Abstract group data - 1944.3492

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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': '8.2', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 5, 'aut_exponent': 24, 'aut_gen_orders': [4, 24, 6, 8], 'aut_gens': [[1, 2, 6, 72, 216, 648], [3, 26, 932, 1080, 72, 648], [27, 24, 1760, 1368, 864, 648], [29, 28, 390, 72, 1512, 648], [53, 28, 1244, 1584, 432, 1296]], 'aut_group': None, 'aut_hash': 6992198563583357107, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 62208, 'aut_permdeg': 27, 'aut_perms': [1023462545638829264040694592, 10465160581169422306993687711, 10790849156737860139260352345, 7385058856736974379224674512], 'aut_phi_ratio': 96.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 9, 1, 2], [2, 81, 1, 1], [3, 1, 2, 1], [3, 2, 4, 1], [3, 2, 8, 1], [3, 12, 2, 1], [3, 24, 8, 1], [4, 9, 2, 1], [4, 81, 2, 1], [6, 9, 2, 2], [6, 18, 4, 1], [6, 18, 8, 1], [6, 81, 2, 1], [6, 108, 2, 1], [12, 9, 4, 1], [12, 18, 8, 1], [12, 18, 16, 1], [12, 81, 4, 1]], 'aut_supersolvable': False, 'aut_tex': 'C_3:S_3.C_6^2.C_{24}.C_2^2', 'autcent_abelian': True, 'autcent_cyclic': True, 'autcent_exponent': 1, 'autcent_group': '1.1', 'autcent_hash': 1, 'autcent_nilpotent': True, 'autcent_order': 1, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_1', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 24, 'autcentquo_group': None, 'autcentquo_hash': 6992198563583357107, 'autcentquo_nilpotent': False, 'autcentquo_order': 62208, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'C_3:S_3.C_6^2.C_{24}.C_2^2', 'cc_stats': [[1, 1, 1], [2, 9, 2], [2, 81, 1], [3, 1, 2], [3, 2, 12], [3, 12, 2], [3, 24, 8], [4, 9, 2], [4, 81, 2], [6, 9, 4], [6, 18, 12], [6, 81, 2], [6, 108, 2], [12, 9, 4], [12, 18, 24], [12, 81, 4]], 'center_label': '3.1', 'center_order': 3, 'central_product': True, 'central_quotient': '648.715', 'commutator_count': 1, 'commutator_label': '243.62', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '3.1', '3.1', '3.1', '3.1', '3.1'], 'composition_length': 8, 'conjugacy_classes_known': True, 'counter': 3492, 'cyclic': False, 'derived_length': 3, 'dihedral': False, 'direct_factorization': [['108.15', 1], ['18.4', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 9, 1, 2], [2, 81, 1, 1], [3, 1, 2, 1], [3, 2, 1, 4], [3, 2, 2, 4], [3, 12, 1, 2], [3, 24, 1, 8], [4, 9, 2, 1], [4, 81, 2, 1], [6, 9, 2, 2], [6, 18, 1, 4], [6, 18, 2, 4], [6, 81, 2, 1], [6, 108, 1, 2], [12, 9, 4, 1], [12, 18, 2, 4], [12, 18, 4, 4], [12, 81, 4, 1]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 45360, 'exponent': 12, 'exponents_of_order': [5, 3], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [], 'familial': False, 'frattini_label': '3.1', 'frattini_quotient': '648.715', 'hash': 3492, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 12, 'inner_gen_orders': [2, 3, 12, 3, 3, 1], 'inner_gens': [[1, 4, 30, 72, 216, 648], [5, 2, 6, 72, 216, 648], [49, 2, 6, 1224, 360, 648], [1, 2, 366, 72, 1512, 648], [1, 2, 726, 720, 216, 648], [1, 2, 6, 72, 216, 648]], 'inner_hash': 715, 'inner_nilpotent': False, 'inner_order': 648, 'inner_split': False, 'inner_tex': 'C_3^3:(C_4\\times S_3)', 'inner_used': [1, 2, 3, 4], 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': -1, 'irrep_stats': [[1, 8], [2, 16], [3, 16], [4, 4], [6, 32], [8, 8]], 'label': '1944.3492', 'linC_count': None, 'linC_degree': None, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': None, 'linQ_degree_count': None, 'linQ_dim': None, 'linQ_dim_count': None, 'linR_count': None, 'linR_degree': None, 'maximal_subgroups_known': True, 'metabelian': False, 'metacyclic': False, 'monomial': None, 'name': 'C3^4:C6:C4', '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], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 21, 'number_characteristic_subgroups': 17, 'number_conjugacy_classes': 84, 'number_divisions': 48, 'number_normal_subgroups': 37, 'number_subgroup_autclasses': 127, 'number_subgroup_classes': 448, 'number_subgroups': 8000, 'old_label': None, 'order': 1944, 'order_factorization_type': 33, 'order_stats': [[1, 1], [2, 99], [3, 242], [4, 180], [6, 630], [12, 792]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': True, 'outer_exponent': 12, 'outer_gen_orders': [2, 2, 6, 2, 2], 'outer_gen_pows': [54, 0, 684, 1, 1], 'outer_gens': [[1, 2, 6, 1008, 720, 1296], [1, 4, 6, 72, 216, 648], [1, 28, 66, 504, 1224, 648], [1, 50, 34, 1440, 1728, 648], [1, 24, 58, 1440, 1728, 648]], 'outer_group': '96.226', 'outer_hash': 226, 'outer_nilpotent': False, 'outer_order': 96, 'outer_permdeg': 8, 'outer_perms': [7, 10800, 10936, 16680, 11520], 'outer_solvable': True, 'outer_supersolvable': False, 'outer_tex': 'C_2^2\\times S_4', 'pc_rank': 6, 'perfect': False, 'permutation_degree': 24, 'pgroup': 0, 'primary_abelian_invariants': [2, 4], 'quasisimple': False, 'rank': 3, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 4], [2, 10], [4, 8], [6, 4], [8, 8], [12, 10], [24, 4]], 'representations': {'PC': {'code': 13578168519082134907772596812681040691364072527, 'gens': [1, 2, 3, 6, 7, 8], 'pres': [8, -2, -3, -2, -2, -3, -3, 3, -3, 65, 722, 66, 1923, 91, 1924, 9813, 5789, 3382, 8094, 1222]}, 'Perm': {'d': 24, 'gens': [25, 26117869331394411303600, 310016953837762542000, 55400658145031599147440, 4858936915236366695040, 144, 3, 83605394283800126895360]}}, 'schur_multiplier': [6], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 4], 'solvability_type': 12, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': 'C_3^4:C_6:C_4', 'transitive_degree': 108, '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: 136995226
    {'aut_label': '1A', 'centralizer': '1.a1', 'counter': 1, 'group_counter': 3492, 'group_order': 1944, 'label': '1A', 'order': 1, 'powers': [1, 1], 'representative': 0, 'size': 1}
  • id: 136995237
    {'aut_label': '2A', 'centralizer': '9.a1', 'counter': 2, 'group_counter': 3492, 'group_order': 1944, 'label': '2A', 'order': 2, 'powers': [1, 2], 'representative': 1, 'size': 9}
  • id: 136995248
    {'aut_label': '2B', 'centralizer': '9.b1', 'counter': 3, 'group_counter': 3492, 'group_order': 1944, 'label': '2B', 'order': 2, 'powers': [1, 3], 'representative': 36, 'size': 9}
  • id: 136995259
    {'aut_label': '2C', 'centralizer': '81.a1', 'counter': 4, 'group_counter': 3492, 'group_order': 1944, 'label': '2C', 'order': 2, 'powers': [1, 4], 'representative': 1599, 'size': 81}
  • id: 136995270
    {'aut_label': '3A1', 'centralizer': '1.a1', 'counter': 5, 'group_counter': 3492, 'group_order': 1944, 'label': '3A1', 'order': 3, 'powers': [6, 1], 'representative': 1296, 'size': 1}
  • id: 136995281
    {'aut_label': '3A1', 'centralizer': '1.a1', 'counter': 6, 'group_counter': 3492, 'group_order': 1944, 'label': '3A-1', 'order': 3, 'powers': [5, 1], 'representative': 648, 'size': 1}
  • id: 136995292
    {'aut_label': '3B', 'centralizer': '2.b1', 'counter': 7, 'group_counter': 3492, 'group_order': 1944, 'label': '3B', 'order': 3, 'powers': [7, 1], 'representative': 24, 'size': 2}
  • id: 136995303
    {'aut_label': '3B', 'centralizer': '2.b1', 'counter': 8, 'group_counter': 3492, 'group_order': 1944, 'label': '3C', 'order': 3, 'powers': [8, 1], 'representative': 26, 'size': 2}
  • id: 136995309
    {'aut_label': '3B', 'centralizer': '2.b1', 'counter': 9, 'group_counter': 3492, 'group_order': 1944, 'label': '3D', 'order': 3, 'powers': [9, 1], 'representative': 28, 'size': 2}
  • id: 136995227
    {'aut_label': '3B', 'centralizer': '2.b1', 'counter': 10, 'group_counter': 3492, 'group_order': 1944, 'label': '3E', 'order': 3, 'powers': [10, 1], 'representative': 2, 'size': 2}
  • id: 136995228
    {'aut_label': '3F1', 'centralizer': '2.b1', 'counter': 11, 'group_counter': 3492, 'group_order': 1944, 'label': '3F1', 'order': 3, 'powers': [12, 1], 'representative': 672, 'size': 2}
  • id: 136995229
    {'aut_label': '3F1', 'centralizer': '2.b1', 'counter': 12, 'group_counter': 3492, 'group_order': 1944, 'label': '3F-1', 'order': 3, 'powers': [11, 1], 'representative': 1344, 'size': 2}
  • id: 136995230
    {'aut_label': '3F1', 'centralizer': '2.b1', 'counter': 13, 'group_counter': 3492, 'group_order': 1944, 'label': '3G1', 'order': 3, 'powers': [14, 1], 'representative': 674, 'size': 2}
  • id: 136995231
    {'aut_label': '3F1', 'centralizer': '2.b1', 'counter': 14, 'group_counter': 3492, 'group_order': 1944, 'label': '3G-1', 'order': 3, 'powers': [13, 1], 'representative': 1348, 'size': 2}
  • id: 136995232
    {'aut_label': '3F1', 'centralizer': '2.b1', 'counter': 15, 'group_counter': 3492, 'group_order': 1944, 'label': '3H1', 'order': 3, 'powers': [16, 1], 'representative': 676, 'size': 2}
  • id: 136995233
    {'aut_label': '3F1', 'centralizer': '2.b1', 'counter': 16, 'group_counter': 3492, 'group_order': 1944, 'label': '3H-1', 'order': 3, 'powers': [15, 1], 'representative': 1346, 'size': 2}
  • id: 136995234
    {'aut_label': '3F1', 'centralizer': '2.b1', 'counter': 17, 'group_counter': 3492, 'group_order': 1944, 'label': '3I1', 'order': 3, 'powers': [18, 1], 'representative': 650, 'size': 2}
  • id: 136995235
    {'aut_label': '3F1', 'centralizer': '2.b1', 'counter': 18, 'group_counter': 3492, 'group_order': 1944, 'label': '3I-1', 'order': 3, 'powers': [17, 1], 'representative': 1300, 'size': 2}
  • id: 136995236
    {'aut_label': '3J', 'centralizer': '12.c1', 'counter': 19, 'group_counter': 3492, 'group_order': 1944, 'label': '3J', 'order': 3, 'powers': [19, 1], 'representative': 1152, 'size': 12}
  • id: 136995238
    {'aut_label': '3J', 'centralizer': '12.c1', 'counter': 20, 'group_counter': 3492, 'group_order': 1944, 'label': '3K', 'order': 3, 'powers': [20, 1], 'representative': 792, 'size': 12}
  • id: 136995239
    {'aut_label': '3L', 'centralizer': '24.c1', 'counter': 21, 'group_counter': 3492, 'group_order': 1944, 'label': '3L', 'order': 3, 'powers': [21, 1], 'representative': 240, 'size': 24}
  • id: 136995240
    {'aut_label': '3L', 'centralizer': '24.c1', 'counter': 22, 'group_counter': 3492, 'group_order': 1944, 'label': '3M', 'order': 3, 'powers': [22, 1], 'representative': 96, 'size': 24}
  • id: 136995241
    {'aut_label': '3L', 'centralizer': '24.c1', 'counter': 23, 'group_counter': 3492, 'group_order': 1944, 'label': '3N', 'order': 3, 'powers': [23, 1], 'representative': 218, 'size': 24}
  • id: 136995242
    {'aut_label': '3L', 'centralizer': '24.c1', 'counter': 24, 'group_counter': 3492, 'group_order': 1944, 'label': '3O', 'order': 3, 'powers': [24, 1], 'representative': 74, 'size': 24}
  • id: 136995243
    {'aut_label': '3L', 'centralizer': '24.c1', 'counter': 25, 'group_counter': 3492, 'group_order': 1944, 'label': '3P', 'order': 3, 'powers': [25, 1], 'representative': 242, 'size': 24}
  • id: 136995244
    {'aut_label': '3L', 'centralizer': '24.c1', 'counter': 26, 'group_counter': 3492, 'group_order': 1944, 'label': '3Q', 'order': 3, 'powers': [26, 1], 'representative': 98, 'size': 24}
  • id: 136995245
    {'aut_label': '3L', 'centralizer': '24.c1', 'counter': 27, 'group_counter': 3492, 'group_order': 1944, 'label': '3R', 'order': 3, 'powers': [27, 1], 'representative': 266, 'size': 24}
  • id: 136995246
    {'aut_label': '3L', 'centralizer': '24.c1', 'counter': 28, 'group_counter': 3492, 'group_order': 1944, 'label': '3S', 'order': 3, 'powers': [28, 1], 'representative': 122, 'size': 24}
  • id: 136995247
    {'aut_label': '4A1', 'centralizer': '9.b1', 'counter': 29, 'group_counter': 3492, 'group_order': 1944, 'label': '4A1', 'order': 4, 'powers': [3, 30], 'representative': 54, 'size': 9}
  • id: 136995249
    {'aut_label': '4A1', 'centralizer': '9.b1', 'counter': 30, 'group_counter': 3492, 'group_order': 1944, 'label': '4A-1', 'order': 4, 'powers': [3, 29], 'representative': 18, 'size': 9}
  • id: 136995250
    {'aut_label': '4B1', 'centralizer': '81.a1', 'counter': 31, 'group_counter': 3492, 'group_order': 1944, 'label': '4B1', 'order': 4, 'powers': [3, 32], 'representative': 55, 'size': 81}
  • id: 136995251
    {'aut_label': '4B1', 'centralizer': '81.a1', 'counter': 32, 'group_counter': 3492, 'group_order': 1944, 'label': '4B-1', 'order': 4, 'powers': [3, 31], 'representative': 19, 'size': 81}
  • id: 136995252
    {'aut_label': '6A1', 'centralizer': '9.a1', 'counter': 33, 'group_counter': 3492, 'group_order': 1944, 'label': '6A1', 'order': 6, 'powers': [5, 2], 'representative': 649, 'size': 9}
  • id: 136995253
    {'aut_label': '6A1', 'centralizer': '9.a1', 'counter': 34, 'group_counter': 3492, 'group_order': 1944, 'label': '6A-1', 'order': 6, 'powers': [6, 2], 'representative': 1297, 'size': 9}
  • id: 136995254
    {'aut_label': '6B1', 'centralizer': '9.b1', 'counter': 35, 'group_counter': 3492, 'group_order': 1944, 'label': '6B1', 'order': 6, 'powers': [6, 3], 'representative': 1332, 'size': 9}
  • id: 136995255
    {'aut_label': '6B1', 'centralizer': '9.b1', 'counter': 36, 'group_counter': 3492, 'group_order': 1944, 'label': '6B-1', 'order': 6, 'powers': [5, 3], 'representative': 684, 'size': 9}
  • id: 136995256
    {'aut_label': '6C', 'centralizer': '18.f1', 'counter': 37, 'group_counter': 3492, 'group_order': 1944, 'label': '6C', 'order': 6, 'powers': [7, 3], 'representative': 12, 'size': 18}
  • id: 136995257
    {'aut_label': '6C', 'centralizer': '18.f1', 'counter': 38, 'group_counter': 3492, 'group_order': 1944, 'label': '6D', 'order': 6, 'powers': [8, 3], 'representative': 16, 'size': 18}
  • id: 136995258
    {'aut_label': '6C', 'centralizer': '18.f1', 'counter': 39, 'group_counter': 3492, 'group_order': 1944, 'label': '6E', 'order': 6, 'powers': [9, 3], 'representative': 14, 'size': 18}
  • id: 136995260
    {'aut_label': '6C', 'centralizer': '18.f1', 'counter': 40, 'group_counter': 3492, 'group_order': 1944, 'label': '6F', 'order': 6, 'powers': [10, 3], 'representative': 40, 'size': 18}
  • id: 136995261
    {'aut_label': '6G1', 'centralizer': '18.f1', 'counter': 41, 'group_counter': 3492, 'group_order': 1944, 'label': '6G1', 'order': 6, 'powers': [11, 3], 'representative': 1308, 'size': 18}
  • id: 136995262
    {'aut_label': '6G1', 'centralizer': '18.f1', 'counter': 42, 'group_counter': 3492, 'group_order': 1944, 'label': '6G-1', 'order': 6, 'powers': [12, 3], 'representative': 708, 'size': 18}
  • id: 136995263
    {'aut_label': '6G1', 'centralizer': '18.f1', 'counter': 43, 'group_counter': 3492, 'group_order': 1944, 'label': '6H1', 'order': 6, 'powers': [13, 3], 'representative': 1312, 'size': 18}
  • id: 136995264
    {'aut_label': '6G1', 'centralizer': '18.f1', 'counter': 44, 'group_counter': 3492, 'group_order': 1944, 'label': '6H-1', 'order': 6, 'powers': [14, 3], 'representative': 710, 'size': 18}
  • id: 136995265
    {'aut_label': '6G1', 'centralizer': '18.f1', 'counter': 45, 'group_counter': 3492, 'group_order': 1944, 'label': '6I1', 'order': 6, 'powers': [15, 3], 'representative': 1310, 'size': 18}
  • id: 136995266
    {'aut_label': '6G1', 'centralizer': '18.f1', 'counter': 46, 'group_counter': 3492, 'group_order': 1944, 'label': '6I-1', 'order': 6, 'powers': [16, 3], 'representative': 712, 'size': 18}
  • id: 136995267
    {'aut_label': '6G1', 'centralizer': '18.f1', 'counter': 47, 'group_counter': 3492, 'group_order': 1944, 'label': '6J1', 'order': 6, 'powers': [17, 3], 'representative': 1336, 'size': 18}
  • id: 136995268
    {'aut_label': '6G1', 'centralizer': '18.f1', 'counter': 48, 'group_counter': 3492, 'group_order': 1944, 'label': '6J-1', 'order': 6, 'powers': [18, 3], 'representative': 686, 'size': 18}
  • id: 136995269
    {'aut_label': '6K1', 'centralizer': '81.a1', 'counter': 49, 'group_counter': 3492, 'group_order': 1944, 'label': '6K1', 'order': 6, 'powers': [6, 4], 'representative': 951, 'size': 81}
  • id: 136995271
    {'aut_label': '6K1', 'centralizer': '81.a1', 'counter': 50, 'group_counter': 3492, 'group_order': 1944, 'label': '6K-1', 'order': 6, 'powers': [5, 4], 'representative': 303, 'size': 81}
  • id: 136995272
    {'aut_label': '6L', 'centralizer': '108.b1', 'counter': 51, 'group_counter': 3492, 'group_order': 1944, 'label': '6L', 'order': 6, 'powers': [19, 2], 'representative': 365, 'size': 108}
  • id: 136995273
    {'aut_label': '6L', 'centralizer': '108.b1', 'counter': 52, 'group_counter': 3492, 'group_order': 1944, 'label': '6M', 'order': 6, 'powers': [20, 2], 'representative': 1419, 'size': 108}
  • id: 136995274
    {'aut_label': '12A1', 'centralizer': '9.b1', 'counter': 53, 'group_counter': 3492, 'group_order': 1944, 'label': '12A1', 'order': 12, 'powers': [35, 29], 'representative': 666, 'size': 9}
  • id: 136995275
    {'aut_label': '12A1', 'centralizer': '9.b1', 'counter': 54, 'group_counter': 3492, 'group_order': 1944, 'label': '12A-1', 'order': 12, 'powers': [36, 30], 'representative': 126, 'size': 9}
  • id: 136995276
    {'aut_label': '12A1', 'centralizer': '9.b1', 'counter': 55, 'group_counter': 3492, 'group_order': 1944, 'label': '12A5', 'order': 12, 'powers': [36, 29], 'representative': 234, 'size': 9}
  • id: 136995277
    {'aut_label': '12A1', 'centralizer': '9.b1', 'counter': 56, 'group_counter': 3492, 'group_order': 1944, 'label': '12A-5', 'order': 12, 'powers': [35, 30], 'representative': 702, 'size': 9}
  • id: 136995278
    {'aut_label': '12B1', 'centralizer': '18.f1', 'counter': 57, 'group_counter': 3492, 'group_order': 1944, 'label': '12B1', 'order': 12, 'powers': [37, 30], 'representative': 6, 'size': 18}
  • id: 136995279
    {'aut_label': '12B1', 'centralizer': '18.f1', 'counter': 58, 'group_counter': 3492, 'group_order': 1944, 'label': '12B-1', 'order': 12, 'powers': [37, 29], 'representative': 42, 'size': 18}
  • id: 136995280
    {'aut_label': '12B1', 'centralizer': '18.f1', 'counter': 59, 'group_counter': 3492, 'group_order': 1944, 'label': '12C1', 'order': 12, 'powers': [38, 30], 'representative': 8, 'size': 18}
  • id: 136995282
    {'aut_label': '12B1', 'centralizer': '18.f1', 'counter': 60, 'group_counter': 3492, 'group_order': 1944, 'label': '12C-1', 'order': 12, 'powers': [38, 29], 'representative': 44, 'size': 18}
  • id: 136995283
    {'aut_label': '12B1', 'centralizer': '18.f1', 'counter': 61, 'group_counter': 3492, 'group_order': 1944, 'label': '12D1', 'order': 12, 'powers': [39, 30], 'representative': 10, 'size': 18}
  • id: 136995284
    {'aut_label': '12B1', 'centralizer': '18.f1', 'counter': 62, 'group_counter': 3492, 'group_order': 1944, 'label': '12D-1', 'order': 12, 'powers': [39, 29], 'representative': 68, 'size': 18}
  • id: 136995285
    {'aut_label': '12B1', 'centralizer': '18.f1', 'counter': 63, 'group_counter': 3492, 'group_order': 1944, 'label': '12E1', 'order': 12, 'powers': [40, 29], 'representative': 20, 'size': 18}
  • id: 136995286
    {'aut_label': '12B1', 'centralizer': '18.f1', 'counter': 64, 'group_counter': 3492, 'group_order': 1944, 'label': '12E-1', 'order': 12, 'powers': [40, 30], 'representative': 56, 'size': 18}
  • id: 136995287
    {'aut_label': '12F1', 'centralizer': '18.f1', 'counter': 65, 'group_counter': 3492, 'group_order': 1944, 'label': '12F1', 'order': 12, 'powers': [41, 30], 'representative': 654, 'size': 18}
  • id: 136995288
    {'aut_label': '12F1', 'centralizer': '18.f1', 'counter': 66, 'group_counter': 3492, 'group_order': 1944, 'label': '12F-1', 'order': 12, 'powers': [42, 29], 'representative': 258, 'size': 18}
  • id: 136995289
    {'aut_label': '12F1', 'centralizer': '18.f1', 'counter': 67, 'group_counter': 3492, 'group_order': 1944, 'label': '12F5', 'order': 12, 'powers': [42, 30], 'representative': 78, 'size': 18}
  • id: 136995290
    {'aut_label': '12F1', 'centralizer': '18.f1', 'counter': 68, 'group_counter': 3492, 'group_order': 1944, 'label': '12F-5', 'order': 12, 'powers': [41, 29], 'representative': 690, 'size': 18}
  • id: 136995291
    {'aut_label': '12F1', 'centralizer': '18.f1', 'counter': 69, 'group_counter': 3492, 'group_order': 1944, 'label': '12G1', 'order': 12, 'powers': [43, 30], 'representative': 656, 'size': 18}
  • id: 136995293
    {'aut_label': '12F1', 'centralizer': '18.f1', 'counter': 70, 'group_counter': 3492, 'group_order': 1944, 'label': '12G-1', 'order': 12, 'powers': [44, 29], 'representative': 260, 'size': 18}
  • id: 136995294
    {'aut_label': '12F1', 'centralizer': '18.f1', 'counter': 71, 'group_counter': 3492, 'group_order': 1944, 'label': '12G5', 'order': 12, 'powers': [44, 30], 'representative': 80, 'size': 18}
  • id: 136995295
    {'aut_label': '12F1', 'centralizer': '18.f1', 'counter': 72, 'group_counter': 3492, 'group_order': 1944, 'label': '12G-5', 'order': 12, 'powers': [43, 29], 'representative': 692, 'size': 18}
  • id: 136995296
    {'aut_label': '12F1', 'centralizer': '18.f1', 'counter': 73, 'group_counter': 3492, 'group_order': 1944, 'label': '12H1', 'order': 12, 'powers': [45, 30], 'representative': 658, 'size': 18}
  • id: 136995297
    {'aut_label': '12F1', 'centralizer': '18.f1', 'counter': 74, 'group_counter': 3492, 'group_order': 1944, 'label': '12H-1', 'order': 12, 'powers': [46, 29], 'representative': 284, 'size': 18}
  • id: 136995298
    {'aut_label': '12F1', 'centralizer': '18.f1', 'counter': 75, 'group_counter': 3492, 'group_order': 1944, 'label': '12H5', 'order': 12, 'powers': [46, 30], 'representative': 82, 'size': 18}
  • id: 136995299
    {'aut_label': '12F1', 'centralizer': '18.f1', 'counter': 76, 'group_counter': 3492, 'group_order': 1944, 'label': '12H-5', 'order': 12, 'powers': [45, 29], 'representative': 716, 'size': 18}
  • id: 136995300
    {'aut_label': '12F1', 'centralizer': '18.f1', 'counter': 77, 'group_counter': 3492, 'group_order': 1944, 'label': '12I1', 'order': 12, 'powers': [47, 29], 'representative': 668, 'size': 18}
  • id: 136995301
    {'aut_label': '12F1', 'centralizer': '18.f1', 'counter': 78, 'group_counter': 3492, 'group_order': 1944, 'label': '12I-1', 'order': 12, 'powers': [48, 30], 'representative': 128, 'size': 18}
  • id: 136995302
    {'aut_label': '12F1', 'centralizer': '18.f1', 'counter': 79, 'group_counter': 3492, 'group_order': 1944, 'label': '12I5', 'order': 12, 'powers': [48, 29], 'representative': 236, 'size': 18}
  • id: 136995304
    {'aut_label': '12F1', 'centralizer': '18.f1', 'counter': 80, 'group_counter': 3492, 'group_order': 1944, 'label': '12I-5', 'order': 12, 'powers': [47, 30], 'representative': 704, 'size': 18}
  • id: 136995305
    {'aut_label': '12J1', 'centralizer': '81.a1', 'counter': 81, 'group_counter': 3492, 'group_order': 1944, 'label': '12J1', 'order': 12, 'powers': [36, 31], 'representative': 1315, 'size': 81}
