a1', '144.s1.a1', '144.w1.a1', '144.x1.a1', '144.y1.a1', '144.z1.a1', '216.f1.a1', '216.t1.a1', '216.t1.b1', '216.ba1.a1', '216.ba1.b1', '216.bh1.a1', '216.bh1.b1'], 'contains': ['1296.a1.a1'], 'core': '1296.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7373, -1, 1833, -1, 6637, -1, 2359, -1], 'generators': [434], 'label': '1296.3190.432.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '144.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '432.e1.a1', 'projective_image': '1296.3190', '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: 71060591
    {'ambient': '1296.3190', 'aut_centralizer_order': 864, 'aut_label': '432.f1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1728, 'centralizer': '2.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.b1.a1', '144.k1.a1', '144.t1.a1', '144.w1.a1', '144.ba1.a1', '144.bb1.a1', '144.bc1.a1', '216.g1.a1', '216.u1.a1', '216.u1.b1'], 'contains': ['1296.a1.a1'], 'core': '1296.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7348, -1, 3623, -1, 6584, -1, 4220, -1], 'generators': [146], 'label': '1296.3190.432.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '144.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '432.f1.a1', 'projective_image': '1296.3190', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.f1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 71060592
    {'ambient': '1296.3190', 'aut_centralizer_order': 864, 'aut_label': '432.g1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1728, 'centralizer': '2.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.c1.a1', '144.l1.a1', '144.p1.a1', '144.x1.a1', '144.ba1.a1', '144.bd1.a1', '144.be1.a1', '216.h1.a1', '216.bb1.a1', '216.bn1.a1'], 'contains': ['1296.a1.a1'], 'core': '1296.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2817, -1, 3437, -1, 5582, -1, 5132, -1], 'generators': [14], 'label': '1296.3190.432.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '144.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.a1', 'old_label': '432.g1.a1', 'projective_image': '1296.3190', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.g1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 71060593
    {'ambient': '1296.3190', 'aut_centralizer_order': 864, 'aut_label': '432.h1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1728, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.d1.a1', '144.g1.a1', '144.u1.a1', '144.w1.a1', '144.bd1.a1', '144.bf1.a1', '144.bg1.a1', '216.i1.a1', '216.v1.a1', '216.v1.b1', '216.bq1.a1', '216.bq1.a2', '216.bv1.a1', '216.bv1.a2'], 'contains': ['1296.a1.a1'], 'core': '1296.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7999, -1, 4655, -1, 6751, -1, 4434, -1], 'generators': [576], 'label': '1296.3190.432.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '144.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '432.h1.a1', 'projective_image': '1296.3190', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.h1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 71060594
    {'ambient': '1296.3190', 'aut_centralizer_order': 864, 'aut_label': '432.i1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1728, 'centralizer': '4.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.e1.a1', '144.h1.a1', '144.q1.a1', '144.x1.a1', '144.bb1.a1', '144.bf1.a1', '144.bh1.a1', '216.j1.a1', '216.bc1.a1', '216.bw1.a1'], 'contains': ['1296.a1.a1'], 'core': '1296.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2677, -1, 3677, -1, 5004, -1, 5537, -1], 'generators': [444], 'label': '1296.3190.432.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '144.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.e1.a1', 'old_label': '432.i1.a1', 'projective_image': '1296.3190', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.i1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 71060595
    {'ambient': '1296.3190', 'aut_centralizer_order': 864, 'aut_label': '432.j1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1728, 'centralizer': '4.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.f1.a1', '144.i1.a1', '144.m1.a1', '144.y1.a1', '144.ba1.a1', '144.bf1.a1', '144.bi1.a1', '216.k1.a1', '216.bk1.a1', '216.bx1.a1'], 'contains': ['1296.a1.a1'], 'core': '1296.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [5374, -1, 4820, -1, 5434, -1, 5693, -1], 'generators': [156], 'label': '1296.3190.432.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '144.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.g1.a1', 'old_label': '432.j1.a1', 'projective_image': '1296.3190', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.j1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 71060596