  • id: 136995306
    {'aut_label': '12J1', 'centralizer': '81.a1', 'counter': 82, 'group_counter': 3492, 'group_order': 1944, 'label': '12J-1', 'order': 12, 'powers': [35, 32], 'representative': 703, 'size': 81}
  • id: 136995307
    {'aut_label': '12J1', 'centralizer': '81.a1', 'counter': 83, 'group_counter': 3492, 'group_order': 1944, 'label': '12J5', 'order': 12, 'powers': [35, 31], 'representative': 667, 'size': 81}
  • id: 136995308
    {'aut_label': '12J1', 'centralizer': '81.a1', 'counter': 84, 'group_counter': 3492, 'group_order': 1944, 'label': '12J-5', 'order': 12, 'powers': [36, 32], 'representative': 1351, 'size': 81}
• 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: 12109890
    {'cdim': 1, 'counter': 1, 'faithful': False, 'group': '1944.3492', 'group_order': 1944, 'image': None, 'label': '1944.3492.1a', '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], 'schur_index': 1}
  • id: 12109901
    {'cdim': 1, 'counter': 2, 'faithful': False, 'group': '1944.3492', 'group_order': 1944, 'image': None, 'label': '1944.3492.1b', '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], 'schur_index': 1}
  • id: 12109912
    {'cdim': 1, 'counter': 3, 'faithful': False, 'group': '1944.3492', 'group_order': 1944, 'image': None, 'label': '1944.3492.1c', '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], 'schur_index': 1}
  • id: 12109923
    {'cdim': 1, 'counter': 4, 'faithful': False, 'group': '1944.3492', 'group_order': 1944, 'image': None, 'label': '1944.3492.1d', '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], 'schur_index': 1}
  • id: 12109933
    {'cdim': 1, 'counter': 5, 'faithful': False, 'group': '1944.3492', 'group_order': 1944, 'image': None, 'label': '1944.3492.1e', 'multiplicity': 2, 'nt': [4, 1], 'qdim': 2, 'qvalues': [2, -2, -2, 2, 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, 0, 0, 0, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, 2, 2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 12109934
    {'cdim': 1, 'counter': 6, 'faithful': False, 'group': '1944.3492', 'group_order': 1944, 'image': None, 'label': '1944.3492.1f', 'multiplicity': 2, 'nt': [4, 1], 'qdim': 2, 'qvalues': [2, 2, -2, -2, 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, 0, 0, 0, 2, 2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 12109935
    {'cdim': 2, 'counter': 7, 'faithful': False, 'group': '1944.3492', 'group_order': 1944, 'image': None, 'label': '1944.3492.2a', 'multiplicity': 1, 'nt': [3, 2], 'qdim': 2, 'qvalues': [2, 0, 2, 0, 2, 2, -1, -1, -1, 2, -1, -1, -1, -1, -1, -1, 2, 2, 2, 2, -1, -1, 2, 2, -1, -1, -1, -1, 2, 2, 0, 0, 0, 0, 2, 2, -1, -1, -1, 2, -1, -1, -1, -1, -1, -1, 2, 2, 0, 0, 0, 0, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, 2, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 2, 2, 2, 2, 0, 0, 0, 0], 'schur_index': 1}
  • id: 12109936
    {'cdim': 2, 'counter': 8, 'faithful': False, 'group': '1944.3492', 'group_order': 1944, 'image': None, 'label': '1944.3492.2b', 'multiplicity': 1, 'nt': [3, 2], 'qdim': 2, 'qvalues': [2, 0, 2, 0, 2, 2, -1, -1, 2, -1, -1, -1, -1, -1, 2, 2, -1, -1, 2, 2, -1, -1, -1, -1, -1, -1, 2, 2, 2, 2, 0, 0, 0, 0, 2, 2, -1, -1, 2, -1, -1, -1, -1, -1, 2, 2, -1, -1, 0, 0, 0, 0, 2, 2, 2, 2, -1, -1, -1, -1, 2, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 2, 2, 2, 2, -1, -1, -1, -1, 0, 0, 0, 0], 'schur_index': 1}
  • id: 12109937
    {'cdim': 2, 'counter': 9, 'faithful': False, 'group': '1944.3492', 'group_order': 1944, 'image': None, 'label': '1944.3492.2c', 'multiplicity': 1, 'nt': [3, 2], 'qdim': 2, 'qvalues': [2, 0, 2, 0, 2, 2, -1, 2, -1, -1, -1, -1, 2, 2, -1, -1, -1, -1, 2, 2, -1, -1, -1, -1, 2, 2, -1, -1, 2, 2, 0, 0, 0, 0, 2, 2, -1, 2, -1, -1, -1, -1, 2, 2, -1, -1, -1, -1, 0, 0, 0, 0, 2, 2, 2, 2, -1, -1, 2, 2, -1, -1, -1, -1, -1, -1, -1, -1, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, -1, -1, 0, 0, 0, 0], 'schur_index': 1}
  • id: 12109891
    {'cdim': 2, 'counter': 10, 'faithful': False, 'group': '1944.3492', 'group_order': 1944, 'image': None, 'label': '1944.3492.2d', 'multiplicity': 1, 'nt': [3, 2], 'qdim': 2, 'qvalues': [2, 0, 2, 0, 2, 2, 2, -1, -1, -1, 2, 2, -1, -1, -1, -1, -1, -1, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, 2, 2, 0, 0, 0, 0, 2, 2, 2, -1, -1, -1, 2, 2, -1, -1, -1, -1, -1, -1, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 0, 0, 0, 0], 'schur_index': 1}
  • id: 12109892
    {'cdim': 2, 'counter': 11, 'faithful': False, 'group': '1944.3492', 'group_order': 1944, 'image': None, 'label': '1944.3492.2e', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, 0, 2, 0, 2, 2, -1, -1, -1, 2, -1, -1, -1, -1, -1, -1, 2, 2, 2, 2, -1, -1, 2, 2, -1, -1, -1, -1, -2, -2, 0, 0, 0, 0, 2, 2, -1, -1, -1, 2, -1, -1, -1, -1, -1, -1, 2, 2, 0, 0, 0, 0, -2, -2, -2, -2, 1, 1, 1, 1, 1, 1, -2, -2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -2, -2, -2, -2, 0, 0, 0, 0], 'schur_index': 1}
  • id: 12109893
    {'cdim': 2, 'counter': 12, 'faithful': False, 'group': '1944.3492', 'group_order': 1944, 'image': None, 'label': '1944.3492.2f', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, 0, 2, 0, 2, 2, -1, -1, 2, -1, -1, -1, -1, -1, 2, 2, -1, -1, 2, 2, -1, -1, -1, -1, -1, -1, 2, 2, -2, -2, 0, 0, 0, 0, 2, 2, -1, -1, 2, -1, -1, -1, -1, -1, 2, 2, -1, -1, 0, 0, 0, 0, -2, -2, -2, -2, 1, 1, 1, 1, -2, -2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -2, -2, -2, -2, 1, 1, 1, 1, 0, 0, 0, 0], 'schur_index': 1}
  • id: 12109894
    {'cdim': 2, 'counter': 13, 'faithful': False, 'group': '1944.3492', 'group_order': 1944, 'image': None, 'label': '1944.3492.2g', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, 0, 2, 0, 2, 2, -1, 2, -1, -1, -1, -1, 2, 2, -1, -1, -1, -1, 2, 2, -1, -1, -1, -1, 2, 2, -1, -1, -2, -2, 0, 0, 0, 0, 2, 2, -1, 2, -1, -1, -1, -1, 2, 2, -1, -1, -1, -1, 0, 0, 0, 0, -2, -2, -2, -2, 1, 1, -2, -2, 1, 1, 1, 1, 1, 1, 1, 1, -2, -2, -2, -2, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0], 'schur_index': 1}
  • id: 12109895
    {'cdim': 2, 'counter': 14, 'faithful': False, 'group': '1944.3492', 'group_order': 1944, 'image': None, 'label': '1944.3492.2h', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, 0, 2, 0, 2, 2, 2, -1, -1, -1, 2, 2, -1, -1, -1, -1, -1, -1, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, -2, -2, 0, 0, 0, 0, 2, 2, 2, -1, -1, -1, 2, 2, -1, -1, -1, -1, -1, -1, 0, 0, 0, 0, -2, -2, -2, -2, -2, -2, 1, 1, 1, 1, 1, 1, -2, -2, -2, -2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0], 'schur_index': 1}
  • id: 12109896
    {'cdim': 2, 'counter': 15, 'faithful': False, 'group': '1944.3492', 'group_order': 1944, 'image': None, 'label': '1944.3492.2i', 'multiplicity': 2, 'nt': [12, 11], 'qdim': 4, 'qvalues': [4, 0, -4, 0, 4, 4, -2, -2, -2, 4, -2, -2, -2, -2, -2, -2, 4, 4, 4, 4, -2, -2, 4, 4, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, -4, -4, 2, 2, 2, -4, 2, 2, 2, 2, 2, 2, -4, -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], 'schur_index': 1}
  • id: 12109897
    {'cdim': 2, 'counter': 16, 'faithful': False, 'group': '1944.3492', 'group_order': 1944, 'image': None, 'label': '1944.3492.2j', 'multiplicity': 2, 'nt': [12, 11], 'qdim': 4, 'qvalues': [4, 0, -4, 0, 4, 4, -2, -2, 4, -2, -2, -2, -2, -2, 4, 4, -2, -2, 4, 4, -2, -2, -2, -2, -2, -2, 4, 4, 0, 0, 0, 0, 0, 0, -4, -4, 2, 2, -4, 2, 2, 2, 2, 2, -4, -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], 'schur_index': 1}
  • id: 12109898
    {'cdim': 2, 'counter': 17, 'faithful': False, 'group': '1944.3492', 'group_order': 1944, 'image': None, 'label': '1944.3492.2k', 'multiplicity': 2, 'nt': [12, 11], 'qdim': 4, 'qvalues': [4, 0, -4, 0, 4, 4, -2, 4, -2, -2, -2, -2, 4, 4, -2, -2, -2, -2, 4, 4, -2, -2, -2, -2, 4, 4, -2, -2, 0, 0, 0, 0, 0, 0, -4, -4, 2, -4, 2, 2, 2, 2, -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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 12109899
    {'cdim': 2, 'counter': 18, 'faithful': False, 'group': '1944.3492', 'group_order': 1944, 'image': None, 'label': '1944.3492.2l', 'multiplicity': 2, 'nt': [12, 11], 'qdim': 4, 'qvalues': [4, 0, -4, 0, 4, 4, 4, -2, -2, -2, 4, 4, -2, -2, -2, -2, -2, -2, 4, 4, 4, 4, -2, -2, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, -4, -4, -4, 2, 2, 2, -4, -4, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 12109907
    {'cdim': 4, 'counter': 25, 'faithful': False, 'group': '1944.3492', 'group_order': 1944, 'image': None, 'label': '1944.3492.4a', 'multiplicity': 1, 'nt': [6, 10], 'qdim': 4, 'qvalues': [4, 4, 0, 0, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, -2, 1, -2, 1, -2, 1, -2, 1, -2, 1, 0, 0, 0, 0, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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], 'schur_index': 1}
  • id: 12109908
    {'cdim': 4, 'counter': 26, 'faithful': False, 'group': '1944.3492', 'group_order': 1944, 'image': None, 'label': '1944.3492.4b', 'multiplicity': 1, 'nt': [6, 10], 'qdim': 4, 'qvalues': [4, 4, 0, 0, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 1, -2, 1, -2, 1, -2, 1, -2, 1, -2, 0, 0, 0, 0, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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, 0, 0], 'schur_index': 1}
  • id: 12109909
    {'cdim': 4, 'counter': 27, 'faithful': False, 'group': '1944.3492', 'group_order': 1944, 'image': None, 'label': '1944.3492.4c', 'multiplicity': 1, 'nt': [12, 40], 'qdim': 4, 'qvalues': [4, -4, 0, 0, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, -2, 1, -2, 1, -2, 1, -2, 1, -2, 1, 0, 0, 0, 0, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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], 'schur_index': 1}
  • id: 12109910
    {'cdim': 4, 'counter': 28, 'faithful': False, 'group': '1944.3492', 'group_order': 1944, 'image': None, 'label': '1944.3492.4d', 'multiplicity': 1, 'nt': [12, 40], 'qdim': 4, 'qvalues': [4, -4, 0, 0, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 1, -2, 1, -2, 1, -2, 1, -2, 1, -2, 0, 0, 0, 0, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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, 0, 0], 'schur_index': 1}
  • id: 12109900
    {'cdim': 3, 'counter': 19, 'faithful': False, 'group': '1944.3492', 'group_order': 1944, 'image': None, 'label': '1944.3492.3a', 'multiplicity': 2, 'nt': [27, 32], 'qdim': 6, 'qvalues': [6, 6, -2, -2, -3, -3, 6, 6, 6, 6, -3, -3, -3, -3, -3, -3, -3, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, -3, -3, 1, 1, -2, -2, -2, -2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, -1, -1, -1, -1, 2, 2, 2, 2, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], 'schur_index': 1}
  • id: 12109902
    {'cdim': 3, 'counter': 20, 'faithful': False, 'group': '1944.3492', 'group_order': 1944, 'image': None, 'label': '1944.3492.3b', 'multiplicity': 2, 'nt': [36, 85], 'qdim': 6, 'qvalues': [6, 6, -2, -2, -3, -3, 6, 6, 6, 6, -3, -3, -3, -3, -3, -3, -3, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, -2, -3, -3, 1, 1, -2, -2, -2, -2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, -2, -2, -2, -2, -2, -2, -2, -2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 'schur_index': 1}
  • id: 12109903
    {'cdim': 3, 'counter': 21, 'faithful': False, 'group': '1944.3492', 'group_order': 1944, 'image': None, 'label': '1944.3492.3c', 'multiplicity': 2, 'nt': [36, 224], 'qdim': 6, 'qvalues': [6, -6, -2, 2, -3, -3, 6, 6, 6, 6, -3, -3, -3, -3, -3, -3, -3, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, 2, 2, 3, 3, 1, 1, -2, -2, -2, -2, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 0, 0, 1, 1, 1, 1, -2, -2, -2, -2, -2, -2, -2, -2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1], 'schur_index': 1}
  • id: 12109904
    {'cdim': 3, 'counter': 22, 'faithful': False, 'group': '1944.3492', 'group_order': 1944, 'image': None, 'label': '1944.3492.3d', 'multiplicity': 2, 'nt': [36, 224], 'qdim': 6, 'qvalues': [6, -6, -2, 2, -3, -3, 6, 6, 6, 6, -3, -3, -3, -3, -3, -3, -3, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, -2, -2, 3, 3, 1, 1, -2, -2, -2, -2, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 0, 0, -1, -1, -1, -1, 2, 2, 2, 2, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1], 'schur_index': 1}
  • id: 12109925
    {'cdim': 8, 'counter': 41, 'faithful': False, 'group': '1944.3492', 'group_order': 1944, 'image': None, 'label': '1944.3492.8a', 'multiplicity': 1, 'nt': [12, 119], 'qdim': 8, 'qvalues': [8, 0, 0, 0, 8, 8, -4, -4, -4, 8, -4, -4, -4, -4, -4, -4, 8, 8, -4, 2, 2, -1, -4, 2, 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], 'schur_index': 1}
  • id: 12109926
    {'cdim': 8, 'counter': 42, 'faithful': False, 'group': '1944.3492', 'group_order': 1944, 'image': None, 'label': '1944.3492.8b', 'multiplicity': 1, 'nt': [12, 119], 'qdim': 8, 'qvalues': [8, 0, 0, 0, 8, 8, -4, -4, -4, 8, -4, -4, -4, -4, -4, -4, 8, 8, 2, -4, -1, 2, 2, -4, -1, 2, -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], 'schur_index': 1}
  • id: 12109927
    {'cdim': 8, 'counter': 43, 'faithful': False, 'group': '1944.3492', 'group_order': 1944, 'image': None, 'label': '1944.3492.8c', 'multiplicity': 1, 'nt': [12, 119], 'qdim': 8, 'qvalues': [8, 0, 0, 0, 8, 8, -4, -4, 8, -4, -4, -4, -4, -4, 8, 8, -4, -4, -4, 2, 2, -1, 2, -1, 2, -1, -4, 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], 'schur_index': 1}
  • id: 12109928
    {'cdim': 8, 'counter': 44, 'faithful': False, 'group': '1944.3492', 'group_order': 1944, 'image': None, 'label': '1944.3492.8d', 'multiplicity': 1, 'nt': [12, 119], 'qdim': 8, 'qvalues': [8, 0, 0, 0, 8, 8, -4, -4, 8, -4, -4, -4, -4, -4, 8, 8, -4, -4, 2, -4, -1, 2, -1, 2, -1, 2, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 12109929
    {'cdim': 8, 'counter': 45, 'faithful': False, 'group': '1944.3492', 'group_order': 1944, 'image': None, 'label': '1944.3492.8e', 'multiplicity': 1, 'nt': [12, 119], 'qdim': 8, 'qvalues': [8, 0, 0, 0, 8, 8, -4, 8, -4, -4, -4, -4, 8, 8, -4, -4, -4, -4, -4, 2, 2, -1, 2, -1, -4, 2, 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], 'schur_index': 1}
  • id: 12109930
    {'cdim': 8, 'counter': 46, 'faithful': False, 'group': '1944.3492', 'group_order': 1944, 'image': None, 'label': '1944.3492.8f', 'multiplicity': 1, 'nt': [12, 119], 'qdim': 8, 'qvalues': [8, 0, 0, 0, 8, 8, -4, 8, -4, -4, -4, -4, 8, 8, -4, -4, -4, -4, 2, -4, -1, 2, -1, 2, 2, -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], 'schur_index': 1}
  • id: 12109931
    {'cdim': 8, 'counter': 47, 'faithful': False, 'group': '1944.3492', 'group_order': 1944, 'image': None, 'label': '1944.3492.8g', 'multiplicity': 1, 'nt': [12, 119], 'qdim': 8, 'qvalues': [8, 0, 0, 0, 8, 8, 8, -4, -4, -4, 8, 8, -4, -4, -4, -4, -4, -4, -4, 2, -4, 2, 2, -1, 2, -1, 2, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 12109932
    {'cdim': 8, 'counter': 48, 'faithful': False, 'group': '1944.3492', 'group_order': 1944, 'image': None, 'label': '1944.3492.8h', 'multiplicity': 1, 'nt': [12, 119], 'qdim': 8, 'qvalues': [8, 0, 0, 0, 8, 8, 8, -4, -4, -4, 8, 8, -4, -4, -4, -4, -4, -4, 2, -4, 2, -4, -1, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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: 12109905
    {'cdim': 3, 'counter': 23, 'faithful': False, 'group': '1944.3492', 'group_order': 1944, 'image': None, 'label': '1944.3492.3e', 'multiplicity': 4, 'nt': [18, 49], 'qdim': 12, 'qvalues': [12, 12, 4, 4, -6, -6, 12, 12, 12, 12, -6, -6, -6, -6, -6, -6, -6, -6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6, -6, -2, -2, 4, 4, 4, 4, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 12109906
    {'cdim': 3, 'counter': 24, 'faithful': False, 'group': '1944.3492', 'group_order': 1944, 'image': None, 'label': '1944.3492.3f', 'multiplicity': 4, 'nt': [36, 225], 'qdim': 12, 'qvalues': [12, -12, 4, -4, -6, -6, 12, 12, 12, 12, -6, -6, -6, -6, -6, -6, -6, -6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 6, -2, -2, 4, 4, 4, 4, -2, -2, -2, -2, -2, -2, -2, -2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 12109911
    {'cdim': 6, 'counter': 29, 'faithful': False, 'group': '1944.3492', 'group_order': 1944, 'image': None, 'label': '1944.3492.6a', 'multiplicity': 2, 'nt': [54, 0], 'qdim': 12, 'qvalues': [12, 0, -4, 0, -6, -6, -6, -6, -6, 12, 3, 3, 3, 3, 3, 3, -6, -6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 0, 0, 0, 0, 2, 2, 2, 2, 2, -4, -1, -1, -1, -1, -1, -1, 2, 2, 0, 0, 0, 0, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, 4, 4, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -2, -2, -2, -2, 0, 0, 0, 0], 'schur_index': 1}
  • id: 12109913
    {'cdim': 6, 'counter': 30, 'faithful': False, 'group': '1944.3492', 'group_order': 1944, 'image': None, 'label': '1944.3492.6b', 'multiplicity': 2, 'nt': [54, 0], 'qdim': 12, 'qvalues': [12, 0, -4, 0, -6, -6, -6, -6, 12, -6, 3, 3, 3, 3, -6, -6, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 0, 0, 0, 0, 2, 2, 2, 2, -4, 2, -1, -1, -1, -1, 2, 2, -1, -1, 0, 0, 0, 0, -2, -2, -2, -2, -2, -2, -2, -2, 4, 4, -2, -2, 1, 1, 1, 1, 1, 1, 1, 1, -2, -2, -2, -2, 1, 1, 1, 1, 0, 0, 0, 0], 'schur_index': 1}
  • id: 12109914
    {'cdim': 6, 'counter': 31, 'faithful': False, 'group': '1944.3492', 'group_order': 1944, 'image': None, 'label': '1944.3492.6c', 'multiplicity': 2, 'nt': [54, 0], 'qdim': 12, 'qvalues': [12, 0, -4, 0, -6, -6, -6, 12, -6, -6, 3, 3, -6, -6, 3, 3, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 0, 0, 0, 0, 2, 2, 2, -4, 2, 2, -1, -1, 2, 2, -1, -1, -1, -1, 0, 0, 0, 0, -2, -2, -2, -2, -2, -2, 4, 4, -2, -2, -2, -2, 1, 1, 1, 1, -2, -2, -2, -2, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0], 'schur_index': 1}
  • id: 12109915
    {'cdim': 6, 'counter': 32, 'faithful': False, 'group': '1944.3492', 'group_order': 1944, 'image': None, 'label': '1944.3492.6d', 'multiplicity': 2, 'nt': [54, 0], 'qdim': 12, 'qvalues': [12, 0, -4, 0, -6, -6, 12, -6, -6, -6, -6, -6, 3, 3, 3, 3, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 0, 0, 0, 0, 2, 2, -4, 2, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, 0, 0, 0, 0, -2, -2, -2, -2, 4, 4, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0], 'schur_index': 1}
  • id: 12109916
    {'cdim': 6, 'counter': 33, 'faithful': False, 'group': '1944.3492', 'group_order': 1944, 'image': None, 'label': '1944.3492.6e', 'multiplicity': 2, 'nt': [72, 0], 'qdim': 12, 'qvalues': [12, 0, -4, 0, -6, -6, -6, -6, -6, 12, 3, 3, 3, 3, 3, 3, -6, -6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, -4, 0, 0, 0, 0, 2, 2, 2, 2, 2, -4, -1, -1, -1, -1, -1, -1, 2, 2, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -4, -4, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 2, 2, 2, 2, 0, 0, 0, 0], 'schur_index': 1}
  • id: 12109917
    {'cdim': 6, 'counter': 34, 'faithful': False, 'group': '1944.3492', 'group_order': 1944, 'image': None, 'label': '1944.3492.6f', 'multiplicity': 2, 'nt': [72, 0], 'qdim': 12, 'qvalues': [12, 0, -4, 0, -6, -6, -6, -6, 12, -6, 3, 3, 3, 3, -6, -6, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, -4, 0, 0, 0, 0, 2, 2, 2, 2, -4, 2, -1, -1, -1, -1, 2, 2, -1, -1, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, -4, -4, 2, 2, -1, -1, -1, -1, -1, -1, -1, -1, 2, 2, 2, 2, -1, -1, -1, -1, 0, 0, 0, 0], 'schur_index': 1}
  • id: 12109918
    {'cdim': 6, 'counter': 35, 'faithful': False, 'group': '1944.3492', 'group_order': 1944, 'image': None, 'label': '1944.3492.6g', 'multiplicity': 2, 'nt': [72, 0], 'qdim': 12, 'qvalues': [12, 0, -4, 0, -6, -6, -6, 12, -6, -6, 3, 3, -6, -6, 3, 3, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, -4, 0, 0, 0, 0, 2, 2, 2, -4, 2, 2, -1, -1, 2, 2, -1, -1, -1, -1, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, -4, -4, 2, 2, 2, 2, -1, -1, -1, -1, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, -1, -1, 0, 0, 0, 0], 'schur_index': 1}
  • id: 12109919
    {'cdim': 6, 'counter': 36, 'faithful': False, 'group': '1944.3492', 'group_order': 1944, 'image': None, 'label': '1944.3492.6h', 'multiplicity': 2, 'nt': [72, 0], 'qdim': 12, 'qvalues': [12, 0, -4, 0, -6, -6, 12, -6, -6, -6, -6, -6, 3, 3, 3, 3, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, -4, 0, 0, 0, 0, 2, 2, -4, 2, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, 0, 0, 0, 0, 2, 2, 2, 2, -4, -4, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 0, 0, 0, 0], 'schur_index': 1}
  • id: 12109920
    {'cdim': 6, 'counter': 37, 'faithful': False, 'group': '1944.3492', 'group_order': 1944, 'image': None, 'label': '1944.3492.6i', 'multiplicity': 4, 'nt': [36, 1197], 'qdim': 24, 'qvalues': [24, 0, 8, 0, -12, -12, -12, -12, -12, 24, 6, 6, 6, 6, 6, 6, -12, -12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, -4, -4, -4, -4, 8, 2, 2, 2, 2, 2, 2, -4, -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], 'schur_index': 1}
  • id: 12109921
    {'cdim': 6, 'counter': 38, 'faithful': False, 'group': '1944.3492', 'group_order': 1944, 'image': None, 'label': '1944.3492.6j', 'multiplicity': 4, 'nt': [36, 1197], 'qdim': 24, 'qvalues': [24, 0, 8, 0, -12, -12, -12, -12, 24, -12, 6, 6, 6, 6, -12, -12, 6, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, -4, -4, -4, 8, -4, 2, 2, 2, 2, -4, -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], 'schur_index': 1}
  • id: 12109922
    {'cdim': 6, 'counter': 39, 'faithful': False, 'group': '1944.3492', 'group_order': 1944, 'image': None, 'label': '1944.3492.6k', 'multiplicity': 4, 'nt': [36, 1197], 'qdim': 24, 'qvalues': [24, 0, 8, 0, -12, -12, -12, 24, -12, -12, 6, 6, -12, -12, 6, 6, 6, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, -4, -4, 8, -4, -4, 2, 2, -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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 12109924
    {'cdim': 6, 'counter': 40, 'faithful': False, 'group': '1944.3492', 'group_order': 1944, 'image': None, 'label': '1944.3492.6l', 'multiplicity': 4, 'nt': [36, 1197], 'qdim': 24, 'qvalues': [24, 0, 8, 0, -12, -12, 24, -12, -12, -12, -12, -12, 6, 6, 6, 6, 6, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, -4, 8, -4, -4, -4, -4, -4, 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, 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: 27676676
    {'center': '1.a1', 'center_index': 1, 'center_order': 1944, 'counter': 1, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '1944.3492', 'group_counter': 3492, 'group_order': 1944, 'image': None, 'image_isoclass': '1.1', 'image_order': 1, 'indicator': 1, 'kernel': '1.a1', 'kernel_order': 1944, 'label': '1944.3492.1a', '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]]]}
  • id: 27676687
    {'center': '1.a1', 'center_index': 1, 'center_order': 1944, 'counter': 2, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '1944.3492', 'group_counter': 3492, 'group_order': 1944, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.c1', 'kernel_order': 972, 'label': '1944.3492.1b', '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]]]}
  • id: 27676698
    {'center': '1.a1', 'center_index': 1, 'center_order': 1944, 'counter': 3, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '1944.3492', 'group_counter': 3492, 'group_order': 1944, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.b1', 'kernel_order': 972, 'label': '1944.3492.1c', '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]]]}
  • id: 27676709
    {'center': '1.a1', 'center_index': 1, 'center_order': 1944, 'counter': 4, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '1944.3492', 'group_counter': 3492, 'group_order': 1944, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.a1', 'kernel_order': 972, 'label': '1944.3492.1d', '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]]]}
  • id: 27676720
    {'center': '1.a1', 'center_index': 1, 'center_order': 1944, 'counter': 5, 'cyclotomic_n': 4, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '1944.3492', 'group_counter': 3492, 'group_order': 1944, 'image': None, 'image_isoclass': '4.1', 'image_order': 4, 'indicator': 0, 'kernel': '4.c1', 'kernel_order': 486, 'label': '1944.3492.1e1', 'nt': [4, 1], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]]]}
  • id: 27676731
    {'center': '1.a1', 'center_index': 1, 'center_order': 1944, 'counter': 6, 'cyclotomic_n': 4, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '1944.3492', 'group_counter': 3492, 'group_order': 1944, 'image': None, 'image_isoclass': '4.1', 'image_order': 4, 'indicator': 0, 'kernel': '4.c1', 'kernel_order': 486, 'label': '1944.3492.1e2', 'nt': [4, 2], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]]]}
  • id: 27676742
    {'center': '1.a1', 'center_index': 1, 'center_order': 1944, 'counter': 7, 'cyclotomic_n': 4, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '1944.3492', 'group_counter': 3492, 'group_order': 1944, 'image': None, 'image_isoclass': '4.1', 'image_order': 4, 'indicator': 0, 'kernel': '4.a1', 'kernel_order': 486, 'label': '1944.3492.1f1', 'nt': [4, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]]]}
  • id: 27676753
    {'center': '1.a1', 'center_index': 1, 'center_order': 1944, 'counter': 8, 'cyclotomic_n': 4, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '1944.3492', 'group_counter': 3492, 'group_order': 1944, 'image': None, 'image_isoclass': '4.1', 'image_order': 4, 'indicator': 0, 'kernel': '4.a1', 'kernel_order': 486, 'label': '1944.3492.1f2', 'nt': [4, 2], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]]]}
  • id: 27676759
    {'center': '6.a1', 'center_index': 6, 'center_order': 324, 'counter': 9, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '1944.3492', 'group_counter': 3492, 'group_order': 1944, 'image': None, 'image_isoclass': '6.1', 'image_order': 6, 'indicator': 1, 'kernel': '6.a1', 'kernel_order': 324, 'label': '1944.3492.2a', 'nt': [3, 2], 'q_character': None, 'values': [[[2, 0]], [[0, 0]], [[2, 0]], [[0, 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]], [[2, 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]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 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]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 27676677
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  • id: 27676678
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  • id: 27676679
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  • id: 27676680
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  • id: 27676681
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  • id: 27676682
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  • id: 27676683
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  • id: 27676684
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  • id: 27676685
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  • id: 27676686
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  • id: 27676688
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  • id: 27676689
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  • id: 27676690
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  • id: 27676691
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  • id: 27676692
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  • id: 27676693
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  • id: 27676694
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  • id: 27676695
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  • id: 27676696
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  • id: 27676697
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  • id: 27676699
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  • id: 27676700
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  • id: 27676701
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  • id: 27676702
    {'center': '36.a1', 'center_index': 36, 'center_order': 54, 'counter': 33, 'cyclotomic_n': 12, 'dim': 3, 'faithful': False, 'field': [1, 0, 1], 'group': '1944.3492', 'group_counter': 3492, 'group_order': 1944, 'image': None, 'image_isoclass': '108.15', 'image_order': 108, 'indicator': 0, 'kernel': '108.a1', 'kernel_order': 18, 'label': '1944.3492.3e1', 'nt': [18, 49], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[1, 0]], [[1, 0]], [[-3, 2]], [[3, 4]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 4]], [[-3, 2]], [[3, 4]], [[-3, 2]], [[3, 4]], [[-3, 2]], [[3, 4]], [[-3, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 3]], [[1, 3]], [[-1, 3]], [[1, 3]], [[3, 4]], [[-3, 2]], [[-1, 2]], [[1, 4]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 2]], [[1, 4]], [[-1, 2]], [[1, 4]], [[-1, 2]], [[1, 4]], [[-1, 2]], [[1, 4]], [[-1, 2]], [[1, 4]], [[0, 0]], [[0, 0]], [[-1, 1]], [[1, 5]], [[-1, 5]], [[1, 1]], [[-1, 3]], [[1, 3]], [[-1, 3]], [[1, 3]], [[-1, 3]], [[1, 3]], [[1, 3]], [[-1, 3]], [[1, 1]], [[-1, 5]], [[1, 5]], [[-1, 1]], [[1, 1]], [[-1, 5]], [[1, 5]], [[-1, 1]], [[1, 1]], [[-1, 5]], [[1, 5]], [[-1, 1]], [[-1, 1]], [[1, 5]], [[-1, 5]], [[1, 1]], [[-1, 5]], [[1, 1]], [[-1, 1]], [[1, 5]]]}
  • id: 27676703
    {'center': '36.a1', 'center_index': 36, 'center_order': 54, 'counter': 34, 'cyclotomic_n': 12, 'dim': 3, 'faithful': False, 'field': [1, 0, 1], 'group': '1944.3492', 'group_counter': 3492, 'group_order': 1944, 'image': None, 'image_isoclass': '108.15', 'image_order': 108, 'indicator': 0, 'kernel': '108.a1', 'kernel_order': 18, 'label': '1944.3492.3e2', 'nt': [18, 4], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[1, 0]], [[1, 0]], [[3, 4]], [[-3, 2]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[-3, 2]], [[3, 4]], [[-3, 2]], [[3, 4]], [[-3, 2]], [[3, 4]], [[-3, 2]], [[3, 4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 3]], [[-1, 3]], [[1, 3]], [[-1, 3]], [[-3, 2]], [[3, 4]], [[1, 4]], [[-1, 2]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 4]], [[-1, 2]], [[1, 4]], [[-1, 2]], [[1, 4]], [[-1, 2]], [[1, 4]], [[-1, 2]], [[1, 4]], [[-1, 2]], [[0, 0]], [[0, 0]], [[1, 5]], [[-1, 1]], [[1, 1]], [[-1, 5]], [[1, 3]], [[-1, 3]], [[1, 3]], [[-1, 3]], [[1, 3]], [[-1, 3]], [[-1, 3]], [[1, 3]], [[-1, 5]], [[1, 1]], [[-1, 1]], [[1, 5]], [[-1, 5]], [[1, 1]], [[-1, 1]], [[1, 5]], [[-1, 5]], [[1, 1]], [[-1, 1]], [[1, 5]], [[1, 5]], [[-1, 1]], [[1, 1]], [[-1, 5]], [[1, 1]], [[-1, 5]], [[1, 5]], [[-1, 1]]]}
  • id: 27676704
    {'center': '36.a1', 'center_index': 36, 'center_order': 54, 'counter': 35, 'cyclotomic_n': 12, 'dim': 3, 'faithful': False, 'field': [1, 0, 1], 'group': '1944.3492', 'group_counter': 3492, 'group_order': 1944, 'image': None, 'image_isoclass': '108.15', 'image_order': 108, 'indicator': 0, 'kernel': '108.a1', 'kernel_order': 18, 'label': '1944.3492.3e3', 'nt': [18, 49], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[1, 0]], [[1, 0]], [[-3, 2]], [[3, 4]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 4]], [[-3, 2]], [[3, 4]], [[-3, 2]], [[3, 4]], [[-3, 2]], [[3, 4]], [[-3, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 3]], [[-1, 3]], [[1, 3]], [[-1, 3]], [[3, 4]], [[-3, 2]], [[-1, 2]], [[1, 4]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 2]], [[1, 4]], [[-1, 2]], [[1, 4]], [[-1, 2]], [[1, 4]], [[-1, 2]], [[1, 4]], [[-1, 2]], [[1, 4]], [[0, 0]], [[0, 0]], [[1, 1]], [[-1, 5]], [[1, 5]], [[-1, 1]], [[1, 3]], [[-1, 3]], [[1, 3]], [[-1, 3]], [[1, 3]], [[-1, 3]], [[-1, 3]], [[1, 3]], [[-1, 1]], [[1, 5]], [[-1, 5]], [[1, 1]], [[-1, 1]], [[1, 5]], [[-1, 5]], [[1, 1]], [[-1, 1]], [[1, 5]], [[-1, 5]], [[1, 1]], [[1, 1]], [[-1, 5]], [[1, 5]], [[-1, 1]], [[1, 5]], [[-1, 1]], [[1, 1]], [[-1, 5]]]}
  • id: 27676705
    {'center': '36.a1', 'center_index': 36, 'center_order': 54, 'counter': 36, 'cyclotomic_n': 12, 'dim': 3, 'faithful': False, 'field': [1, 0, 1], 'group': '1944.3492', 'group_counter': 3492, 'group_order': 1944, 'image': None, 'image_isoclass': '108.15', 'image_order': 108, 'indicator': 0, 'kernel': '108.a1', 'kernel_order': 18, 'label': '1944.3492.3e4', 'nt': [18, 4], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[1, 0]], [[1, 0]], [[3, 4]], [[-3, 2]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[-3, 2]], [[3, 4]], [[-3, 2]], [[3, 4]], [[-3, 2]], [[3, 4]], [[-3, 2]], [[3, 4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 3]], [[1, 3]], [[-1, 3]], [[1, 3]], [[-3, 2]], [[3, 4]], [[1, 4]], [[-1, 2]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 4]], [[-1, 2]], [[1, 4]], [[-1, 2]], [[1, 4]], [[-1, 2]], [[1, 4]], [[-1, 2]], [[1, 4]], [[-1, 2]], [[0, 0]], [[0, 0]], [[-1, 5]], [[1, 1]], [[-1, 1]], [[1, 5]], [[-1, 3]], [[1, 3]], [[-1, 3]], [[1, 3]], [[-1, 3]], [[1, 3]], [[1, 3]], [[-1, 3]], [[1, 5]], [[-1, 1]], [[1, 1]], [[-1, 5]], [[1, 5]], [[-1, 1]], [[1, 1]], [[-1, 5]], [[1, 5]], [[-1, 1]], [[1, 1]], [[-1, 5]], [[-1, 5]], [[1, 1]], [[-1, 1]], [[1, 5]], [[-1, 1]], [[1, 5]], [[-1, 5]], [[1, 1]]]}
  • id: 27676706
    {'center': '36.a1', 'center_index': 36, 'center_order': 54, 'counter': 37, 'cyclotomic_n': 12, 'dim': 3, 'faithful': False, 'field': [1, 0, 1], 'group': '1944.3492', 'group_counter': 3492, 'group_order': 1944, 'image': None, 'image_isoclass': '216.100', 'image_order': 216, 'indicator': 0, 'kernel': '216.b1', 'kernel_order': 9, 'label': '1944.3492.3f1', 'nt': [36, 225], 'q_character': None, 'values': [[[3, 0]], [[-3, 0]], [[1, 0]], [[-1, 0]], [[-3, 2]], [[3, 4]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 4]], [[-3, 2]], [[3, 4]], [[-3, 2]], [[3, 4]], [[-3, 2]], [[3, 4]], [[-3, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 3]], [[1, 3]], [[1, 3]], [[-1, 3]], [[-3, 4]], [[3, 2]], [[-1, 2]], [[1, 4]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 2]], [[1, 4]], [[-1, 2]], [[1, 4]], [[-1, 2]], [[1, 4]], [[-1, 2]], [[1, 4]], [[1, 2]], [[-1, 4]], [[0, 0]], [[0, 0]], [[-1, 1]], [[1, 5]], [[-1, 5]], [[1, 1]], [[-1, 3]], [[1, 3]], [[-1, 3]], [[1, 3]], [[-1, 3]], [[1, 3]], [[1, 3]], [[-1, 3]], [[1, 1]], [[-1, 5]], [[1, 5]], [[-1, 1]], [[1, 1]], [[-1, 5]], [[1, 5]], [[-1, 1]], [[1, 1]], [[-1, 5]], [[1, 5]], [[-1, 1]], [[-1, 1]], [[1, 5]], [[-1, 5]], [[1, 1]], [[1, 5]], [[-1, 1]], [[1, 1]], [[-1, 5]]]}
  • id: 27676707
    {'center': '36.a1', 'center_index': 36, 'center_order': 54, 'counter': 38, 'cyclotomic_n': 12, 'dim': 3, 'faithful': False, 'field': [1, 0, 1], 'group': '1944.3492', 'group_counter': 3492, 'group_order': 1944, 'image': None, 'image_isoclass': '216.100', 'image_order': 216, 'indicator': 0, 'kernel': '216.b1', 'kernel_order': 9, 'label': '1944.3492.3f2', 'nt': [36, 4], 'q_character': None, 'values': [[[3, 0]], [[-3, 0]], [[1, 0]], [[-1, 0]], [[3, 4]], [[-3, 2]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[-3, 2]], [[3, 4]], [[-3, 2]], [[3, 4]], [[-3, 2]], [[3, 4]], [[-3, 2]], [[3, 4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 3]], [[-1, 3]], [[-1, 3]], [[1, 3]], [[3, 2]], [[-3, 4]], [[1, 4]], [[-1, 2]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 4]], [[-1, 2]], [[1, 4]], [[-1, 2]], [[1, 4]], [[-1, 2]], [[1, 4]], [[-1, 2]], [[-1, 4]], [[1, 2]], [[0, 0]], [[0, 0]], [[1, 5]], [[-1, 1]], [[1, 1]], [[-1, 5]], [[1, 3]], [[-1, 3]], [[1, 3]], [[-1, 3]], [[1, 3]], [[-1, 3]], [[-1, 3]], [[1, 3]], [[-1, 5]], [[1, 1]], [[-1, 1]], [[1, 5]], [[-1, 5]], [[1, 1]], [[-1, 1]], [[1, 5]], [[-1, 5]], [[1, 1]], [[-1, 1]], [[1, 5]], [[1, 5]], [[-1, 1]], [[1, 1]], [[-1, 5]], [[-1, 1]], [[1, 5]], [[-1, 5]], [[1, 1]]]}
  • id: 27676708
    {'center': '36.a1', 'center_index': 36, 'center_order': 54, 'counter': 39, 'cyclotomic_n': 12, 'dim': 3, 'faithful': False, 'field': [1, 0, 1], 'group': '1944.3492', 'group_counter': 3492, 'group_order': 1944, 'image': None, 'image_isoclass': '216.100', 'image_order': 216, 'indicator': 0, 'kernel': '216.b1', 'kernel_order': 9, 'label': '1944.3492.3f3', 'nt': [36, 225], 'q_character': None, 'values': [[[3, 0]], [[-3, 0]], [[1, 0]], [[-1, 0]], [[-3, 2]], [[3, 4]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 4]], [[-3, 2]], [[3, 4]], [[-3, 2]], [[3, 4]], [[-3, 2]], [[3, 4]], [[-3, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 3]], [[-1, 3]], [[-1, 3]], [[1, 3]], [[-3, 4]], [[3, 2]], [[-1, 2]], [[1, 4]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 2]], [[1, 4]], [[-1, 2]], [[1, 4]], [[-1, 2]], [[1, 4]], [[-1, 2]], [[1, 4]], [[1, 2]], [[-1, 4]], [[0, 0]], [[0, 0]], [[1, 1]], [[-1, 5]], [[1, 5]], [[-1, 1]], [[1, 3]], [[-1, 3]], [[1, 3]], [[-1, 3]], [[1, 3]], [[-1, 3]], [[-1, 3]], [[1, 3]], [[-1, 1]], [[1, 5]], [[-1, 5]], [[1, 1]], [[-1, 1]], [[1, 5]], [[-1, 5]], [[1, 1]], [[-1, 1]], [[1, 5]], [[-1, 5]], [[1, 1]], [[1, 1]], [[-1, 5]], [[1, 5]], [[-1, 1]], [[-1, 5]], [[1, 1]], [[-1, 1]], [[1, 5]]]}
  • id: 27676710
    {'center': '36.a1', 'center_index': 36, 'center_order': 54, 'counter': 40, 'cyclotomic_n': 12, 'dim': 3, 'faithful': False, 'field': [1, 0, 1], 'group': '1944.3492', 'group_counter': 3492, 'group_order': 1944, 'image': None, 'image_isoclass': '216.100', 'image_order': 216, 'indicator': 0, 'kernel': '216.b1', 'kernel_order': 9, 'label': '1944.3492.3f4', 'nt': [36, 4], 'q_character': None, 'values': [[[3, 0]], [[-3, 0]], [[1, 0]], [[-1, 0]], [[3, 4]], [[-3, 2]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[-3, 2]], [[3, 4]], [[-3, 2]], [[3, 4]], [[-3, 2]], [[3, 4]], [[-3, 2]], [[3, 4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 3]], [[1, 3]], [[1, 3]], [[-1, 3]], [[3, 2]], [[-3, 4]], [[1, 4]], [[-1, 2]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 4]], [[-1, 2]], [[1, 4]], [[-1, 2]], [[1, 4]], [[-1, 2]], [[1, 4]], [[-1, 2]], [[-1, 4]], [[1, 2]], [[0, 0]], [[0, 0]], [[-1, 5]], [[1, 1]], [[-1, 1]], [[1, 5]], [[-1, 3]], [[1, 3]], [[-1, 3]], [[1, 3]], [[-1, 3]], [[1, 3]], [[1, 3]], [[-1, 3]], [[1, 5]], [[-1, 1]], [[1, 1]], [[-1, 5]], [[1, 5]], [[-1, 1]], [[1, 1]], [[-1, 5]], [[1, 5]], [[-1, 1]], [[1, 1]], [[-1, 5]], [[-1, 5]], [[1, 1]], [[-1, 1]], [[1, 5]], [[1, 1]], [[-1, 5]], [[1, 5]], [[-1, 1]]]}
  • id: 27676711
    {'center': '36.a1', 'center_index': 36, 'center_order': 54, 'counter': 41, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '1944.3492', 'group_counter': 3492, 'group_order': 1944, 'image': None, 'image_isoclass': '36.9', 'image_order': 36, 'indicator': 1, 'kernel': '36.a1', 'kernel_order': 54, 'label': '1944.3492.4a', 'nt': [6, 10], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[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]], [[-2, 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]]]}
  • id: 27676712
    {'center': '36.a1', 'center_index': 36, 'center_order': 54, 'counter': 42, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '1944.3492', 'group_counter': 3492, 'group_order': 1944, 'image': None, 'image_isoclass': '36.9', 'image_order': 36, 'indicator': 1, 'kernel': '36.a1', 'kernel_order': 54, 'label': '1944.3492.4b', 'nt': [6, 10], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[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]], [[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]]]}
  • id: 27676713
    {'center': '36.a1', 'center_index': 36, 'center_order': 54, 'counter': 43, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '1944.3492', 'group_counter': 3492, 'group_order': 1944, 'image': None, 'image_isoclass': '72.45', 'image_order': 72, 'indicator': 1, 'kernel': '72.a1', 'kernel_order': 27, 'label': '1944.3492.4c', 'nt': [12, 40], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[-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]], [[2, 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]]]}
  • id: 27676714
    {'center': '36.a1', 'center_index': 36, 'center_order': 54, 'counter': 44, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '1944.3492', 'group_counter': 3492, 'group_order': 1944, 'image': None, 'image_isoclass': '72.45', 'image_order': 72, 'indicator': 1, 'kernel': '72.a1', 'kernel_order': 27, 'label': '1944.3492.4d', 'nt': [12, 40], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[-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]], [[-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]]]}
  • id: 27676715
    {'center': '216.a1', 'center_index': 216, 'center_order': 9, 'counter': 45, 'cyclotomic_n': 3, 'dim': 6, 'faithful': False, 'field': [1, -1, 1], 'group': '1944.3492', 'group_counter': 3492, 'group_order': 1944, 'image': None, 'image_isoclass': '648.541', 'image_order': 648, 'indicator': 0, 'kernel': '648.b1', 'kernel_order': 3, 'label': '1944.3492.6a1', 'nt': [54, 0], 'q_character': None, 'values': [[[6, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[6, -1]], [[6, 1]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[6, 0]], [[-3, 1]], [[-3, -1]], [[-3, 1]], [[-3, -1]], [[-3, 1]], [[-3, -1]], [[6, 1]], [[6, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, -1]], [[-2, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[-2, -1]], [[-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1]], [[2, -1]], [[2, -1]], [[2, 1]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 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]], [[2, 1]], [[2, -1]], [[2, -1]], [[2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 27676716
    {'center': '216.a1', 'center_index': 216, 'center_order': 9, 'counter': 46, 'cyclotomic_n': 3, 'dim': 6, 'faithful': False, 'field': [1, -1, 1], 'group': '1944.3492', 'group_counter': 3492, 'group_order': 1944, 'image': None, 'image_isoclass': '648.541', 'image_order': 648, 'indicator': 0, 'kernel': '648.b1', 'kernel_order': 3, 'label': '1944.3492.6a2', 'nt': [54, 2], 'q_character': None, 'values': [[[6, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[6, 1]], [[6, -1]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[6, 0]], [[-3, -1]], [[-3, 1]], [[-3, -1]], [[-3, 1]], [[-3, -1]], [[-3, 1]], [[6, -1]], [[6, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1]], [[-2, -1]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[-2, 1]], [[-2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, -1]], [[2, 1]], [[2, 1]], [[2, -1]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 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]], [[2, -1]], [[2, 1]], [[2, 1]], [[2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 27676717
    {'center': '216.a1', 'center_index': 216, 'center_order': 9, 'counter': 47, 'cyclotomic_n': 3, 'dim': 6, 'faithful': False, 'field': [1, -1, 1], 'group': '1944.3492', 'group_counter': 3492, 'group_order': 1944, 'image': None, 'image_isoclass': '648.541', 'image_order': 648, 'indicator': 0, 'kernel': '648.b1', 'kernel_order': 3, 'label': '1944.3492.6b1', 'nt': [54, 0], 'q_character': None, 'values': [[[6, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[6, -1]], [[6, 1]], [[-3, 0]], [[-3, 0]], [[6, 0]], [[-3, 0]], [[-3, 1]], [[-3, -1]], [[-3, 1]], [[-3, -1]], [[6, 1]], [[6, -1]], [[-3, 1]], [[-3, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, -1]], [[-2, 1]], [[1, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[-2, -1]], [[-2, 1]], [[1, -1]], [[1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1]], [[2, -1]], [[2, -1]], [[2, 1]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[2, 1]], [[2, -1]], [[2, -1]], [[2, 1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 27676718
    {'center': '216.a1', 'center_index': 216, 'center_order': 9, 'counter': 48, 'cyclotomic_n': 3, 'dim': 6, 'faithful': False, 'field': [1, -1, 1], 'group': '1944.3492', 'group_counter': 3492, 'group_order': 1944, 'image': None, 'image_isoclass': '648.541', 'image_order': 648, 'indicator': 0, 'kernel': '648.b1', 'kernel_order': 3, 'label': '1944.3492.6b2', 'nt': [54, 2], 'q_character': None, 'values': [[[6, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[6, 1]], [[6, -1]], [[-3, 0]], [[-3, 0]], [[6, 0]], [[-3, 0]], [[-3, -1]], [[-3, 1]], [[-3, -1]], [[-3, 1]], [[6, -1]], [[6, 1]], [[-3, -1]], [[-3, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1]], [[-2, -1]], [[1, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[-2, 1]], [[-2, -1]], [[1, 1]], [[1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, -1]], [[2, 1]], [[2, 1]], [[2, -1]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[2, -1]], [[2, 1]], [[2, 1]], [[2, -1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 27676719
    {'center': '216.a1', 'center_index': 216, 'center_order': 9, 'counter': 49, 'cyclotomic_n': 3, 'dim': 6, 'faithful': False, 'field': [1, -1, 1], 'group': '1944.3492', 'group_counter': 3492, 'group_order': 1944, 'image': None, 'image_isoclass': '648.541', 'image_order': 648, 'indicator': 0, 'kernel': '648.b1', 'kernel_order': 3, 'label': '1944.3492.6c1', 'nt': [54, 0], 'q_character': None, 'values': [[[6, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[6, -1]], [[6, 1]], [[-3, 0]], [[6, 0]], [[-3, 0]], [[-3, 0]], [[-3, 1]], [[-3, -1]], [[6, 1]], [[6, -1]], [[-3, 1]], [[-3, -1]], [[-3, 1]], [[-3, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, -1]], [[-2, 1]], [[1, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[-2, -1]], [[-2, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1]], [[2, -1]], [[2, -1]], [[2, 1]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[2, 1]], [[2, -1]], [[2, -1]], [[2, 1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 27676721