    {'ambient': '1296.3190', 'aut_centralizer_order': 432, 'aut_label': '432.k1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1728, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.g1.a1', '144.k1.a1', '144.o1.a1', '144.v1.a1', '144.w1.a1', '144.be1.a1', '144.bh1.a1', '144.bi1.a1', '144.bj1.a1', '216.l1.a1', '216.w1.a1', '216.w1.b1'], 'contains': ['1296.a1.a1'], 'core': '1296.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [7264, -1, 3500, -1, 6610, -1, 4197, -1], 'generators': [578], 'label': '1296.3190.432.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '432.k1.a1', 'projective_image': '1296.3190', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.k1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 71060597
    {'ambient': '1296.3190', 'aut_centralizer_order': 24, 'aut_label': '12.h1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '144.192', 'aut_weyl_index': 24, 'centralizer': '72.a1.a1', 'complements': ['108.cc1.a1', '108.cc1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['4.c1.a1', '6.b1.a1', '6.i1.a1', '6.j1.a1'], 'contains': ['24.d1.a1', '24.bj1.a1', '36.g1.a1', '36.bm1.a1', '36.bn1.a1', '36.bo1.a1'], 'core': '12.h1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4884, 6974, 6959, 3482, 5664, 4615, 4980, 3396], 'generators': [9, 144, 216, 432, 12], 'label': '1296.3190.12.h1.a1', 'mobius_quo': 0, 'mobius_sub': -2, 'normal_closure': '12.h1.a1', 'normal_contained_in': ['4.c1.a1', '6.b1.a1', '6.i1.a1', '6.j1.a1'], 'normal_contains': ['24.d1.a1', '36.g1.a1'], 'normalizer': '1.a1.a1', 'old_label': '12.h1.a1', 'projective_image': '648.731', 'quotient_action_image': '4.2', 'quotient_action_kernel': '3.1', 'quotient_action_kernel_order': 3, 'quotient_fusion': None, 'short_label': '12.h1.a1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 71060598
    {'ambient': '1296.3190', 'aut_centralizer_order': 432, 'aut_label': '432.l1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1728, 'centralizer': '4.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.h1.a1', '144.l1.a1', '144.r1.a1', '144.s1.a1', '144.x1.a1', '144.bc1.a1', '144.bg1.a1', '144.bi1.a1', '144.bj1.a1', '216.m1.a1', '216.bd1.a1', '216.bd1.b1'], 'contains': ['1296.a1.a1'], 'core': '1296.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [2456, -1, 3470, -1, 5127, -1, 5110, -1], 'generators': [446], 'label': '1296.3190.432.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.a1', 'old_label': '432.l1.a1', 'projective_image': '1296.3190', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.l1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 71060599
    {'ambient': '1296.3190', 'aut_centralizer_order': 432, 'aut_label': '432.m1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1728, 'centralizer': '4.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.i1.a1', '144.n1.a1', '144.p1.a1', '144.t1.a1', '144.z1.a1', '144.ba1.a1', '144.bg1.a1', '144.bh1.a1', '144.bj1.a1', '216.n1.a1'], 'contains': ['1296.a1.a1'], 'core': '1296.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [3886, -1, 3751, -1, 5373, -1, 5560, -1], 'generators': [158], 'label': '1296.3190.432.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.f1.a1', 'old_label': '432.m1.a1', 'projective_image': '1296.3190', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.m1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 71060600
    {'ambient': '1296.3190', 'aut_centralizer_order': 432, 'aut_label': '432.n1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1728, 'centralizer': '8.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.j1.a1', '144.m1.a1', '144.q1.a1', '144.u1.a1', '144.z1.a1', '144.bc1.a1', '144.be1.a1', '144.bf1.a1', '144.bj1.a1', '216.o1.a1', '216.by1.a1', '216.by1.a2'], 'contains': ['1296.a1.a1'], 'core': '1296.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [3442, -1, 4790, -1, 5204, -1, 5719, -1], 'generators': [588], 'label': '1296.3190.432.n1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.e1.a1', 'old_label': '432.n1.a1', 'projective_image': '1296.3190', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.n1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 71060601