    {'center': '216.a1', 'center_index': 216, 'center_order': 9, 'counter': 50, 'cyclotomic_n': 3, 'dim': 6, 'faithful': False, 'field': [1, -1, 1], 'group': '1944.3492', 'group_counter': 3492, 'group_order': 1944, 'image': None, 'image_isoclass': '648.541', 'image_order': 648, 'indicator': 0, 'kernel': '648.b1', 'kernel_order': 3, 'label': '1944.3492.6c2', 'nt': [54, 2], 'q_character': None, 'values': [[[6, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[6, 1]], [[6, -1]], [[-3, 0]], [[6, 0]], [[-3, 0]], [[-3, 0]], [[-3, -1]], [[-3, 1]], [[6, -1]], [[6, 1]], [[-3, -1]], [[-3, 1]], [[-3, -1]], [[-3, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1]], [[-2, -1]], [[1, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[-2, 1]], [[-2, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, -1]], [[2, 1]], [[2, 1]], [[2, -1]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[2, -1]], [[2, 1]], [[2, 1]], [[2, -1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 27676722
    {'center': '216.a1', 'center_index': 216, 'center_order': 9, 'counter': 51, 'cyclotomic_n': 3, 'dim': 6, 'faithful': False, 'field': [1, -1, 1], 'group': '1944.3492', 'group_counter': 3492, 'group_order': 1944, 'image': None, 'image_isoclass': '648.541', 'image_order': 648, 'indicator': 0, 'kernel': '648.b1', 'kernel_order': 3, 'label': '1944.3492.6d1', 'nt': [54, 0], 'q_character': None, 'values': [[[6, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[6, -1]], [[6, 1]], [[6, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[6, 1]], [[6, -1]], [[-3, 1]], [[-3, -1]], [[-3, 1]], [[-3, -1]], [[-3, 1]], [[-3, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, -1]], [[-2, 1]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, -1]], [[-2, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1]], [[2, -1]], [[2, -1]], [[2, 1]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 1]], [[2, -1]], [[2, -1]], [[2, 1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 27676723
    {'center': '216.a1', 'center_index': 216, 'center_order': 9, 'counter': 52, 'cyclotomic_n': 3, 'dim': 6, 'faithful': False, 'field': [1, -1, 1], 'group': '1944.3492', 'group_counter': 3492, 'group_order': 1944, 'image': None, 'image_isoclass': '648.541', 'image_order': 648, 'indicator': 0, 'kernel': '648.b1', 'kernel_order': 3, 'label': '1944.3492.6d2', 'nt': [54, 2], 'q_character': None, 'values': [[[6, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[6, 1]], [[6, -1]], [[6, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[6, -1]], [[6, 1]], [[-3, -1]], [[-3, 1]], [[-3, -1]], [[-3, 1]], [[-3, -1]], [[-3, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1]], [[-2, -1]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 1]], [[-2, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, -1]], [[2, 1]], [[2, 1]], [[2, -1]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, -1]], [[2, 1]], [[2, 1]], [[2, -1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, 1]], [[-1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 27676724
    {'center': '216.a1', 'center_index': 216, 'center_order': 9, 'counter': 53, 'cyclotomic_n': 3, 'dim': 6, 'faithful': False, 'field': [1, -1, 1], 'group': '1944.3492', 'group_counter': 3492, 'group_order': 1944, 'image': None, 'image_isoclass': '648.541', 'image_order': 648, 'indicator': 0, 'kernel': '648.b1', 'kernel_order': 3, 'label': '1944.3492.6e1', 'nt': [72, 0], 'q_character': None, 'values': [[[6, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[6, -1]], [[6, 1]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[6, 0]], [[-3, 1]], [[-3, -1]], [[-3, 1]], [[-3, -1]], [[-3, 1]], [[-3, -1]], [[6, 1]], [[6, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, -1]], [[-2, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[-2, -1]], [[-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1]], [[-2, -1]], [[-2, -1]], [[-2, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[-2, 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]], [[-2, 1]], [[-2, -1]], [[-2, -1]], [[-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 27676725
    {'center': '216.a1', 'center_index': 216, 'center_order': 9, 'counter': 54, 'cyclotomic_n': 3, 'dim': 6, 'faithful': False, 'field': [1, -1, 1], 'group': '1944.3492', 'group_counter': 3492, 'group_order': 1944, 'image': None, 'image_isoclass': '648.541', 'image_order': 648, 'indicator': 0, 'kernel': '648.b1', 'kernel_order': 3, 'label': '1944.3492.6e2', 'nt': [72, 2], 'q_character': None, 'values': [[[6, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[6, 1]], [[6, -1]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[6, 0]], [[-3, -1]], [[-3, 1]], [[-3, -1]], [[-3, 1]], [[-3, -1]], [[-3, 1]], [[6, -1]], [[6, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1]], [[-2, -1]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[-2, 1]], [[-2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, -1]], [[-2, 1]], [[-2, 1]], [[-2, -1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[-2, 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]], [[-2, -1]], [[-2, 1]], [[-2, 1]], [[-2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 27676726
    {'center': '216.a1', 'center_index': 216, 'center_order': 9, 'counter': 55, 'cyclotomic_n': 3, 'dim': 6, 'faithful': False, 'field': [1, -1, 1], 'group': '1944.3492', 'group_counter': 3492, 'group_order': 1944, 'image': None, 'image_isoclass': '648.541', 'image_order': 648, 'indicator': 0, 'kernel': '648.b1', 'kernel_order': 3, 'label': '1944.3492.6f1', 'nt': [72, 0], 'q_character': None, 'values': [[[6, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[6, -1]], [[6, 1]], [[-3, 0]], [[-3, 0]], [[6, 0]], [[-3, 0]], [[-3, 1]], [[-3, -1]], [[-3, 1]], [[-3, -1]], [[6, 1]], [[6, -1]], [[-3, 1]], [[-3, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, -1]], [[-2, 1]], [[1, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[-2, -1]], [[-2, 1]], [[1, -1]], [[1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1]], [[-2, -1]], [[-2, -1]], [[-2, 1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[-2, 1]], [[-2, -1]], [[-2, -1]], [[-2, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 27676727
    {'center': '216.a1', 'center_index': 216, 'center_order': 9, 'counter': 56, 'cyclotomic_n': 3, 'dim': 6, 'faithful': False, 'field': [1, -1, 1], 'group': '1944.3492', 'group_counter': 3492, 'group_order': 1944, 'image': None, 'image_isoclass': '648.541', 'image_order': 648, 'indicator': 0, 'kernel': '648.b1', 'kernel_order': 3, 'label': '1944.3492.6f2', 'nt': [72, 2], 'q_character': None, 'values': [[[6, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[6, 1]], [[6, -1]], [[-3, 0]], [[-3, 0]], [[6, 0]], [[-3, 0]], [[-3, -1]], [[-3, 1]], [[-3, -1]], [[-3, 1]], [[6, -1]], [[6, 1]], [[-3, -1]], [[-3, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1]], [[-2, -1]], [[1, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[-2, 1]], [[-2, -1]], [[1, 1]], [[1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, -1]], [[-2, 1]], [[-2, 1]], [[-2, -1]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[-2, -1]], [[-2, 1]], [[-2, 1]], [[-2, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 27676728
    {'center': '216.a1', 'center_index': 216, 'center_order': 9, 'counter': 57, 'cyclotomic_n': 3, 'dim': 6, 'faithful': False, 'field': [1, -1, 1], 'group': '1944.3492', 'group_counter': 3492, 'group_order': 1944, 'image': None, 'image_isoclass': '648.541', 'image_order': 648, 'indicator': 0, 'kernel': '648.b1', 'kernel_order': 3, 'label': '1944.3492.6g1', 'nt': [72, 0], 'q_character': None, 'values': [[[6, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[6, -1]], [[6, 1]], [[-3, 0]], [[6, 0]], [[-3, 0]], [[-3, 0]], [[-3, 1]], [[-3, -1]], [[6, 1]], [[6, -1]], [[-3, 1]], [[-3, -1]], [[-3, 1]], [[-3, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, -1]], [[-2, 1]], [[1, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[-2, -1]], [[-2, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1]], [[-2, -1]], [[-2, -1]], [[-2, 1]], [[1, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[-2, 1]], [[-2, -1]], [[-2, -1]], [[-2, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 27676729
    {'center': '216.a1', 'center_index': 216, 'center_order': 9, 'counter': 58, 'cyclotomic_n': 3, 'dim': 6, 'faithful': False, 'field': [1, -1, 1], 'group': '1944.3492', 'group_counter': 3492, 'group_order': 1944, 'image': None, 'image_isoclass': '648.541', 'image_order': 648, 'indicator': 0, 'kernel': '648.b1', 'kernel_order': 3, 'label': '1944.3492.6g2', 'nt': [72, 2], 'q_character': None, 'values': [[[6, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[6, 1]], [[6, -1]], [[-3, 0]], [[6, 0]], [[-3, 0]], [[-3, 0]], [[-3, -1]], [[-3, 1]], [[6, -1]], [[6, 1]], [[-3, -1]], [[-3, 1]], [[-3, -1]], [[-3, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1]], [[-2, -1]], [[1, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -1]], [[-2, 1]], [[-2, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, -1]], [[-2, 1]], [[-2, 1]], [[-2, -1]], [[1, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[-2, -1]], [[-2, 1]], [[-2, 1]], [[-2, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 27676730
    {'center': '216.a1', 'center_index': 216, 'center_order': 9, 'counter': 59, 'cyclotomic_n': 3, 'dim': 6, 'faithful': False, 'field': [1, -1, 1], 'group': '1944.3492', 'group_counter': 3492, 'group_order': 1944, 'image': None, 'image_isoclass': '648.541', 'image_order': 648, 'indicator': 0, 'kernel': '648.b1', 'kernel_order': 3, 'label': '1944.3492.6h1', 'nt': [72, 0], 'q_character': None, 'values': [[[6, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[6, -1]], [[6, 1]], [[6, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[6, 1]], [[6, -1]], [[-3, 1]], [[-3, -1]], [[-3, 1]], [[-3, -1]], [[-3, 1]], [[-3, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, -1]], [[-2, 1]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, -1]], [[-2, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1]], [[-2, -1]], [[-2, -1]], [[-2, 1]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 1]], [[-2, -1]], [[-2, -1]], [[-2, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 27676732
    {'center': '216.a1', 'center_index': 216, 'center_order': 9, 'counter': 60, 'cyclotomic_n': 3, 'dim': 6, 'faithful': False, 'field': [1, -1, 1], 'group': '1944.3492', 'group_counter': 3492, 'group_order': 1944, 'image': None, 'image_isoclass': '648.541', 'image_order': 648, 'indicator': 0, 'kernel': '648.b1', 'kernel_order': 3, 'label': '1944.3492.6h2', 'nt': [72, 2], 'q_character': None, 'values': [[[6, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[6, 1]], [[6, -1]], [[6, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[6, -1]], [[6, 1]], [[-3, -1]], [[-3, 1]], [[-3, -1]], [[-3, 1]], [[-3, -1]], [[-3, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1]], [[-2, -1]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 1]], [[-2, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[1, 1]], [[1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, -1]], [[-2, 1]], [[-2, 1]], [[-2, -1]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, -1]], [[-2, 1]], [[-2, 1]], [[-2, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 1]], [[1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 27676733
    {'center': '216.a1', 'center_index': 216, 'center_order': 9, 'counter': 61, 'cyclotomic_n': 12, 'dim': 6, 'faithful': False, 'field': [1, 0, 1], 'group': '1944.3492', 'group_counter': 3492, 'group_order': 1944, 'image': None, 'image_isoclass': '648.541', 'image_order': 648, 'indicator': 0, 'kernel': '648.b1', 'kernel_order': 3, 'label': '1944.3492.6i1', 'nt': [36, 1197], 'q_character': None, 'values': [[[6, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-6, 2]], [[6, 4]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[6, 0]], [[-3, 4]], [[3, 2]], [[-3, 4]], [[3, 2]], [[-3, 4]], [[3, 2]], [[6, 4]], [[-6, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 3]], [[2, 3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 2]], [[2, 4]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[1, 2]], [[-1, 4]], [[1, 2]], [[-1, 4]], [[1, 2]], [[-1, 4]], [[-2, 2]], [[2, 4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1]], [[2, 5]], [[-2, 5]], [[2, 1]], [[1, 3]], [[-1, 3]], [[1, 3]], [[-1, 3]], [[1, 3]], [[-1, 3]], [[2, 3]], [[-2, 3]], [[-1, 1]], [[1, 5]], [[-1, 5]], [[1, 1]], [[-1, 1]], [[1, 5]], [[-1, 5]], [[1, 1]], [[-1, 1]], [[1, 5]], [[-1, 5]], [[1, 1]], [[-2, 1]], [[2, 5]], [[-2, 5]], [[2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 27676734
    {'center': '216.a1', 'center_index': 216, 'center_order': 9, 'counter': 62, 'cyclotomic_n': 12, 'dim': 6, 'faithful': False, 'field': [1, 0, 1], 'group': '1944.3492', 'group_counter': 3492, 'group_order': 1944, 'image': None, 'image_isoclass': '648.541', 'image_order': 648, 'indicator': 0, 'kernel': '648.b1', 'kernel_order': 3, 'label': '1944.3492.6i2', 'nt': [36, 4], 'q_character': None, 'values': [[[6, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[6, 4]], [[-6, 2]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[6, 0]], [[3, 2]], [[-3, 4]], [[3, 2]], [[-3, 4]], [[3, 2]], [[-3, 4]], [[-6, 2]], [[6, 4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 3]], [[-2, 3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 4]], [[-2, 2]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 4]], [[1, 2]], [[-1, 4]], [[1, 2]], [[-1, 4]], [[1, 2]], [[2, 4]], [[-2, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 5]], [[-2, 1]], [[2, 1]], [[-2, 5]], [[-1, 3]], [[1, 3]], [[-1, 3]], [[1, 3]], [[-1, 3]], [[1, 3]], [[-2, 3]], [[2, 3]], [[1, 5]], [[-1, 1]], [[1, 1]], [[-1, 5]], [[1, 5]], [[-1, 1]], [[1, 1]], [[-1, 5]], [[1, 5]], [[-1, 1]], [[1, 1]], [[-1, 5]], [[2, 5]], [[-2, 1]], [[2, 1]], [[-2, 5]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 27676735
    {'center': '216.a1', 'center_index': 216, 'center_order': 9, 'counter': 63, 'cyclotomic_n': 12, 'dim': 6, 'faithful': False, 'field': [1, 0, 1], 'group': '1944.3492', 'group_counter': 3492, 'group_order': 1944, 'image': None, 'image_isoclass': '648.541', 'image_order': 648, 'indicator': 0, 'kernel': '648.b1', 'kernel_order': 3, 'label': '1944.3492.6i3', 'nt': [36, 1197], 'q_character': None, 'values': [[[6, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-6, 2]], [[6, 4]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[6, 0]], [[-3, 4]], [[3, 2]], [[-3, 4]], [[3, 2]], [[-3, 4]], [[3, 2]], [[6, 4]], [[-6, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 3]], [[-2, 3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 2]], [[2, 4]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[1, 2]], [[-1, 4]], [[1, 2]], [[-1, 4]], [[1, 2]], [[-1, 4]], [[-2, 2]], [[2, 4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1]], [[-2, 5]], [[2, 5]], [[-2, 1]], [[-1, 3]], [[1, 3]], [[-1, 3]], [[1, 3]], [[-1, 3]], [[1, 3]], [[-2, 3]], [[2, 3]], [[1, 1]], [[-1, 5]], [[1, 5]], [[-1, 1]], [[1, 1]], [[-1, 5]], [[1, 5]], [[-1, 1]], [[1, 1]], [[-1, 5]], [[1, 5]], [[-1, 1]], [[2, 1]], [[-2, 5]], [[2, 5]], [[-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 27676736
    {'center': '216.a1', 'center_index': 216, 'center_order': 9, 'counter': 64, 'cyclotomic_n': 12, 'dim': 6, 'faithful': False, 'field': [1, 0, 1], 'group': '1944.3492', 'group_counter': 3492, 'group_order': 1944, 'image': None, 'image_isoclass': '648.541', 'image_order': 648, 'indicator': 0, 'kernel': '648.b1', 'kernel_order': 3, 'label': '1944.3492.6i4', 'nt': [36, 4], 'q_character': None, 'values': [[[6, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[6, 4]], [[-6, 2]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[6, 0]], [[3, 2]], [[-3, 4]], [[3, 2]], [[-3, 4]], [[3, 2]], [[-3, 4]], [[-6, 2]], [[6, 4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 3]], [[2, 3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 4]], [[-2, 2]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 4]], [[1, 2]], [[-1, 4]], [[1, 2]], [[-1, 4]], [[1, 2]], [[2, 4]], [[-2, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 5]], [[2, 1]], [[-2, 1]], [[2, 5]], [[1, 3]], [[-1, 3]], [[1, 3]], [[-1, 3]], [[1, 3]], [[-1, 3]], [[2, 3]], [[-2, 3]], [[-1, 5]], [[1, 1]], [[-1, 1]], [[1, 5]], [[-1, 5]], [[1, 1]], [[-1, 1]], [[1, 5]], [[-1, 5]], [[1, 1]], [[-1, 1]], [[1, 5]], [[-2, 5]], [[2, 1]], [[-2, 1]], [[2, 5]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 27676737
    {'center': '216.a1', 'center_index': 216, 'center_order': 9, 'counter': 65, 'cyclotomic_n': 12, 'dim': 6, 'faithful': False, 'field': [1, 0, 1], 'group': '1944.3492', 'group_counter': 3492, 'group_order': 1944, 'image': None, 'image_isoclass': '648.541', 'image_order': 648, 'indicator': 0, 'kernel': '648.b1', 'kernel_order': 3, 'label': '1944.3492.6j1', 'nt': [36, 1197], 'q_character': None, 'values': [[[6, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-6, 2]], [[6, 4]], [[-3, 0]], [[-3, 0]], [[6, 0]], [[-3, 0]], [[-3, 4]], [[3, 2]], [[-3, 4]], [[3, 2]], [[6, 4]], [[-6, 2]], [[-3, 4]], [[3, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 3]], [[2, 3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 2]], [[2, 4]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[1, 2]], [[-1, 4]], [[1, 2]], [[-1, 4]], [[-2, 2]], [[2, 4]], [[1, 2]], [[-1, 4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1]], [[2, 5]], [[-2, 5]], [[2, 1]], [[1, 3]], [[-1, 3]], [[1, 3]], [[-1, 3]], [[-2, 3]], [[2, 3]], [[-1, 3]], [[1, 3]], [[-1, 1]], [[1, 5]], [[-1, 5]], [[1, 1]], [[-1, 1]], [[1, 5]], [[-1, 5]], [[1, 1]], [[2, 1]], [[-2, 5]], [[2, 5]], [[-2, 1]], [[1, 1]], [[-1, 5]], [[1, 5]], [[-1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 27676738
    {'center': '216.a1', 'center_index': 216, 'center_order': 9, 'counter': 66, 'cyclotomic_n': 12, 'dim': 6, 'faithful': False, 'field': [1, 0, 1], 'group': '1944.3492', 'group_counter': 3492, 'group_order': 1944, 'image': None, 'image_isoclass': '648.541', 'image_order': 648, 'indicator': 0, 'kernel': '648.b1', 'kernel_order': 3, 'label': '1944.3492.6j2', 'nt': [36, 4], 'q_character': None, 'values': [[[6, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[6, 4]], [[-6, 2]], [[-3, 0]], [[-3, 0]], [[6, 0]], [[-3, 0]], [[3, 2]], [[-3, 4]], [[3, 2]], [[-3, 4]], [[-6, 2]], [[6, 4]], [[3, 2]], [[-3, 4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 3]], [[-2, 3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 4]], [[-2, 2]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 4]], [[1, 2]], [[-1, 4]], [[1, 2]], [[2, 4]], [[-2, 2]], [[-1, 4]], [[1, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 5]], [[-2, 1]], [[2, 1]], [[-2, 5]], [[-1, 3]], [[1, 3]], [[-1, 3]], [[1, 3]], [[2, 3]], [[-2, 3]], [[1, 3]], [[-1, 3]], [[1, 5]], [[-1, 1]], [[1, 1]], [[-1, 5]], [[1, 5]], [[-1, 1]], [[1, 1]], [[-1, 5]], [[-2, 5]], [[2, 1]], [[-2, 1]], [[2, 5]], [[-1, 5]], [[1, 1]], [[-1, 1]], [[1, 5]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 27676739
    {'center': '216.a1', 'center_index': 216, 'center_order': 9, 'counter': 67, 'cyclotomic_n': 12, 'dim': 6, 'faithful': False, 'field': [1, 0, 1], 'group': '1944.3492', 'group_counter': 3492, 'group_order': 1944, 'image': None, 'image_isoclass': '648.541', 'image_order': 648, 'indicator': 0, 'kernel': '648.b1', 'kernel_order': 3, 'label': '1944.3492.6j3', 'nt': [36, 1197], 'q_character': None, 'values': [[[6, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-6, 2]], [[6, 4]], [[-3, 0]], [[-3, 0]], [[6, 0]], [[-3, 0]], [[-3, 4]], [[3, 2]], [[-3, 4]], [[3, 2]], [[6, 4]], [[-6, 2]], [[-3, 4]], [[3, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 3]], [[-2, 3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 2]], [[2, 4]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[1, 2]], [[-1, 4]], [[1, 2]], [[-1, 4]], [[-2, 2]], [[2, 4]], [[1, 2]], [[-1, 4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1]], [[-2, 5]], [[2, 5]], [[-2, 1]], [[-1, 3]], [[1, 3]], [[-1, 3]], [[1, 3]], [[2, 3]], [[-2, 3]], [[1, 3]], [[-1, 3]], [[1, 1]], [[-1, 5]], [[1, 5]], [[-1, 1]], [[1, 1]], [[-1, 5]], [[1, 5]], [[-1, 1]], [[-2, 1]], [[2, 5]], [[-2, 5]], [[2, 1]], [[-1, 1]], [[1, 5]], [[-1, 5]], [[1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 27676740
    {'center': '216.a1', 'center_index': 216, 'center_order': 9, 'counter': 68, 'cyclotomic_n': 12, 'dim': 6, 'faithful': False, 'field': [1, 0, 1], 'group': '1944.3492', 'group_counter': 3492, 'group_order': 1944, 'image': None, 'image_isoclass': '648.541', 'image_order': 648, 'indicator': 0, 'kernel': '648.b1', 'kernel_order': 3, 'label': '1944.3492.6j4', 'nt': [36, 4], 'q_character': None, 'values': [[[6, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[6, 4]], [[-6, 2]], [[-3, 0]], [[-3, 0]], [[6, 0]], [[-3, 0]], [[3, 2]], [[-3, 4]], [[3, 2]], [[-3, 4]], [[-6, 2]], [[6, 4]], [[3, 2]], [[-3, 4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 3]], [[2, 3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 4]], [[-2, 2]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 4]], [[1, 2]], [[-1, 4]], [[1, 2]], [[2, 4]], [[-2, 2]], [[-1, 4]], [[1, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 5]], [[2, 1]], [[-2, 1]], [[2, 5]], [[1, 3]], [[-1, 3]], [[1, 3]], [[-1, 3]], [[-2, 3]], [[2, 3]], [[-1, 3]], [[1, 3]], [[-1, 5]], [[1, 1]], [[-1, 1]], [[1, 5]], [[-1, 5]], [[1, 1]], [[-1, 1]], [[1, 5]], [[2, 5]], [[-2, 1]], [[2, 1]], [[-2, 5]], [[1, 5]], [[-1, 1]], [[1, 1]], [[-1, 5]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 27676741