    {'ambient': '1296.3190', 'aut_centralizer_order': 216, 'aut_label': '432.o1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '2.1', 'aut_weyl_index': 1728, 'centralizer': '8.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.j1.a1', '144.n1.a1', '144.r1.a1', '144.v1.a1', '144.y1.a1', '144.z1.a1', '144.bb1.a1', '144.bc1.a1', '144.bd1.a1', '144.be1.a1', '144.bg1.a1', '144.bh1.a1', '144.bi1.a1', '216.p1.a1'], 'contains': ['1296.a1.a1'], 'core': '1296.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [3678, -1, 3801, -1, 5280, -1, 5513, -1], 'generators': [590], 'label': '1296.3190.432.o1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.a1.a1', 'old_label': '432.o1.a1', 'projective_image': '1296.3190', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.o1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 71060602
    {'ambient': '1296.3190', 'aut_centralizer_order': 3456, 'aut_label': '648.a1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '1.1', 'aut_weyl_index': 3456, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['216.a1.a1', '216.b1.a1', '216.c1.a1', '216.d1.a1', '216.f1.a1', '216.g1.a1', '216.h1.a1', '216.i1.a1', '216.j1.a1', '216.k1.a1', '216.l1.a1', '216.m1.a1', '216.n1.a1', '216.o1.a1', '216.p1.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': '648.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2761, 4873, 7181, 5224, 3616, 4781, 6415, 5348], 'generators': [216], 'label': '1296.3190.648.a1.a1', 'mobius_quo': -1, 'mobius_sub': -216, 'normal_closure': '648.a1.a1', 'normal_contained_in': ['216.a1.a1', '216.b1.a1', '216.c1.a1', '216.d1.a1'], 'normal_contains': ['1296.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '648.a1.a1', 'projective_image': '648.731', 'quotient_action_image': '1.1', 'quotient_action_kernel': '648.731', 'quotient_action_kernel_order': 648, 'quotient_fusion': None, 'short_label': '648.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 71060603
    {'ambient': '1296.3190', 'aut_centralizer_order': 576, 'aut_label': '648.b1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '1.1', 'aut_weyl_index': 3456, 'centralizer': '3.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.e1.a1', '216.q1.a1', '216.r1.a1', '216.s1.a1', '216.t1.a1', '216.u1.a1', '216.v1.a1', '216.w1.a1', '324.a1.a1', '324.h1.a1', '324.i1.a1'], 'contains': ['1296.a1.a1'], 'core': '1296.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8832, -1, 2890, -1, 8274, -1, 2273, -1], 'generators': [3], 'label': '1296.3190.648.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '216.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '648.b1.a1', 'projective_image': '1296.3190', '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: 71060604
    {'ambient': '1296.3190', 'aut_centralizer_order': 576, 'aut_label': '648.b1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '1.1', 'aut_weyl_index': 3456, 'centralizer': '3.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.e1.b1', '216.q1.b1', '216.r1.b1', '216.s1.b1', '216.t1.b1', '216.u1.b1', '216.v1.b1', '216.w1.b1', '324.a1.a1', '324.h1.b1', '324.i1.b1'], 'contains': ['1296.a1.a1'], 'core': '1296.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8832, -1, 3838, -1, 8274, -1, 2691, -1], 'generators': [219], 'label': '1296.3190.648.b1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '216.e1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '648.b1.b1', 'projective_image': '1296.3190', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.b1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 71060605
    {'ambient': '1296.3190', 'aut_centralizer_order': 576, 'aut_label': '648.c1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '1.1', 'aut_weyl_index': 3456, 'centralizer': '6.n1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.x1.a1', '216.y1.a1', '216.z1.a1', '216.ba1.a1', '216.ba1.b1', '216.bb1.a1', '216.bc1.a1', '216.bd1.a1', '216.bd1.b1', '216.be1.a1', '324.b1.a1', '324.h1.a1', '324.h1.b1'], 'contains': ['1296.a1.a1'], 'core': '1296.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [6425, -1, 1666, -1, 5555, -1, 2337, -1], 'generators': [18], 'label': '1296.3190.648.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '108.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.n1.a1', 'old_label': '648.c1.a1', 'projective_image': '1296.3190', '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: 71060606
    {'ambient': '1296.3190', 'aut_centralizer_order': 192, 'aut_label': '648.d1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '1.1', 'aut_weyl_index': 3456, 'centralizer': '18.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.bf1.a1', '216.bg1.a1', '216.bh1.a1', '216.bh1.b1', '216.bi1.a1', '216.bj1.a1', '216.bk1.a1', '324.c1.a1', '324.h1.a1', '324.h1.b1'], 'contains': ['1296.a1.a1'], 'core': '1296.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [8562, -1, 1812, -1, 7521, -1, 1133, -1], 'generators': [9], 'label': '1296.3190.648.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.d1.a1', 'old_label': '648.d1.a1', 'projective_image': '1296.3190', '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: 71060607