    {'center': '216.a1', 'center_index': 216, 'center_order': 9, 'counter': 69, 'cyclotomic_n': 12, 'dim': 6, 'faithful': False, 'field': [1, 0, 1], 'group': '1944.3492', 'group_counter': 3492, 'group_order': 1944, 'image': None, 'image_isoclass': '648.541', 'image_order': 648, 'indicator': 0, 'kernel': '648.b1', 'kernel_order': 3, 'label': '1944.3492.6k1', 'nt': [36, 1197], 'q_character': None, 'values': [[[6, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-6, 2]], [[6, 4]], [[-3, 0]], [[6, 0]], [[-3, 0]], [[-3, 0]], [[-3, 4]], [[3, 2]], [[6, 4]], [[-6, 2]], [[-3, 4]], [[3, 2]], [[-3, 4]], [[3, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 3]], [[2, 3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 2]], [[2, 4]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[1, 2]], [[-1, 4]], [[-2, 2]], [[2, 4]], [[1, 2]], [[-1, 4]], [[1, 2]], [[-1, 4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1]], [[2, 5]], [[-2, 5]], [[2, 1]], [[1, 3]], [[-1, 3]], [[-2, 3]], [[2, 3]], [[1, 3]], [[-1, 3]], [[-1, 3]], [[1, 3]], [[-1, 1]], [[1, 5]], [[-1, 5]], [[1, 1]], [[2, 1]], [[-2, 5]], [[2, 5]], [[-2, 1]], [[-1, 1]], [[1, 5]], [[-1, 5]], [[1, 1]], [[1, 1]], [[-1, 5]], [[1, 5]], [[-1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 27676743
    {'center': '216.a1', 'center_index': 216, 'center_order': 9, 'counter': 70, 'cyclotomic_n': 12, 'dim': 6, 'faithful': False, 'field': [1, 0, 1], 'group': '1944.3492', 'group_counter': 3492, 'group_order': 1944, 'image': None, 'image_isoclass': '648.541', 'image_order': 648, 'indicator': 0, 'kernel': '648.b1', 'kernel_order': 3, 'label': '1944.3492.6k2', 'nt': [36, 4], 'q_character': None, 'values': [[[6, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[6, 4]], [[-6, 2]], [[-3, 0]], [[6, 0]], [[-3, 0]], [[-3, 0]], [[3, 2]], [[-3, 4]], [[-6, 2]], [[6, 4]], [[3, 2]], [[-3, 4]], [[3, 2]], [[-3, 4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 3]], [[-2, 3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 4]], [[-2, 2]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 4]], [[1, 2]], [[2, 4]], [[-2, 2]], [[-1, 4]], [[1, 2]], [[-1, 4]], [[1, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 5]], [[-2, 1]], [[2, 1]], [[-2, 5]], [[-1, 3]], [[1, 3]], [[2, 3]], [[-2, 3]], [[-1, 3]], [[1, 3]], [[1, 3]], [[-1, 3]], [[1, 5]], [[-1, 1]], [[1, 1]], [[-1, 5]], [[-2, 5]], [[2, 1]], [[-2, 1]], [[2, 5]], [[1, 5]], [[-1, 1]], [[1, 1]], [[-1, 5]], [[-1, 5]], [[1, 1]], [[-1, 1]], [[1, 5]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 27676744
    {'center': '216.a1', 'center_index': 216, 'center_order': 9, 'counter': 71, 'cyclotomic_n': 12, 'dim': 6, 'faithful': False, 'field': [1, 0, 1], 'group': '1944.3492', 'group_counter': 3492, 'group_order': 1944, 'image': None, 'image_isoclass': '648.541', 'image_order': 648, 'indicator': 0, 'kernel': '648.b1', 'kernel_order': 3, 'label': '1944.3492.6k3', 'nt': [36, 1197], 'q_character': None, 'values': [[[6, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-6, 2]], [[6, 4]], [[-3, 0]], [[6, 0]], [[-3, 0]], [[-3, 0]], [[-3, 4]], [[3, 2]], [[6, 4]], [[-6, 2]], [[-3, 4]], [[3, 2]], [[-3, 4]], [[3, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 3]], [[-2, 3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 2]], [[2, 4]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[1, 2]], [[-1, 4]], [[-2, 2]], [[2, 4]], [[1, 2]], [[-1, 4]], [[1, 2]], [[-1, 4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1]], [[-2, 5]], [[2, 5]], [[-2, 1]], [[-1, 3]], [[1, 3]], [[2, 3]], [[-2, 3]], [[-1, 3]], [[1, 3]], [[1, 3]], [[-1, 3]], [[1, 1]], [[-1, 5]], [[1, 5]], [[-1, 1]], [[-2, 1]], [[2, 5]], [[-2, 5]], [[2, 1]], [[1, 1]], [[-1, 5]], [[1, 5]], [[-1, 1]], [[-1, 1]], [[1, 5]], [[-1, 5]], [[1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 27676745
    {'center': '216.a1', 'center_index': 216, 'center_order': 9, 'counter': 72, 'cyclotomic_n': 12, 'dim': 6, 'faithful': False, 'field': [1, 0, 1], 'group': '1944.3492', 'group_counter': 3492, 'group_order': 1944, 'image': None, 'image_isoclass': '648.541', 'image_order': 648, 'indicator': 0, 'kernel': '648.b1', 'kernel_order': 3, 'label': '1944.3492.6k4', 'nt': [36, 4], 'q_character': None, 'values': [[[6, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[6, 4]], [[-6, 2]], [[-3, 0]], [[6, 0]], [[-3, 0]], [[-3, 0]], [[3, 2]], [[-3, 4]], [[-6, 2]], [[6, 4]], [[3, 2]], [[-3, 4]], [[3, 2]], [[-3, 4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 3]], [[2, 3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 4]], [[-2, 2]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 4]], [[1, 2]], [[2, 4]], [[-2, 2]], [[-1, 4]], [[1, 2]], [[-1, 4]], [[1, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 5]], [[2, 1]], [[-2, 1]], [[2, 5]], [[1, 3]], [[-1, 3]], [[-2, 3]], [[2, 3]], [[1, 3]], [[-1, 3]], [[-1, 3]], [[1, 3]], [[-1, 5]], [[1, 1]], [[-1, 1]], [[1, 5]], [[2, 5]], [[-2, 1]], [[2, 1]], [[-2, 5]], [[-1, 5]], [[1, 1]], [[-1, 1]], [[1, 5]], [[1, 5]], [[-1, 1]], [[1, 1]], [[-1, 5]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 27676746
    {'center': '216.a1', 'center_index': 216, 'center_order': 9, 'counter': 73, 'cyclotomic_n': 12, 'dim': 6, 'faithful': False, 'field': [1, 0, 1], 'group': '1944.3492', 'group_counter': 3492, 'group_order': 1944, 'image': None, 'image_isoclass': '648.541', 'image_order': 648, 'indicator': 0, 'kernel': '648.b1', 'kernel_order': 3, 'label': '1944.3492.6l1', 'nt': [36, 1197], 'q_character': None, 'values': [[[6, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-6, 2]], [[6, 4]], [[6, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[6, 4]], [[-6, 2]], [[-3, 4]], [[3, 2]], [[-3, 4]], [[3, 2]], [[-3, 4]], [[3, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 3]], [[2, 3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 2]], [[2, 4]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-2, 2]], [[2, 4]], [[1, 2]], [[-1, 4]], [[1, 2]], [[-1, 4]], [[1, 2]], [[-1, 4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1]], [[2, 5]], [[-2, 5]], [[2, 1]], [[-2, 3]], [[2, 3]], [[1, 3]], [[-1, 3]], [[1, 3]], [[-1, 3]], [[-1, 3]], [[1, 3]], [[2, 1]], [[-2, 5]], [[2, 5]], [[-2, 1]], [[-1, 1]], [[1, 5]], [[-1, 5]], [[1, 1]], [[-1, 1]], [[1, 5]], [[-1, 5]], [[1, 1]], [[1, 1]], [[-1, 5]], [[1, 5]], [[-1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 27676747
    {'center': '216.a1', 'center_index': 216, 'center_order': 9, 'counter': 74, 'cyclotomic_n': 12, 'dim': 6, 'faithful': False, 'field': [1, 0, 1], 'group': '1944.3492', 'group_counter': 3492, 'group_order': 1944, 'image': None, 'image_isoclass': '648.541', 'image_order': 648, 'indicator': 0, 'kernel': '648.b1', 'kernel_order': 3, 'label': '1944.3492.6l2', 'nt': [36, 4], 'q_character': None, 'values': [[[6, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[6, 4]], [[-6, 2]], [[6, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-6, 2]], [[6, 4]], [[3, 2]], [[-3, 4]], [[3, 2]], [[-3, 4]], [[3, 2]], [[-3, 4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 3]], [[-2, 3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 4]], [[-2, 2]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 4]], [[-2, 2]], [[-1, 4]], [[1, 2]], [[-1, 4]], [[1, 2]], [[-1, 4]], [[1, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 5]], [[-2, 1]], [[2, 1]], [[-2, 5]], [[2, 3]], [[-2, 3]], [[-1, 3]], [[1, 3]], [[-1, 3]], [[1, 3]], [[1, 3]], [[-1, 3]], [[-2, 5]], [[2, 1]], [[-2, 1]], [[2, 5]], [[1, 5]], [[-1, 1]], [[1, 1]], [[-1, 5]], [[1, 5]], [[-1, 1]], [[1, 1]], [[-1, 5]], [[-1, 5]], [[1, 1]], [[-1, 1]], [[1, 5]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 27676748
    {'center': '216.a1', 'center_index': 216, 'center_order': 9, 'counter': 75, 'cyclotomic_n': 12, 'dim': 6, 'faithful': False, 'field': [1, 0, 1], 'group': '1944.3492', 'group_counter': 3492, 'group_order': 1944, 'image': None, 'image_isoclass': '648.541', 'image_order': 648, 'indicator': 0, 'kernel': '648.b1', 'kernel_order': 3, 'label': '1944.3492.6l3', 'nt': [36, 1197], 'q_character': None, 'values': [[[6, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-6, 2]], [[6, 4]], [[6, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[6, 4]], [[-6, 2]], [[-3, 4]], [[3, 2]], [[-3, 4]], [[3, 2]], [[-3, 4]], [[3, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 3]], [[-2, 3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 2]], [[2, 4]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-2, 2]], [[2, 4]], [[1, 2]], [[-1, 4]], [[1, 2]], [[-1, 4]], [[1, 2]], [[-1, 4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1]], [[-2, 5]], [[2, 5]], [[-2, 1]], [[2, 3]], [[-2, 3]], [[-1, 3]], [[1, 3]], [[-1, 3]], [[1, 3]], [[1, 3]], [[-1, 3]], [[-2, 1]], [[2, 5]], [[-2, 5]], [[2, 1]], [[1, 1]], [[-1, 5]], [[1, 5]], [[-1, 1]], [[1, 1]], [[-1, 5]], [[1, 5]], [[-1, 1]], [[-1, 1]], [[1, 5]], [[-1, 5]], [[1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 27676749
    {'center': '216.a1', 'center_index': 216, 'center_order': 9, 'counter': 76, 'cyclotomic_n': 12, 'dim': 6, 'faithful': False, 'field': [1, 0, 1], 'group': '1944.3492', 'group_counter': 3492, 'group_order': 1944, 'image': None, 'image_isoclass': '648.541', 'image_order': 648, 'indicator': 0, 'kernel': '648.b1', 'kernel_order': 3, 'label': '1944.3492.6l4', 'nt': [36, 4], 'q_character': None, 'values': [[[6, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[6, 4]], [[-6, 2]], [[6, 0]], [[-3, 0]], [[-3, 0]], [[-3, 0]], [[-6, 2]], [[6, 4]], [[3, 2]], [[-3, 4]], [[3, 2]], [[-3, 4]], [[3, 2]], [[-3, 4]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 3]], [[2, 3]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 4]], [[-2, 2]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 4]], [[-2, 2]], [[-1, 4]], [[1, 2]], [[-1, 4]], [[1, 2]], [[-1, 4]], [[1, 2]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 5]], [[2, 1]], [[-2, 1]], [[2, 5]], [[-2, 3]], [[2, 3]], [[1, 3]], [[-1, 3]], [[1, 3]], [[-1, 3]], [[-1, 3]], [[1, 3]], [[2, 5]], [[-2, 1]], [[2, 1]], [[-2, 5]], [[-1, 5]], [[1, 1]], [[-1, 1]], [[1, 5]], [[-1, 5]], [[1, 1]], [[-1, 1]], [[1, 5]], [[1, 5]], [[-1, 1]], [[1, 1]], [[-1, 5]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 27676750
    {'center': '216.a1', 'center_index': 216, 'center_order': 9, 'counter': 77, 'cyclotomic_n': 1, 'dim': 8, 'faithful': False, 'field': [0, 1], 'group': '1944.3492', 'group_counter': 3492, 'group_order': 1944, 'image': None, 'image_isoclass': '216.156', 'image_order': 216, 'indicator': 1, 'kernel': '216.a1', 'kernel_order': 9, 'label': '1944.3492.8a', 'nt': [12, 119], 'q_character': None, 'values': [[[8, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[8, 0]], [[8, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[8, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[8, 0]], [[8, 0]], [[-4, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-4, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[2, 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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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: 27676751
    {'center': '216.a1', 'center_index': 216, 'center_order': 9, 'counter': 78, 'cyclotomic_n': 1, 'dim': 8, 'faithful': False, 'field': [0, 1], 'group': '1944.3492', 'group_counter': 3492, 'group_order': 1944, 'image': None, 'image_isoclass': '216.156', 'image_order': 216, 'indicator': 1, 'kernel': '216.a1', 'kernel_order': 9, 'label': '1944.3492.8b', 'nt': [12, 119], 'q_character': None, 'values': [[[8, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[8, 0]], [[8, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[8, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[8, 0]], [[8, 0]], [[2, 0]], [[-4, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-4, 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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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: 27676752
    {'center': '216.a1', 'center_index': 216, 'center_order': 9, 'counter': 79, 'cyclotomic_n': 1, 'dim': 8, 'faithful': False, 'field': [0, 1], 'group': '1944.3492', 'group_counter': 3492, 'group_order': 1944, 'image': None, 'image_isoclass': '216.156', 'image_order': 216, 'indicator': 1, 'kernel': '216.a1', 'kernel_order': 9, 'label': '1944.3492.8c', 'nt': [12, 119], 'q_character': None, 'values': [[[8, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[8, 0]], [[8, 0]], [[-4, 0]], [[-4, 0]], [[8, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[8, 0]], [[8, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-4, 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]], [[0, 0]], [[0, 0]], [[0, 0]], [[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: 27676754
    {'center': '216.a1', 'center_index': 216, 'center_order': 9, 'counter': 80, 'cyclotomic_n': 1, 'dim': 8, 'faithful': False, 'field': [0, 1], 'group': '1944.3492', 'group_counter': 3492, 'group_order': 1944, 'image': None, 'image_isoclass': '216.156', 'image_order': 216, 'indicator': 1, 'kernel': '216.a1', 'kernel_order': 9, 'label': '1944.3492.8d', 'nt': [12, 119], 'q_character': None, 'values': [[[8, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[8, 0]], [[8, 0]], [[-4, 0]], [[-4, 0]], [[8, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[8, 0]], [[8, 0]], [[-4, 0]], [[-4, 0]], [[2, 0]], [[-4, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-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, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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: 27676755
    {'center': '216.a1', 'center_index': 216, 'center_order': 9, 'counter': 81, 'cyclotomic_n': 1, 'dim': 8, 'faithful': False, 'field': [0, 1], 'group': '1944.3492', 'group_counter': 3492, 'group_order': 1944, 'image': None, 'image_isoclass': '216.156', 'image_order': 216, 'indicator': 1, 'kernel': '216.a1', 'kernel_order': 9, 'label': '1944.3492.8e', 'nt': [12, 119], 'q_character': None, 'values': [[[8, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[8, 0]], [[8, 0]], [[-4, 0]], [[8, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[8, 0]], [[8, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-4, 0]], [[2, 0]], [[2, 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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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: 27676756
    {'center': '216.a1', 'center_index': 216, 'center_order': 9, 'counter': 82, 'cyclotomic_n': 1, 'dim': 8, 'faithful': False, 'field': [0, 1], 'group': '1944.3492', 'group_counter': 3492, 'group_order': 1944, 'image': None, 'image_isoclass': '216.156', 'image_order': 216, 'indicator': 1, 'kernel': '216.a1', 'kernel_order': 9, 'label': '1944.3492.8f', 'nt': [12, 119], 'q_character': None, 'values': [[[8, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[8, 0]], [[8, 0]], [[-4, 0]], [[8, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[8, 0]], [[8, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[2, 0]], [[-4, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-4, 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]], [[0, 0]], [[0, 0]], [[0, 0]], [[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: 27676757
    {'center': '216.a1', 'center_index': 216, 'center_order': 9, 'counter': 83, 'cyclotomic_n': 1, 'dim': 8, 'faithful': False, 'field': [0, 1], 'group': '1944.3492', 'group_counter': 3492, 'group_order': 1944, 'image': None, 'image_isoclass': '216.156', 'image_order': 216, 'indicator': 1, 'kernel': '216.a1', 'kernel_order': 9, 'label': '1944.3492.8g', 'nt': [12, 119], 'q_character': None, 'values': [[[8, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[8, 0]], [[8, 0]], [[8, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[8, 0]], [[8, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[2, 0]], [[-4, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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: 27676758
    {'center': '216.a1', 'center_index': 216, 'center_order': 9, 'counter': 84, 'cyclotomic_n': 1, 'dim': 8, 'faithful': False, 'field': [0, 1], 'group': '1944.3492', 'group_counter': 3492, 'group_order': 1944, 'image': None, 'image_isoclass': '216.156', 'image_order': 216, 'indicator': 1, 'kernel': '216.a1', 'kernel_order': 9, 'label': '1944.3492.8h', 'nt': [12, 119], 'q_character': None, 'values': [[[8, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[8, 0]], [[8, 0]], [[8, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[8, 0]], [[8, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[2, 0]], [[-4, 0]], [[2, 0]], [[-4, 0]], [[-1, 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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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: 107638010
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3492', 'ambient_counter': 3492, 'ambient_order': 1944, 'ambient_tex': 'C_3^4:C_6:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': True, 'core_order': 1944, 'counter': 1, 'cyclic': False, 'direct': True, 'hall': 6, 'label': '1944.3492.1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '1.a1', 'outer_equivalence': True, 'perfect': False, 'proper': False, 'quotient': '1.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 1, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_1', 'simple': False, 'solvable': True, 'special_labels': ['R', 'L0', 'D0', 'C0'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '1944.3492', 'subgroup_hash': 3492, 'subgroup_order': 1944, 'subgroup_tex': 'C_3^4:C_6:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 107638049
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3492', 'ambient_counter': 3492, 'ambient_order': 1944, 'ambient_tex': 'C_3^4:C_6:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': True, 'core_order': 972, 'counter': 2, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1944.3492.2.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '972.810', 'subgroup_hash': 810, 'subgroup_order': 972, 'subgroup_tex': 'C_3^3:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 107638060
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3492', 'ambient_counter': 3492, 'ambient_order': 1944, 'ambient_tex': 'C_3^4:C_6:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': True, 'core_order': 972, 'counter': 3, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1944.3492.2.b1', 'maximal': True, 'maximal_normal': True, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': ['C1'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '972.759', 'subgroup_hash': 759, 'subgroup_order': 972, 'subgroup_tex': 'C_3\\times \\He_3:C_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 107638071
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3492', 'ambient_counter': 3492, 'ambient_order': 1944, 'ambient_tex': 'C_3^4:C_6:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': True, 'core_order': 972, 'counter': 4, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1944.3492.2.c1', 'maximal': True, 'maximal_normal': True, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '972.773', 'subgroup_hash': 773, 'subgroup_order': 972, 'subgroup_tex': '(C_3^2\\times \\He_3):C_4', 'supersolvable': False, 'sylow': 0}
  • id: 107638082
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3492', 'ambient_counter': 3492, 'ambient_order': 1944, 'ambient_tex': 'C_3^4:C_6:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 324, 'counter': 5, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3492.3.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '648.541', 'subgroup_hash': 541, 'subgroup_order': 648, 'subgroup_tex': 'S_3\\times \\He_3:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 107638093
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3492', 'ambient_counter': 3492, 'ambient_order': 1944, 'ambient_tex': 'C_3^4:C_6:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': True, 'core_order': 486, 'counter': 6, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1944.3492.4.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '4.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '486.231', 'subgroup_hash': 231, 'subgroup_order': 486, 'subgroup_tex': 'C_3^4:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 107638104
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3492', 'ambient_counter': 3492, 'ambient_order': 1944, 'ambient_tex': 'C_3^4:C_6:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': True, 'core_order': 486, 'counter': 7, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1944.3492.4.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '486.230', 'subgroup_hash': 230, 'subgroup_order': 486, 'subgroup_tex': 'C_3^4:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 107638115
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3492', 'ambient_counter': 3492, 'ambient_order': 1944, 'ambient_tex': 'C_3^4:C_6:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': True, 'core_order': 486, 'counter': 8, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1944.3492.4.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '4.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '486.248', 'subgroup_hash': 248, 'subgroup_order': 486, 'subgroup_tex': 'C_3^4:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 107638126
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3492', 'ambient_counter': 3492, 'ambient_order': 1944, 'ambient_tex': 'C_3^4:C_6:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 324, 'counter': 9, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1944.3492.6.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '6.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '6.1', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 6, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3', 'simple': False, 'solvable': True, 'special_labels': ['C2'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '324.110', 'subgroup_hash': 110, 'subgroup_order': 324, 'subgroup_tex': '\\He_3:C_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 107638011
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3492', 'ambient_counter': 3492, 'ambient_order': 1944, 'ambient_tex': 'C_3^4:C_6:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 162, 'counter': 10, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3492.6.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '324.122', 'subgroup_hash': 122, 'subgroup_order': 324, 'subgroup_tex': 'C_3^2:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 107638022
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3492', 'ambient_counter': 3492, 'ambient_order': 1944, 'ambient_tex': 'C_3^4:C_6:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 54, 'counter': 11, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3492.6.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '324.166', 'subgroup_hash': 166, 'subgroup_order': 324, 'subgroup_tex': 'C_3^2:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 107638033