    {'ambient': '1296.3190', 'aut_centralizer_order': 192, 'aut_label': '648.e1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '1.1', 'aut_weyl_index': 3456, 'centralizer': '18.s1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.bl1.a1', '216.bm1.a1', '216.bn1.a1', '216.bo1.a1', '216.bp1.a1', '216.bq1.a1', '216.bq1.a2', '324.d1.a1', '324.i1.a1', '324.i1.b1'], 'contains': ['1296.a1.a1'], 'core': '1296.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [9086, -1, 4406, -1, 8395, -1, 4242, -1], 'generators': [54], 'label': '1296.3190.648.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.h1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.s1.a1', 'old_label': '648.e1.a1', 'projective_image': '1296.3190', '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: 71060608
    {'ambient': '1296.3190', 'aut_centralizer_order': 24, 'aut_label': '12.i1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '144.192', 'aut_weyl_index': 24, 'centralizer': '36.a1.a1', 'complements': ['108.cg1.a1', '108.cg1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['4.d1.a1', '6.f1.a1', '6.l1.a1', '6.bc1.a1'], 'contains': ['24.a1.a1', '24.bo1.a1', '36.h1.a1', '36.bt1.a1', '36.bu1.a1', '36.bv1.a1'], 'core': '12.i1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6919, 835, 7491, 9157, 6518, 9504, 5739, 9046], 'generators': [54, 432, 216, 2, 144], 'label': '1296.3190.12.i1.a1', 'mobius_quo': 0, 'mobius_sub': -6, 'normal_closure': '12.i1.a1', 'normal_contained_in': ['4.d1.a1', '6.f1.a1'], 'normal_contains': ['24.a1.a1', '36.h1.a1'], 'normalizer': '1.a1.a1', 'old_label': '12.i1.a1', 'projective_image': '216.162', 'quotient_action_image': '2.1', 'quotient_action_kernel': '6.1', 'quotient_action_kernel_order': 6, 'quotient_fusion': None, 'short_label': '12.i1.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 71060609
    {'ambient': '1296.3190', 'aut_centralizer_order': 64, 'aut_label': '648.f1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '1.1', 'aut_weyl_index': 3456, 'centralizer': '54.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['216.br1.a1', '216.bs1.a1', '216.bt1.a1', '216.bu1.a1', '216.bv1.a1', '216.bv1.a2', '216.bw1.a1', '216.bx1.a1', '216.by1.a1', '216.by1.a2', '324.e1.a1', '324.i1.a1', '324.i1.b1'], 'contains': ['1296.a1.a1'], 'core': '1296.a1.a1', 'coset_action_label': None, 'count': 54, 'diagramx': [7701, -1, 5251, -1, 5863, -1, 5582, -1], 'generators': [45], 'label': '1296.3190.648.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.k1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.e1.a1', 'old_label': '648.f1.a1', 'projective_image': '1296.3190', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.f1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 71060610
    {'ambient': '1296.3190', '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', '432.f1.a1', '432.g1.a1', '432.h1.a1', '432.i1.a1', '432.j1.a1', '432.k1.a1', '432.l1.a1', '432.m1.a1', '432.n1.a1', '432.o1.a1', '648.a1.a1', '648.b1.a1', '648.b1.b1', '648.c1.a1', '648.d1.a1', '648.e1.a1', '648.f1.a1'], 'contains': [], 'core': '1296.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7348, 5371, 3666, 4806, 6584, 4591, 4231, 4944], 'generators': [], 'label': '1296.3190.1296.a1.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '1296.a1.a1', 'normal_contained_in': ['432.a1.a1', '432.b1.a1', '432.c1.a1', '432.d1.a1', '648.a1.a1'], 'normal_contains': [], 'normalizer': '1.a1.a1', 'old_label': '1296.a1.a1', 'projective_image': '1296.3190', '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: 71060611
    {'ambient': '1296.3190', 'aut_centralizer_order': 2, 'aut_label': '2.g1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '1728.47915', 'aut_weyl_index': 2, 'centralizer': '216.a1.a1', 'complements': ['648.c1.a1', '648.e1.a1', '648.b1.a1', '648.b1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.c1.a1', '4.e1.a1', '4.f1.a1', '6.j1.a1', '6.bd1.a1', '6.be1.a1', '6.bf1.a1', '6.bh1.a1'], 'core': '2.g1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3891, 6033, 7916, 4351, 3293, 6510, 6852, 4259], 'generators': [9, 144, 12, 108, 432, 2, 216], 'label': '1296.3190.2.g1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.g1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.c1.a1', '4.e1.a1', '4.f1.a1', '6.j1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.g1.a1', 'projective_image': '216.162', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.g1.a1', 'subgroup_fusion': None, 'weyl_group': '216.162'}
  • id: 71060612
    {'ambient': '1296.3190', 'aut_centralizer_order': 24, 'aut_label': '12.j1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '144.192', 'aut_weyl_index': 24, 'centralizer': '72.c1.a1', 'complements': ['108.by1.a1', '108.ca1.a1', '108.ca1.b1', '108.by1.b1', '108.ca1.c1', '108.ca1.d1'], 'conjugacy_class_count': 1, 'contained_in': ['4.d1.a1', '6.c1.a1', '6.g1.a1', '6.i1.a1'], 'contains': ['24.d1.a1', '24.bp1.a1', '36.h1.a1', '36.bw1.a1', '36.by1.a1', '36.ca1.a1'], 'core': '12.j1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7081, 3663, 6502, 6596, 6720, 8014, 5621, 7137], 'generators': [54, 432, 216, 12, 144], 'label': '1296.3190.12.j1.a1', 'mobius_quo': 0, 'mobius_sub': -2, 'normal_closure': '12.j1.a1', 'normal_contained_in': ['4.d1.a1', '6.c1.a1', '6.g1.a1', '6.i1.a1'], 'normal_contains': ['24.d1.a1', '36.h1.a1'], 'normalizer': '1.a1.a1', 'old_label': '12.j1.a1', 'projective_image': '648.731', 'quotient_action_image': '4.2', 'quotient_action_kernel': '3.1', 'quotient_action_kernel_order': 3, 'quotient_fusion': None, 'short_label': '12.j1.a1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 71060613
    {'ambient': '1296.3190', 'aut_centralizer_order': 8, 'aut_label': '12.k1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '432.759', 'aut_weyl_index': 8, 'centralizer': '216.a1.a1', 'complements': ['108.by1.a1', '108.ca1.a1', '108.ca1.b1', '108.by1.b1', '108.ca1.c1', '108.ca1.d1'], 'conjugacy_class_count': 1, 'contained_in': ['4.e1.a1', '6.c1.a1', '6.h1.a1', '6.j1.a1'], 'contains': ['24.d1.a1', '24.by1.a1', '36.cj1.a1', '36.ck1.a1', '36.cl1.a1', '36.cm1.a1', '36.cn1.a1', '36.co1.a1', '36.cp1.a1'], 'core': '12.k1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4261, 6482, 8534, 3945, 3725, 6552, 6882, 4378], 'generators': [45, 432, 216, 12, 144], 'label': '1296.3190.12.k1.a1', 'mobius_quo': 0, 'mobius_sub': -2, 'normal_closure': '12.k1.a1', 'normal_contained_in': ['4.e1.a1', '6.c1.a1', '6.h1.a1', '6.j1.a1'], 'normal_contains': ['24.d1.a1'], 'normalizer': '1.a1.a1', 'old_label': '12.k1.a1', 'projective_image': '648.731', 'quotient_action_image': '4.2', 'quotient_action_kernel': '3.1', 'quotient_action_kernel_order': 3, 'quotient_fusion': None, 'short_label': '12.k1.a1', 'subgroup_fusion': None, 'weyl_group': '216.162'}
  • id: 71060614
    {'ambient': '1296.3190', 'aut_centralizer_order': 72, 'aut_label': '12.l1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '48.51', 'aut_weyl_index': 72, 'centralizer': '12.b1.a1', 'complements': ['108.cg1.a1', '108.cg1.b1', '108.ch1.a1', '108.ch1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['4.f1.a1', '6.f1.a1', '6.m1.a1', '6.bd1.a1'], 'contains': ['24.a1.a1', '36.i1.a1', '36.j1.a1', '36.cr1.a1', '36.cy1.a1'], 'core': '12.l1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1264, 237, 9172, 9819, 1040, 9037, 8879, 9784], 'generators': [108, 432, 2, 144, 216], 'label': '1296.3190.12.l1.a1', 'mobius_quo': 0, 'mobius_sub': -6, 'normal_closure': '12.l1.a1', 'normal_contained_in': ['4.f1.a1', '6.f1.a1'], 'normal_contains': ['24.a1.a1', '36.i1.a1', '36.j1.a1'], 'normalizer': '1.a1.a1', 'old_label': '12.l1.a1', 'projective_image': '216.162', 'quotient_action_image': '2.1', 'quotient_action_kernel': '6.1', 'quotient_action_kernel_order': 6, 'quotient_fusion': None, 'short_label': '12.l1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 71060615
    {'ambient': '1296.3190', 'aut_centralizer_order': 72, 'aut_label': '12.m1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '48.51', 'aut_weyl_index': 72, 'centralizer': '24.c1.a1', 'complements': ['108.cb1.a1', '108.cb1.b1', '108.ce1.a1', '108.cf1.a1', '108.cf1.a2', '108.ce1.b1', '108.cf1.b1', '108.cf1.b2'], 'conjugacy_class_count': 1, 'contained_in': ['4.f1.a1', '6.d1.a1', '6.u1.a1', '6.be1.a1'], 'contains': ['24.b1.a1', '36.i1.a1', '36.k1.a1', '36.ct1.a1', '36.da1.a1'], 'core': '12.m1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1499, 2018, 8029, 8693, 1181, 7049, 8569, 8063], 'generators': [108, 432, 2, 12, 216], 'label': '1296.3190.12.m1.a1', 'mobius_quo': 0, 'mobius_sub': -6, 'normal_closure': '12.m1.a1', 'normal_contained_in': ['4.f1.a1', '6.d1.a1'], 'normal_contains': ['24.b1.a1', '36.i1.a1', '36.k1.a1'], 'normalizer': '1.a1.a1', 'old_label': '12.m1.a1', 'projective_image': '216.162', 'quotient_action_image': '4.2', 'quotient_action_kernel': '3.1', 'quotient_action_kernel_order': 3, 'quotient_fusion': None, 'short_label': '12.m1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 71060616