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3492', 'ambient_counter': 3492, 'ambient_order': 1944, 'ambient_tex': 'C_3^4:C_6:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 162, 'counter': 12, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3492.6.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '324.113', 'subgroup_hash': 113, 'subgroup_order': 324, 'subgroup_tex': '(C_3\\times \\He_3):C_4', 'supersolvable': False, 'sylow': 0}
  • id: 107638042
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3492', 'ambient_counter': 3492, 'ambient_order': 1944, 'ambient_tex': 'C_3^4:C_6:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': True, 'core_order': 243, 'counter': 13, 'cyclic': False, 'direct': False, 'hall': 3, 'label': '1944.3492.8.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '8.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_4', 'simple': False, 'solvable': True, 'special_labels': ['D', 'F', 'L1', 'D1'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '243.62', 'subgroup_hash': 62, 'subgroup_order': 243, 'subgroup_tex': 'C_3^2\\times \\He_3', 'supersolvable': True, 'sylow': 3}
  • id: 107638043
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3492', 'ambient_counter': 3492, 'ambient_order': 1944, 'ambient_tex': 'C_3^4:C_6:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 108, 'counter': 14, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3492.9.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '9.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 9, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.100', 'subgroup_hash': 100, 'subgroup_order': 216, 'subgroup_tex': 'C_2\\times \\He_3:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 107638044
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3492', 'ambient_counter': 3492, 'ambient_order': 1944, 'ambient_tex': 'C_3^4:C_6:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 54, 'counter': 15, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3492.9.b1', 'maximal': True, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '9.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 9, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.141', 'subgroup_hash': 141, 'subgroup_order': 216, 'subgroup_tex': 'C_3:S_3\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 107638045
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3492', 'ambient_counter': 3492, 'ambient_order': 1944, 'ambient_tex': 'C_3^4:C_6:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 162, 'counter': 16, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1944.3492.12.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '12.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '12.4', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_6', 'simple': False, 'solvable': True, 'special_labels': ['C3'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '162.41', 'subgroup_hash': 41, 'subgroup_order': 162, 'subgroup_tex': 'C_3^3:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 107638046
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3492', 'ambient_counter': 3492, 'ambient_order': 1944, 'ambient_tex': 'C_3^4:C_6:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 81, 'counter': 17, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3492.12.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.35', 'subgroup_hash': 35, 'subgroup_order': 162, 'subgroup_tex': 'S_3\\times \\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 107638047
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3492', 'ambient_counter': 3492, 'ambient_order': 1944, 'ambient_tex': 'C_3^4:C_6:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 54, 'counter': 18, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3492.12.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.52', 'subgroup_hash': 52, 'subgroup_order': 162, 'subgroup_tex': 'C_3^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 107638048
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3492', 'ambient_counter': 3492, 'ambient_order': 1944, 'ambient_tex': 'C_3^4:C_6:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 27, 'counter': 19, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3492.12.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.51', 'subgroup_hash': 51, 'subgroup_order': 162, 'subgroup_tex': 'S_3\\times C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 107638050
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3492', 'ambient_counter': 3492, 'ambient_order': 1944, 'ambient_tex': 'C_3^4:C_6:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 9, 'counter': 20, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3492.12.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.46', 'subgroup_hash': 46, 'subgroup_order': 162, 'subgroup_tex': 'C_3^3:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 107638051
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3492', 'ambient_counter': 3492, 'ambient_order': 1944, 'ambient_tex': 'C_3^4:C_6:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 81, 'counter': 21, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3492.12.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.46', 'subgroup_hash': 46, 'subgroup_order': 162, 'subgroup_tex': 'C_3^3:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 107638052
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3492', 'ambient_counter': 3492, 'ambient_order': 1944, 'ambient_tex': 'C_3^4:C_6:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 27, 'counter': 22, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3492.12.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '162.53', 'subgroup_hash': 53, 'subgroup_order': 162, 'subgroup_tex': 'C_3^3:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 107638053
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3492', 'ambient_counter': 3492, 'ambient_order': 1944, 'ambient_tex': 'C_3^4:C_6:C_4', 'central': False, 'central_factor': True, 'centralizer_order': 54, 'characteristic': True, 'core_order': 108, 'counter': 23, 'cyclic': False, 'direct': True, 'hall': 0, 'label': '1944.3492.18.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '18.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '18.4', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 18, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3:S_3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '108.15', 'subgroup_hash': 15, 'subgroup_order': 108, 'subgroup_tex': '\\He_3:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 107638054
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3492', 'ambient_counter': 3492, 'ambient_order': 1944, 'ambient_tex': 'C_3^4:C_6:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 54, 'counter': 24, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3492.18.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.28', 'subgroup_hash': 28, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 107638055
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3492', 'ambient_counter': 3492, 'ambient_order': 1944, 'ambient_tex': 'C_3^4:C_6:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 9, 'counter': 25, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3492.18.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.38', 'subgroup_hash': 38, 'subgroup_order': 108, 'subgroup_tex': 'C_3\\times S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 107638056
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3492', 'ambient_counter': 3492, 'ambient_order': 1944, 'ambient_tex': 'C_3^4:C_6:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 54, 'counter': 26, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3492.18.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.43', 'subgroup_hash': 43, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 107638057
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3492', 'ambient_counter': 3492, 'ambient_order': 1944, 'ambient_tex': 'C_3^4:C_6:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 18, 'counter': 27, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3492.18.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.39', 'subgroup_hash': 39, 'subgroup_order': 108, 'subgroup_tex': 'C_3:S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 107638058
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.3492', 'ambient_counter': 3492, 'ambient_order': 1944, 'ambient_tex': 'C_3^4:C_6:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 27, 'counter': 28, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3492.18.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '18.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.35', 'subgroup_hash': 35, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 107638059
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3492', 'ambient_counter': 3492, 'ambient_order': 1944, 'ambient_tex': 'C_3^4:C_6:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 27, 'counter': 29, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3492.18.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.33', 'subgroup_hash': 33, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 107638061
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3492', 'ambient_counter': 3492, 'ambient_order': 1944, 'ambient_tex': 'C_3^4:C_6:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 54, 'counter': 30, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3492.18.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.15', 'subgroup_hash': 15, 'subgroup_order': 108, 'subgroup_tex': '\\He_3:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 107638062
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3492', 'ambient_counter': 3492, 'ambient_order': 1944, 'ambient_tex': 'C_3^4:C_6:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 81, 'counter': 31, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1944.3492.24.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '24.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '24.5', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4\\times S_3', 'simple': False, 'solvable': True, 'special_labels': ['C4'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '81.12', 'subgroup_hash': 12, 'subgroup_order': 81, 'subgroup_tex': 'C_3\\times \\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 107638063
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3492', 'ambient_counter': 3492, 'ambient_order': 1944, 'ambient_tex': 'C_3^4:C_6:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 9, 'counter': 32, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3492.24.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '81.12', 'subgroup_hash': 12, 'subgroup_order': 81, 'subgroup_tex': 'C_3\\times \\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 107638064
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.3492', 'ambient_counter': 3492, 'ambient_order': 1944, 'ambient_tex': 'C_3^4:C_6:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 27, 'counter': 33, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3492.24.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '81.15', 'subgroup_hash': 15, 'subgroup_order': 81, 'subgroup_tex': 'C_3^4', 'supersolvable': True, 'sylow': 0}
  • id: 107638065
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3492', 'ambient_counter': 3492, 'ambient_order': 1944, 'ambient_tex': 'C_3^4:C_6:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 9, 'counter': 34, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3492.27.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '27.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 27, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.27', 'subgroup_hash': 27, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 107638066
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3492', 'ambient_counter': 3492, 'ambient_order': 1944, 'ambient_tex': 'C_3^4:C_6:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 18, 'counter': 35, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3492.27.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '27.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 27, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.32', 'subgroup_hash': 32, 'subgroup_order': 72, 'subgroup_tex': 'C_{12}:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 107638067
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3492', 'ambient_counter': 3492, 'ambient_order': 1944, 'ambient_tex': 'C_3^4:C_6:C_4', 'central': False, 'central_factor': True, 'centralizer_order': 108, 'characteristic': True, 'core_order': 54, 'counter': 36, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1944.3492.36.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '36.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '36.9', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 9, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 36, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_3^2:C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, '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: 107638068
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3492', 'ambient_counter': 3492, 'ambient_order': 1944, 'ambient_tex': 'C_3^4:C_6:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': True, 'core_order': 54, 'counter': 37, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1944.3492.36.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '36.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '36.13', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 13, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 36, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6:S_3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '54.8', 'subgroup_hash': 8, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 107638069
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3492', 'ambient_counter': 3492, 'ambient_order': 1944, 'ambient_tex': 'C_3^4:C_6:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 27, 'counter': 38, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3492.36.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '54.10', 'subgroup_hash': 10, 'subgroup_order': 54, 'subgroup_tex': 'C_2\\times \\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 107638070
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3492', 'ambient_counter': 3492, 'ambient_order': 1944, 'ambient_tex': 'C_3^4:C_6:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 9, 'counter': 39, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3492.36.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.12', 'subgroup_hash': 12, 'subgroup_order': 54, 'subgroup_tex': 'S_3\\times C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 107638072
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3492', 'ambient_counter': 3492, 'ambient_order': 1944, 'ambient_tex': 'C_3^4:C_6:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 18, 'counter': 40, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3492.36.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.13', 'subgroup_hash': 13, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 107638073
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.3492', 'ambient_counter': 3492, 'ambient_order': 1944, 'ambient_tex': 'C_3^4:C_6:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 27, 'counter': 41, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3492.36.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.15', 'subgroup_hash': 15, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 107638074
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3492', 'ambient_counter': 3492, 'ambient_order': 1944, 'ambient_tex': 'C_3^4:C_6:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 9, 'counter': 42, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3492.36.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.12', 'subgroup_hash': 12, 'subgroup_order': 54, 'subgroup_tex': 'S_3\\times C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 107638075
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3492', 'ambient_counter': 3492, 'ambient_order': 1944, 'ambient_tex': 'C_3^4:C_6:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 3, 'counter': 43, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3492.36.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.12', 'subgroup_hash': 12, 'subgroup_order': 54, 'subgroup_tex': 'S_3\\times C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 107638076
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3492', 'ambient_counter': 3492, 'ambient_order': 1944, 'ambient_tex': 'C_3^4:C_6:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 9, 'counter': 44, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3492.36.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.12', 'subgroup_hash': 12, 'subgroup_order': 54, 'subgroup_tex': 'S_3\\times C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 107638077
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3492', 'ambient_counter': 3492, 'ambient_order': 1944, 'ambient_tex': 'C_3^4:C_6:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 9, 'counter': 45, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3492.36.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.13', 'subgroup_hash': 13, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 107638078
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3492', 'ambient_counter': 3492, 'ambient_order': 1944, 'ambient_tex': 'C_3^4:C_6:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 9, 'counter': 46, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3492.36.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.13', 'subgroup_hash': 13, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 107638079
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3492', 'ambient_counter': 3492, 'ambient_order': 1944, 'ambient_tex': 'C_3^4:C_6:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 27, 'counter': 47, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3492.36.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.13', 'subgroup_hash': 13, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:C_6', 'supersolvable': True, 'sylow': 0}
  • id: 107638080
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3492', 'ambient_counter': 3492, 'ambient_order': 1944, 'ambient_tex': 'C_3^4:C_6:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 3, 'counter': 48, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3492.36.m1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.m1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.8', 'subgroup_hash': 8, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 107638081
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3492', 'ambient_counter': 3492, 'ambient_order': 1944, 'ambient_tex': 'C_3^4:C_6:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 27, 'counter': 49, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3492.36.n1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.n1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.8', 'subgroup_hash': 8, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 107638083
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3492', 'ambient_counter': 3492, 'ambient_order': 1944, 'ambient_tex': 'C_3^4:C_6:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 3, 'counter': 50, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3492.36.o1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.o1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '54.8', 'subgroup_hash': 8, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 107638084
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3492', 'ambient_counter': 3492, 'ambient_order': 1944, 'ambient_tex': 'C_3^4:C_6:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 9, 'counter': 51, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3492.36.p1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.p1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '54.14', 'subgroup_hash': 14, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 107638085
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3492', 'ambient_counter': 3492, 'ambient_order': 1944, 'ambient_tex': 'C_3^4:C_6:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 52, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3492.54.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 107638086
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3492', 'ambient_counter': 3492, 'ambient_order': 1944, 'ambient_tex': 'C_3^4:C_6:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 9, 'counter': 53, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3492.54.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 107638087
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3492', 'ambient_counter': 3492, 'ambient_order': 1944, 'ambient_tex': 'C_3^4:C_6:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 3, 'counter': 54, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3492.54.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.10', 'subgroup_hash': 10, 'subgroup_order': 36, 'subgroup_tex': 'S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 107638088
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3492', 'ambient_counter': 3492, 'ambient_order': 1944, 'ambient_tex': 'C_3^4:C_6:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 18, 'counter': 55, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3492.54.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.13', 'subgroup_hash': 13, 'subgroup_order': 36, 'subgroup_tex': 'C_6:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 107638089
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.3492', 'ambient_counter': 3492, 'ambient_order': 1944, 'ambient_tex': 'C_3^4:C_6:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 9, 'counter': 56, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3492.54.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '54.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.8', 'subgroup_hash': 8, 'subgroup_order': 36, 'subgroup_tex': 'C_3\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 107638090