    {'ambient': '1296.3190', 'aut_centralizer_order': 24, 'aut_label': '12.n1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '144.192', 'aut_weyl_index': 24, 'centralizer': '72.b1.a1', 'complements': ['108.cb1.a1', '108.cb1.b1', '108.ce1.a1', '108.cf1.a1', '108.cf1.a2', '108.ce1.b1', '108.cf1.b1', '108.cf1.b2'], 'conjugacy_class_count': 1, 'contained_in': ['4.g1.a1', '6.d1.a1', '6.v1.a1', '6.bb1.a1'], 'contains': ['24.b1.a1', '36.l1.a1', '36.cq1.a1', '36.cu1.a1', '36.cv1.a1'], 'core': '12.n1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1825, 3170, 7323, 7060, 1902, 4147, 7828, 6267], 'generators': [111, 432, 2, 216, 12], 'label': '1296.3190.12.n1.a1', 'mobius_quo': 0, 'mobius_sub': -6, 'normal_closure': '12.n1.a1', 'normal_contained_in': ['4.g1.a1', '6.d1.a1'], 'normal_contains': ['24.b1.a1', '36.l1.a1'], 'normalizer': '1.a1.a1', 'old_label': '12.n1.a1', 'projective_image': '216.162', 'quotient_action_image': '4.2', 'quotient_action_kernel': '3.1', 'quotient_action_kernel_order': 3, 'quotient_fusion': None, 'short_label': '12.n1.a1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 71060617
    {'ambient': '1296.3190', 'aut_centralizer_order': 72, 'aut_label': '12.o1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '48.51', 'aut_weyl_index': 72, 'centralizer': '24.c1.a1', 'complements': ['108.by1.a1', '108.ca1.a1', '108.ca1.b1', '108.by1.b1', '108.ca1.c1', '108.ca1.d1', '108.cc1.a1', '108.cc1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['4.f1.a1', '6.e1.a1', '6.g1.a1', '6.j1.a1'], 'contains': ['24.d1.a1', '36.j1.a1', '36.k1.a1', '36.db1.a1', '36.dd1.a1'], 'core': '12.o1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1427, 2541, 9115, 7652, 1111, 7546, 8044, 7586], 'generators': [108, 432, 12, 144, 216], 'label': '1296.3190.12.o1.a1', 'mobius_quo': 0, 'mobius_sub': -2, 'normal_closure': '12.o1.a1', 'normal_contained_in': ['4.f1.a1', '6.e1.a1', '6.g1.a1', '6.j1.a1'], 'normal_contains': ['24.d1.a1', '36.j1.a1', '36.k1.a1'], 'normalizer': '1.a1.a1', 'old_label': '12.o1.a1', 'projective_image': '648.731', 'quotient_action_image': '4.2', 'quotient_action_kernel': '3.1', 'quotient_action_kernel_order': 3, 'quotient_fusion': None, 'short_label': '12.o1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 71060618
    {'ambient': '1296.3190', 'aut_centralizer_order': 24, 'aut_label': '12.p1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '144.192', 'aut_weyl_index': 24, 'centralizer': '72.b1.a1', 'complements': ['108.by1.a1', '108.ca1.a1', '108.ca1.b1', '108.by1.b1', '108.ca1.c1', '108.ca1.d1', '108.cc1.a1', '108.cc1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['4.g1.a1', '6.e1.a1', '6.h1.a1', '6.i1.a1'], 'contains': ['24.d1.a1', '36.l1.a1', '36.cx1.a1', '36.de1.a1', '36.dg1.a1'], 'core': '12.p1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1877, 4951, 8787, 5484, 1761, 5082, 7561, 5789], 'generators': [111, 432, 144, 216, 12], 'label': '1296.3190.12.p1.a1', 'mobius_quo': 0, 'mobius_sub': -2, 'normal_closure': '12.p1.a1', 'normal_contained_in': ['4.g1.a1', '6.e1.a1', '6.h1.a1', '6.i1.a1'], 'normal_contains': ['24.d1.a1', '36.l1.a1'], 'normalizer': '1.a1.a1', 'old_label': '12.p1.a1', 'projective_image': '648.731', 'quotient_action_image': '4.2', 'quotient_action_kernel': '3.1', 'quotient_action_kernel_order': 3, 'quotient_fusion': None, 'short_label': '12.p1.a1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 71060619
    {'ambient': '1296.3190', 'aut_centralizer_order': 72, 'aut_label': '12.q1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '16.14', 'aut_weyl_index': 216, 'centralizer': '12.q1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '6.k1.a1', '6.l1.a1', '6.m1.a1'], 'contains': ['24.a1.a1', '24.s1.a1', '24.s1.b1', '36.m1.a1', '36.n1.a1', '36.o1.a1', '36.p1.a1', '36.q1.a1', '36.r1.a1', '36.s1.a1'], 'core': '24.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5980, -1, 5595, -1, 7282, -1, 2844, -1], 'generators': [3, 432, 216, 2, 144], 'label': '1296.3190.12.q1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '12.q1.a1', 'projective_image': '216.162', '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': '4.2'}
  • id: 71060620
    {'ambient': '1296.3190', 'aut_centralizer_order': 36, 'aut_label': '12.r1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '48.51', 'aut_weyl_index': 72, 'centralizer': '24.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '6.r1.a1'], 'contains': ['24.j1.a1', '24.t1.a1', '24.t1.b1', '36.a1.a1', '36.o1.a1', '36.v1.a1', '36.w1.a1'], 'core': '36.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [6492, -1, 3326, -1, 8058, -1, 2973, -1], 'generators': [3, 12, 216, 2, 576], 'label': '1296.3190.12.r1.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.r1.a1', 'projective_image': '216.162', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.r1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 71060621
    {'ambient': '1296.3190', 'aut_centralizer_order': 36, 'aut_label': '12.s1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '48.51', 'aut_weyl_index': 72, 'centralizer': '24.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '6.t1.a1'], 'contains': ['24.m1.a1', '24.u1.a1', '24.u1.b1', '36.b1.a1', '36.q1.a1', '36.u1.a1', '36.w1.a1'], 'core': '36.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [6051, -1, 5636, -1, 7213, -1, 2720, -1], 'generators': [3, 12, 216, 146, 432], 'label': '1296.3190.12.s1.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.s1.a1', 'projective_image': '648.731', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.s1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 71060622
    {'ambient': '1296.3190', 'aut_centralizer_order': 2, 'aut_label': '3.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '1728.47915', 'aut_weyl_index': 2, 'centralizer': '216.a1.a1', 'complements': ['432.a1.a1', '432.e1.a1', '432.f1.a1', '432.k1.a1', '432.g1.a1', '432.l1.a1', '432.m1.a1', '432.o1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['6.b1.a1', '6.c1.a1', '6.e1.a1', '6.g1.a1', '6.h1.a1', '6.i1.a1', '6.j1.a1', '9.c1.a1', '9.e1.a1', '9.f1.a1'], 'core': '3.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4383, 5583, 7447, 4576, 4574, 5949, 6324, 5437], 'generators': [3, 144, 12, 18, 432, 108, 216], 'label': '1296.3190.3.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', '6.g1.a1', '6.h1.a1', '6.i1.a1', '6.j1.a1'], 'normalizer': '1.a1.a1', 'old_label': '3.a1.a1', 'projective_image': '648.731', 'quotient_action_image': '1.1', 'quotient_action_kernel': '3.1', 'quotient_action_kernel_order': 3, 'quotient_fusion': None, 'short_label': '3.a1.a1', 'subgroup_fusion': None, 'weyl_group': '216.162'}
  • id: 71060623
    {'ambient': '1296.3190', 'aut_centralizer_order': 36, 'aut_label': '12.t1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '48.51', 'aut_weyl_index': 72, 'centralizer': '24.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '6.o1.a1'], 'contains': ['24.o1.a1', '24.v1.a1', '24.v1.b1', '36.c1.a1', '36.r1.a1', '36.t1.a1', '36.w1.a1'], 'core': '36.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [6357, -1, 833, -1, 7744, -1, 1541, -1], 'generators': [3, 12, 216, 434, 144], 'label': '1296.3190.12.t1.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.t1.a1', 'projective_image': '648.731', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.t1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 71060624
    {'ambient': '1296.3190', 'aut_centralizer_order': 36, 'aut_label': '12.u1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '24.14', 'aut_weyl_index': 144, 'centralizer': '24.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1'], 'contains': ['24.q1.a1', '24.w1.a1', '24.w1.b1', '36.s1.a1', '36.t1.a1', '36.u1.a1', '36.v1.a1', '36.w1.a1'], 'core': '108.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [6422, -1, 1162, -1, 7901, -1, 2367, -1], 'generators': [3, 12, 216, 434, 576], 'label': '1296.3190.12.u1.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.u1.a1', 'projective_image': '648.731', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.u1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 71060625
    {'ambient': '1296.3190', 'aut_centralizer_order': 72, 'aut_label': '12.v1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '16.14', 'aut_weyl_index': 216, 'centralizer': '12.v1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '6.n1.a1', '6.u1.a1', '6.v1.a1'], 'contains': ['24.b1.a1', '24.x1.a1', '36.x1.a1', '36.y1.a1', '36.z1.a1', '36.ba1.a1', '36.bb1.a1', '36.bc1.a1', '36.bd1.a1'], 'core': '24.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4171, -1, 5972, -1, 4316, -1, 5175, -1], 'generators': [18, 432, 216, 2, 12], 'label': '1296.3190.12.v1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1.a1', 'old_label': '12.v1.a1', 'projective_image': '216.162', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.v1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 71060627