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3492', 'ambient_counter': 3492, 'ambient_order': 1944, 'ambient_tex': 'C_3^4:C_6:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 9, 'counter': 57, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3492.54.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.6', 'subgroup_hash': 6, 'subgroup_order': 36, 'subgroup_tex': 'C_3:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 107638091
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.3492', 'ambient_counter': 3492, 'ambient_order': 1944, 'ambient_tex': 'C_3^4:C_6:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 3, 'counter': 58, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3492.54.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '54.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.8', 'subgroup_hash': 8, 'subgroup_order': 36, 'subgroup_tex': 'C_3\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 107638092
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.3492', 'ambient_counter': 3492, 'ambient_order': 1944, 'ambient_tex': 'C_3^4:C_6:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 9, 'counter': 59, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3492.54.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '54.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.8', 'subgroup_hash': 8, 'subgroup_order': 36, 'subgroup_tex': 'C_3\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 107638094
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3492', 'ambient_counter': 3492, 'ambient_order': 1944, 'ambient_tex': 'C_3^4:C_6:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 9, 'counter': 60, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3492.54.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '54.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.7', 'subgroup_hash': 7, 'subgroup_order': 36, 'subgroup_tex': 'C_3^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 107638095
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.3492', 'ambient_counter': 3492, 'ambient_order': 1944, 'ambient_tex': 'C_3^4:C_6:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 972, 'characteristic': True, 'core_order': 27, 'counter': 61, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1944.3492.72.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '72.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '72.45', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 45, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 72, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_2\\times C_3^2:C_4', 'simple': False, 'solvable': True, 'special_labels': ['S'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 107638096
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3492', 'ambient_counter': 3492, 'ambient_order': 1944, 'ambient_tex': 'C_3^4:C_6:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': True, 'core_order': 27, 'counter': 62, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1944.3492.72.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '72.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '72.32', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 32, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 72, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{12}:S_3', 'simple': False, 'solvable': True, 'special_labels': ['C5'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '27.3', 'subgroup_hash': 3, 'subgroup_order': 27, 'subgroup_tex': '\\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 107638097
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.3492', 'ambient_counter': 3492, 'ambient_order': 1944, 'ambient_tex': 'C_3^4:C_6:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 9, 'counter': 63, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3492.72.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 107638098
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.3492', 'ambient_counter': 3492, 'ambient_order': 1944, 'ambient_tex': 'C_3^4:C_6:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 9, 'counter': 64, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3492.72.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 107638099
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3492', 'ambient_counter': 3492, 'ambient_order': 1944, 'ambient_tex': 'C_3^4:C_6:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 3, 'counter': 65, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3492.72.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '27.3', 'subgroup_hash': 3, 'subgroup_order': 27, 'subgroup_tex': '\\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 107638100
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3492', 'ambient_counter': 3492, 'ambient_order': 1944, 'ambient_tex': 'C_3^4:C_6:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 3, 'counter': 66, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3492.72.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '27.3', 'subgroup_hash': 3, 'subgroup_order': 27, 'subgroup_tex': '\\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 107638101
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.3492', 'ambient_counter': 3492, 'ambient_order': 1944, 'ambient_tex': 'C_3^4:C_6:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 3, 'counter': 67, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3492.72.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 107638102
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.3492', 'ambient_counter': 3492, 'ambient_order': 1944, 'ambient_tex': 'C_3^4:C_6:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 9, 'counter': 68, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3492.72.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 107638103
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.3492', 'ambient_counter': 3492, 'ambient_order': 1944, 'ambient_tex': 'C_3^4:C_6:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 3, 'counter': 69, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3492.81.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '81.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 81, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.9', 'subgroup_hash': 9, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 107638105
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3492', 'ambient_counter': 3492, 'ambient_order': 1944, 'ambient_tex': 'C_3^4:C_6:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 70, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3492.81.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '81.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '24.5', 'subgroup_hash': 5, 'subgroup_order': 24, 'subgroup_tex': 'C_4\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 107638106
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3492', 'ambient_counter': 3492, 'ambient_order': 1944, 'ambient_tex': 'C_3^4:C_6:C_4', 'central': False, 'central_factor': True, 'centralizer_order': 108, 'characteristic': True, 'core_order': 18, 'counter': 71, 'cyclic': False, 'direct': True, 'hall': 0, 'label': '1944.3492.108.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '108.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '108.15', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 15, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 108, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': '\\He_3:C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '18.4', 'subgroup_hash': 4, 'subgroup_order': 18, 'subgroup_tex': 'C_3:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 107638107
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.3492', 'ambient_counter': 3492, 'ambient_order': 1944, 'ambient_tex': 'C_3^4:C_6:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 3, 'counter': 72, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3492.108.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 107638108
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3492', 'ambient_counter': 3492, 'ambient_order': 1944, 'ambient_tex': 'C_3^4:C_6:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 9, 'counter': 73, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3492.108.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 107638109
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3492', 'ambient_counter': 3492, 'ambient_order': 1944, 'ambient_tex': 'C_3^4:C_6:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 9, 'characteristic': False, 'core_order': 3, 'counter': 74, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3492.108.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 107638110
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.3492', 'ambient_counter': 3492, 'ambient_order': 1944, 'ambient_tex': 'C_3^4:C_6:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 9, 'counter': 75, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3492.108.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 107638111
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.3492', 'ambient_counter': 3492, 'ambient_order': 1944, 'ambient_tex': 'C_3^4:C_6:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 3, 'counter': 76, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3492.108.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 107638112
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.3492', 'ambient_counter': 3492, 'ambient_order': 1944, 'ambient_tex': 'C_3^4:C_6:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 9, 'counter': 77, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3492.108.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 107638113
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3492', 'ambient_counter': 3492, 'ambient_order': 1944, 'ambient_tex': 'C_3^4:C_6:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 3, 'counter': 78, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3492.108.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 107638114
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3492', 'ambient_counter': 3492, 'ambient_order': 1944, 'ambient_tex': 'C_3^4:C_6:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 3, 'counter': 79, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3492.108.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 107638116
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3492', 'ambient_counter': 3492, 'ambient_order': 1944, 'ambient_tex': 'C_3^4:C_6:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 27, 'characteristic': False, 'core_order': 1, 'counter': 80, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3492.108.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 107638117
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3492', 'ambient_counter': 3492, 'ambient_order': 1944, 'ambient_tex': 'C_3^4:C_6:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 9, 'counter': 81, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3492.108.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 107638118
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3492', 'ambient_counter': 3492, 'ambient_order': 1944, 'ambient_tex': 'C_3^4:C_6:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 82, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3492.108.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 107638119
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3492', 'ambient_counter': 3492, 'ambient_order': 1944, 'ambient_tex': 'C_3^4:C_6:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 3, 'counter': 83, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3492.108.m1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.m1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 107638120
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3492', 'ambient_counter': 3492, 'ambient_order': 1944, 'ambient_tex': 'C_3^4:C_6:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 3, 'counter': 84, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3492.108.n1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.n1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.4', 'subgroup_hash': 4, 'subgroup_order': 18, 'subgroup_tex': 'C_3:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 107638121
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3492', 'ambient_counter': 3492, 'ambient_order': 1944, 'ambient_tex': 'C_3^4:C_6:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 3, 'counter': 85, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3492.108.o1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.o1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.4', 'subgroup_hash': 4, 'subgroup_order': 18, 'subgroup_tex': 'C_3:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 107638122
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3492', 'ambient_counter': 3492, 'ambient_order': 1944, 'ambient_tex': 'C_3^4:C_6:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 9, 'counter': 86, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3492.108.p1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '108.p1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '18.4', 'subgroup_hash': 4, 'subgroup_order': 18, 'subgroup_tex': 'C_3:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 107638123
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.3492', 'ambient_counter': 3492, 'ambient_order': 1944, 'ambient_tex': 'C_3^4:C_6:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 3, 'counter': 87, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3492.162.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '162.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 162, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 107638124
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3492', 'ambient_counter': 3492, 'ambient_order': 1944, 'ambient_tex': 'C_3^4:C_6:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 88, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3492.162.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '162.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 162, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 107638125
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1944.3492', 'ambient_counter': 3492, 'ambient_order': 1944, 'ambient_tex': 'C_3^4:C_6:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 89, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3492.162.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '162.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 162, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 107638127
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1944.3492', 'ambient_counter': 3492, 'ambient_order': 1944, 'ambient_tex': 'C_3^4:C_6:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 216, 'characteristic': False, 'core_order': 3, 'counter': 90, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1944.3492.162.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '162.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 162, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 107638128
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1944.3492', 'ambient_counter': 3492, 'ambient_order': 1944, 'ambient_tex': 'C_3^4:C_6:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 3, 'counter': 91, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1944.3492.162.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '162.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 107638129
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1944.3492', 'ambient_counter': 3492, 'ambient_order': 1944, 'ambient_tex': 'C_3^4:C_6:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 3, 'counter': 92, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1944.3492.162.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '162.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 107638130
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1944.3492', 'ambient_counter': 3492, 'ambient_order': 1944, 'ambient_tex': 'C_3^4:C_6:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 93, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3492.162.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '162.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '12.1', 'subgroup_hash': 1, 'subgroup_order': 12, 'subgroup_tex': 'C_3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 107638131
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1944.3492', 'ambient_counter': 3492, 'ambient_order': 1944, 'ambient_tex': 'C_3^4:C_6:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 1, 'counter': 94, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1944.3492.162.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '162.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 107638132
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.3492', 'ambient_counter': 3492, 'ambient_order': 1944, 'ambient_tex': 'C_3^4:C_6:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 972, 'characteristic': False, 'core_order': 9, 'counter': 95, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1944.3492.216.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '216.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '216.156', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 156, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 216, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_3^2:C_4\\times S_3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 107638133
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.3492', 'ambient_counter': 3492, 'ambient_order': 1944, 'ambient_tex': 'C_3^4:C_6:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 972, 'characteristic': True, 'core_order': 9, 'counter': 96, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1944.3492.216.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '216.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '216.100', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 100, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 216, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_2\\times \\He_3:C_4', '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: 107638134
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.3492', 'ambient_counter': 3492, 'ambient_order': 1944, 'ambient_tex': 'C_3^4:C_6:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': False, 'core_order': 3, 'counter': 97, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3492.216.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 107638135
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.3492', 'ambient_counter': 3492, 'ambient_order': 1944, 'ambient_tex': 'C_3^4:C_6:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 3, 'counter': 98, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3492.216.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 107638136
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.3492', 'ambient_counter': 3492, 'ambient_order': 1944, 'ambient_tex': 'C_3^4:C_6:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 972, 'characteristic': False, 'core_order': 3, 'counter': 99, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3492.216.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 107638012
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.3492', 'ambient_counter': 3492, 'ambient_order': 1944, 'ambient_tex': 'C_3^4:C_6:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 3, 'counter': 100, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3492.216.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 107638013
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.3492', 'ambient_counter': 3492, 'ambient_order': 1944, 'ambient_tex': 'C_3^4:C_6:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 3, 'counter': 101, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3492.216.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 107638014
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.3492', 'ambient_counter': 3492, 'ambient_order': 1944, 'ambient_tex': 'C_3^4:C_6:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 1, 'counter': 102, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3492.216.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 107638015
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.3492', 'ambient_counter': 3492, 'ambient_order': 1944, 'ambient_tex': 'C_3^4:C_6:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 1, 'counter': 103, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3492.216.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 107638016
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.3492', 'ambient_counter': 3492, 'ambient_order': 1944, 'ambient_tex': 'C_3^4:C_6:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 104, 'cyclic': False, 'direct': None, 'hall': 2, 'label': '1944.3492.243.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '243.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 243, 'quotient_simple': 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': 2}
  • id: 107638017
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1944.3492', 'ambient_counter': 3492, 'ambient_order': 1944, 'ambient_tex': 'C_3^4:C_6:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 216, 'characteristic': False, 'core_order': 3, 'counter': 105, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1944.3492.324.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '324.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 107638018
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1944.3492', 'ambient_counter': 3492, 'ambient_order': 1944, 'ambient_tex': 'C_3^4:C_6:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 106, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1944.3492.324.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '324.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 107638019
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1944.3492', 'ambient_counter': 3492, 'ambient_order': 1944, 'ambient_tex': 'C_3^4:C_6:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 3, 'counter': 107, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3492.324.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 107638020
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1944.3492', 'ambient_counter': 3492, 'ambient_order': 1944, 'ambient_tex': 'C_3^4:C_6:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 216, 'characteristic': False, 'core_order': 3, 'counter': 108, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1944.3492.324.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '324.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 107638021