    {'ambient': '1296.3190', 'aut_centralizer_order': 36, 'aut_label': '12.x1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '48.51', 'aut_weyl_index': 72, 'centralizer': '24.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '6.x1.a1'], 'contains': ['24.l1.a1', '24.bc1.a1', '36.e1.a1', '36.bb1.a1', '36.bf1.a1', '36.bh1.a1'], 'core': '36.e1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2638, -1, 7008, -1, 2840, -1, 5430, -1], 'generators': [18, 144, 216, 14, 432], 'label': '1296.3190.12.x1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.a1', 'old_label': '12.x1.a1', 'projective_image': '648.731', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.x1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 71060628
    {'ambient': '1296.3190', 'aut_centralizer_order': 36, 'aut_label': '12.y1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '48.51', 'aut_weyl_index': 72, 'centralizer': '24.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '6.o1.a1'], 'contains': ['24.o1.a1', '24.bd1.a1', '24.bd1.b1', '36.f1.a1', '36.bc1.a1', '36.be1.a1', '36.bh1.a1'], 'core': '36.f1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3762, -1, 3689, -1, 4630, -1, 2169, -1], 'generators': [18, 144, 216, 434, 12], 'label': '1296.3190.12.y1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '12.y1.a1', 'projective_image': '648.731', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.y1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 71060629
    {'ambient': '1296.3190', 'aut_centralizer_order': 36, 'aut_label': '12.z1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '24.14', 'aut_weyl_index': 144, 'centralizer': '24.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1'], 'contains': ['24.p1.a1', '24.be1.a1', '24.be1.b1', '36.bd1.a1', '36.be1.a1', '36.bf1.a1', '36.bg1.a1', '36.bh1.a1'], 'core': '108.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [2026, -1, 6453, -1, 2761, -1, 4549, -1], 'generators': [18, 144, 216, 434, 444], 'label': '1296.3190.12.z1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.a1', 'old_label': '12.z1.a1', 'projective_image': '648.731', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.z1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 71060630
    {'ambient': '1296.3190', 'aut_centralizer_order': 24, 'aut_label': '12.ba1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '48.51', 'aut_weyl_index': 72, 'centralizer': '36.m1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.c1.a1', '6.k1.a1', '6.bc1.a1', '6.bd1.a1'], 'contains': ['24.a1.a1', '24.bf1.a1', '36.bi1.a1', '36.bj1.a1', '36.bm1.a1', '36.bp1.a1'], 'core': '24.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4718, -1, 6910, -1, 5797, -1, 4921, -1], 'generators': [9, 144, 216, 2, 432], 'label': '1296.3190.12.ba1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '12.ba1.a1', 'projective_image': '216.162', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.ba1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 71060631
    {'ambient': '1296.3190', 'aut_centralizer_order': 24, 'aut_label': '12.bb1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '48.51', 'aut_weyl_index': 72, 'centralizer': '36.x1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.c1.a1', '6.n1.a1', '6.bb1.a1', '6.be1.a1'], 'contains': ['24.b1.a1', '24.bg1.a1', '36.bi1.a1', '36.bk1.a1', '36.bn1.a1', '36.bq1.a1'], 'core': '24.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5196, -1, 5449, -1, 5937, -1, 4484, -1], 'generators': [9, 12, 216, 2, 432], 'label': '1296.3190.12.bb1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.c1.a1', 'old_label': '12.bb1.a1', 'projective_image': '216.162', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bb1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 71060632
    {'ambient': '1296.3190', 'aut_centralizer_order': 12, 'aut_label': '12.bc1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '48.51', 'aut_weyl_index': 72, 'centralizer': '72.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.c1.a1', '6.bf1.a1'], 'contains': ['24.h1.a1', '24.bh1.a1', '36.bi1.a1', '36.bl1.a1', '36.bo1.a1', '36.br1.a1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [4651, -1, 8130, -1, 5259, -1, 5091, -1], 'generators': [9, 156, 216, 2, 432], 'label': '1296.3190.12.bc1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.bf1.a1', 'old_label': '12.bc1.a1', 'projective_image': '216.162', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bc1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}