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1944.3492', 'ambient_counter': 3492, 'ambient_order': 1944, 'ambient_tex': 'C_3^4:C_6:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 3, 'counter': 109, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1944.3492.324.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '324.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 107638023
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1944.3492', 'ambient_counter': 3492, 'ambient_order': 1944, 'ambient_tex': 'C_3^4:C_6:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': False, 'core_order': 1, 'counter': 110, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1944.3492.324.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '324.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 107638024
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1944.3492', 'ambient_counter': 3492, 'ambient_order': 1944, 'ambient_tex': 'C_3^4:C_6:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 54, 'characteristic': False, 'core_order': 1, 'counter': 111, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3492.324.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 107638025
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1944.3492', 'ambient_counter': 3492, 'ambient_order': 1944, 'ambient_tex': 'C_3^4:C_6:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 3, 'counter': 112, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1944.3492.324.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '324.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 324, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 107638026
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1944.3492', 'ambient_counter': 3492, 'ambient_order': 1944, 'ambient_tex': 'C_3^4:C_6:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 113, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3492.324.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
  • id: 107638027
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1944.3492', 'ambient_counter': 3492, 'ambient_order': 1944, 'ambient_tex': 'C_3^4:C_6:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 114, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3492.324.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
  • id: 107638028
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1944.3492', 'ambient_counter': 3492, 'ambient_order': 1944, 'ambient_tex': 'C_3^4:C_6:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 3, 'characteristic': False, 'core_order': 1, 'counter': 115, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3492.324.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '324.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
  • id: 107638029
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1944.3492', 'ambient_counter': 3492, 'ambient_order': 1944, 'ambient_tex': 'C_3^4:C_6:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 116, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1944.3492.486.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '486.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 486, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 107638030
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1944.3492', 'ambient_counter': 3492, 'ambient_order': 1944, 'ambient_tex': 'C_3^4:C_6:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 216, 'characteristic': False, 'core_order': 1, 'counter': 117, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1944.3492.486.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '486.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 486, 'quotient_simple': 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: 107638031
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1944.3492', 'ambient_counter': 3492, 'ambient_order': 1944, 'ambient_tex': 'C_3^4:C_6:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 118, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1944.3492.486.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '486.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 486, 'quotient_simple': 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: 107638032
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1944.3492', 'ambient_counter': 3492, 'ambient_order': 1944, 'ambient_tex': 'C_3^4:C_6:C_4', 'central': True, 'central_factor': False, 'centralizer_order': 1944, 'characteristic': True, 'core_order': 3, 'counter': 119, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '1944.3492.648.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '648.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '648.715', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 715, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 648, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_3^3:(C_4\\times S_3)', 'simple': True, 'solvable': True, 'special_labels': ['Z', 'Phi', 'U0', 'D2', 'C6'], 'split': False, 'standard_generators': False, 'stem': True, 'subgroup': '3.1', 'subgroup_hash': 1, 'subgroup_order': 3, 'subgroup_tex': 'C_3', 'supersolvable': True, 'sylow': 0}
  • id: 107638034
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1944.3492', 'ambient_counter': 3492, 'ambient_order': 1944, 'ambient_tex': 'C_3^4:C_6:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 972, 'characteristic': False, 'core_order': 3, 'counter': 120, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '1944.3492.648.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '648.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '648.541', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 541, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 648, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'S_3\\times \\He_3:C_4', '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: 107638035
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1944.3492', 'ambient_counter': 3492, 'ambient_order': 1944, 'ambient_tex': 'C_3^4:C_6:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 972, 'characteristic': False, 'core_order': 1, 'counter': 121, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1944.3492.648.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '3.1', 'subgroup_hash': 1, 'subgroup_order': 3, 'subgroup_tex': 'C_3', 'supersolvable': True, 'sylow': 0}
  • id: 107638036
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1944.3492', 'ambient_counter': 3492, 'ambient_order': 1944, 'ambient_tex': 'C_3^4:C_6:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': False, 'core_order': 1, 'counter': 122, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1944.3492.648.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '3.1', 'subgroup_hash': 1, 'subgroup_order': 3, 'subgroup_tex': 'C_3', 'supersolvable': True, 'sylow': 0}
  • id: 107638037
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1944.3492', 'ambient_counter': 3492, 'ambient_order': 1944, 'ambient_tex': 'C_3^4:C_6:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 81, 'characteristic': False, 'core_order': 1, 'counter': 123, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1944.3492.648.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '648.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '3.1', 'subgroup_hash': 1, 'subgroup_order': 3, 'subgroup_tex': 'C_3', 'supersolvable': True, 'sylow': 0}
  • id: 107638038
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1944.3492', 'ambient_counter': 3492, 'ambient_order': 1944, 'ambient_tex': 'C_3^4:C_6:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 216, 'characteristic': False, 'core_order': 1, 'counter': 124, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1944.3492.972.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '972.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 972, '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: 107638039
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1944.3492', 'ambient_counter': 3492, 'ambient_order': 1944, 'ambient_tex': 'C_3^4:C_6:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 216, 'characteristic': False, 'core_order': 1, 'counter': 125, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1944.3492.972.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '972.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 972, '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: 107638040
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1944.3492', 'ambient_counter': 3492, 'ambient_order': 1944, 'ambient_tex': 'C_3^4:C_6:C_4', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 126, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1944.3492.972.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '972.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 972, '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: 107638041
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1944.3492', 'ambient_counter': 3492, 'ambient_order': 1944, 'ambient_tex': 'C_3^4:C_6:C_4', 'central': True, 'central_factor': False, 'centralizer_order': 1944, 'characteristic': True, 'core_order': 1, 'counter': 127, 'cyclic': True, 'direct': True, 'hall': 1, 'label': '1944.3492.1944.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '1944.a1', 'outer_equivalence': True, 'perfect': True, 'proper': False, 'quotient': '1944.3492', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3492, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 1944, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_3^4:C_6:C_4', 'simple': False, 'solvable': True, 'special_labels': ['PC', 'U1', 'D3', 'C7'], 'split': True, 'standard_generators': False, 'stem': True, 'subgroup': '1.1', 'subgroup_hash': 1, 'subgroup_order': 1, 'subgroup_tex': 'C_1', 'supersolvable': True, 'sylow': 1}
• gps_subgroup_data •

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

  
  
  • id: 107638136
    {'ambient': '1944.3492', 'aut_centralizer_order': 648, 'aut_label': '216.e1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '12.4', 'aut_weyl_index': 5184, 'centralizer': '2.b1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['72.a1', '72.g1', '108.f1'], 'contains': ['648.b1', '648.c1'], 'core': '648.b1', 'coset_action_label': None, 'count': 8, 'diagramx': [4113, -1, 6039, -1], 'generators': [650, 24], 'label': '1944.3492.216.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '72.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1', 'old_label': '216.e1', 'projective_image': '1944.3492', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.e1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 107638010
    {'ambient': '1944.3492', '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': '648.a1', 'complements': ['1944.a1'], 'conjugacy_class_count': 1, 'contained_in': [], 'contains': ['2.a1', '2.b1', '2.c1', '3.a1', '9.b1'], 'core': '1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8022, 4157, 3255, 5747], 'generators': [1, 24, 72, 18, 2, 648, 216, 36], 'label': '1944.3492.1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '1.a1', 'normal_contained_in': [], 'normal_contains': ['2.a1', '2.b1', '2.c1'], 'normalizer': '1.a1', 'old_label': '1.a1', 'projective_image': '648.715', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1.a1', 'subgroup_fusion': None, 'weyl_group': '648.715'}
  • id: 107638011
    {'ambient': '1944.3492', 'aut_centralizer_order': 6, 'aut_label': '6.b1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '864.4662', 'aut_weyl_index': 72, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['2.a1', '3.a1'], 'contains': ['12.a1', '12.b1', '12.f1', '18.b1', '18.c1'], 'core': '12.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [5608, -1, 5252, -1], 'generators': [1, 648, 1512, 36, 2, 1800], 'label': '1944.3492.6.b1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '6.b1', 'projective_image': '648.715', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.b1', 'subgroup_fusion': None, 'weyl_group': '216.156'}
  • id: 107638012
    {'ambient': '1944.3492', 'aut_centralizer_order': 324, 'aut_label': '216.f1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '4.2', 'aut_weyl_index': 15552, 'centralizer': '24.c1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['72.c1', '72.g1', '72.h1', '108.d1', '108.i1', '108.n1'], 'contains': ['648.b1', '648.d1', '648.e1'], 'core': '648.b1', 'coset_action_label': None, 'count': 48, 'diagramx': [2759, -1, 6771, -1], 'generators': [2, 1152], 'label': '1944.3492.216.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.c1', 'old_label': '216.f1', 'projective_image': '1944.3492', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.f1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 107638013
    {'ambient': '1944.3492', 'aut_centralizer_order': 54, 'aut_label': '216.g1', 'aut_quo_index': None, 'aut_stab_index': 96, 'aut_weyl_group': '12.4', 'aut_weyl_index': 5184, 'centralizer': '24.c1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['72.d1', '72.g1', '72.h1', '108.o1'], 'contains': ['648.b1', '648.e1'], 'core': '648.b1', 'coset_action_label': None, 'count': 96, 'diagramx': [1099, -1, 7641, -1], 'generators': [1154, 24], 'label': '1944.3492.216.g1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.g1', 'old_label': '216.g1', 'projective_image': '1944.3492', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.g1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 107638014
    {'ambient': '1944.3492', 'aut_centralizer_order': 162, 'aut_label': '216.h1', 'aut_quo_index': None, 'aut_stab_index': 96, 'aut_weyl_group': '4.2', 'aut_weyl_index': 15552, 'centralizer': '24.c1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['72.c1', '72.g1', '108.j1'], 'contains': ['648.c1', '648.d1', '648.e1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 96, 'diagramx': [3445, -1, 6405, -1], 'generators': [650, 1152], 'label': '1944.3492.216.h1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.d1', 'old_label': '216.h1', 'projective_image': '1944.3492', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.h1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 107638015
    {'ambient': '1944.3492', 'aut_centralizer_order': 27, 'aut_label': '216.i1', 'aut_quo_index': None, 'aut_stab_index': 192, 'aut_weyl_group': '12.4', 'aut_weyl_index': 5184, 'centralizer': '24.c1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['72.d1', '72.g1'], 'contains': ['648.c1', '648.e1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 192, 'diagramx': [1482, -1, 7459, -1], 'generators': [1154, 672], 'label': '1944.3492.216.i1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.c1', 'old_label': '216.i1', 'projective_image': '1944.3492', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.i1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 107638016
    {'ambient': '1944.3492', 'aut_centralizer_order': 384, 'aut_label': '243.a1', 'aut_quo_index': None, 'aut_stab_index': 81, 'aut_weyl_group': '2.1', 'aut_weyl_index': 31104, 'centralizer': '81.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['81.a1', '81.b1'], 'contains': ['486.a1', '486.b1', '486.c1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 81, 'diagramx': [8988, -1, 1666, -1], 'generators': [1, 54], 'label': '1944.3492.243.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1', 'old_label': '243.a1', 'projective_image': '1944.3492', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '243.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 107638017
    {'ambient': '1944.3492', 'aut_centralizer_order': 3456, 'aut_label': '324.a1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '2.1', 'aut_weyl_index': 31104, 'centralizer': '9.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.b1', '108.c1', '162.a1'], 'contains': ['648.a1', '972.a1'], 'core': '648.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [5151, -1, 5691, -1], 'generators': [1, 648], 'label': '1944.3492.324.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '324.a1', 'projective_image': '648.715', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 107638018
    {'ambient': '1944.3492', 'aut_centralizer_order': 288, 'aut_label': '324.b1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '2.1', 'aut_weyl_index': 31104, 'centralizer': '108.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['108.b1', '108.d1', '162.b1'], 'contains': ['648.d1', '972.a1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 108, 'diagramx': [4636, -1, 5852, -1], 'generators': [1, 1152], 'label': '1944.3492.324.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.a1', 'old_label': '324.b1', 'projective_image': '1944.3492', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 107638019
    {'ambient': '1944.3492', 'aut_centralizer_order': 864, 'aut_label': '324.c1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '6.1', 'aut_weyl_index': 10368, 'centralizer': '18.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['108.a1', '108.c1', '108.d1', '162.c1'], 'contains': ['648.b1', '972.a1'], 'core': '648.b1', 'coset_action_label': None, 'count': 12, 'diagramx': [5555, -1, 5531, -1], 'generators': [1, 2], 'label': '1944.3492.324.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '108.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '324.c1', 'projective_image': '1944.3492', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.c1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 107638020
    {'ambient': '1944.3492', 'aut_centralizer_order': 3456, 'aut_label': '324.d1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '2.1', 'aut_weyl_index': 31104, 'centralizer': '9.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.e1', '108.h1', '162.a1', '162.d1', '162.e1'], 'contains': ['648.a1', '972.b1'], 'core': '648.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [7064, -1, 3732, -1], 'generators': [36, 648], 'label': '1944.3492.324.d1', 'mobius_quo': None, 'mobius_sub': -54, 'normal_closure': '36.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '324.d1', 'projective_image': '648.715', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.d1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 107638021
    {'ambient': '1944.3492', 'aut_centralizer_order': 864, 'aut_label': '324.e1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '2.1', 'aut_weyl_index': 31104, 'centralizer': '18.f1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['108.e1', '108.f1', '108.g1', '108.i1', '162.c1', '162.f1', '162.g1'], 'contains': ['648.b1', '972.b1'], 'core': '648.b1', 'coset_action_label': None, 'count': 36, 'diagramx': [7428, -1, 3571, -1], 'generators': [36, 2], 'label': '1944.3492.324.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '324.e1', 'projective_image': '1944.3492', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.e1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 107638022
    {'ambient': '1944.3492', 'aut_centralizer_order': 1, 'aut_label': '6.c1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '5184.qr', 'aut_weyl_index': 12, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['2.a1'], 'contains': ['12.c1', '12.d1', '12.g1', '18.c1', '18.d1', '18.e1'], 'core': '36.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [5096, -1, 4776, -1], 'generators': [1, 1800, 24, 36, 648, 2], 'label': '1944.3492.6.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.c1', 'old_label': '6.c1', 'projective_image': '648.715', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.c1', 'subgroup_fusion': None, 'weyl_group': '108.39'}
  • id: 107638023
    {'ambient': '1944.3492', 'aut_centralizer_order': 432, 'aut_label': '324.f1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '2.1', 'aut_weyl_index': 31104, 'centralizer': '18.f1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['108.e1', '108.f1', '108.j1', '162.h1'], 'contains': ['648.c1', '972.b1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [7246, -1, 3411, -1], 'generators': [36, 650], 'label': '1944.3492.324.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.f1', 'old_label': '324.f1', 'projective_image': '1944.3492', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.f1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 107638024
    {'ambient': '1944.3492', 'aut_centralizer_order': 864, 'aut_label': '324.g1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '6.1', 'aut_weyl_index': 10368, 'centralizer': '36.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['108.h1', '108.i1', '108.j1', '162.b1'], 'contains': ['648.d1', '972.b1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [5946, -1, 4328, -1], 'generators': [36, 1800], 'label': '1944.3492.324.g1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.c1', 'old_label': '324.g1', 'projective_image': '1944.3492', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.g1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 107638025
    {'ambient': '1944.3492', 'aut_centralizer_order': 384, 'aut_label': '324.h1', 'aut_quo_index': None, 'aut_stab_index': 81, 'aut_weyl_group': '2.1', 'aut_weyl_index': 31104, 'centralizer': '81.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['108.k1', '108.l1', '108.m1', '162.a1'], 'contains': ['648.a1', '972.c1'], 'core': '648.a1', 'coset_action_label': None, 'count': 81, 'diagramx': [1891, -1, 7813, -1], 'generators': [37, 648], 'label': '1944.3492.324.h1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1', 'old_label': '324.h1', 'projective_image': '648.715', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.h1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 107638026
    {'ambient': '1944.3492', 'aut_centralizer_order': 96, 'aut_label': '324.i1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '6.1', 'aut_weyl_index': 10368, 'centralizer': '162.d1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['108.k1', '108.n1', '108.o1', '108.p1', '162.c1'], 'contains': ['648.b1', '972.c1'], 'core': '648.b1', 'coset_action_label': None, 'count': 108, 'diagramx': [2157, -1, 6943, -1], 'generators': [37, 2], 'label': '1944.3492.324.i1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '324.i1', 'projective_image': '1944.3492', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.i1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 107638027
    {'ambient': '1944.3492', 'aut_centralizer_order': 96, 'aut_label': '324.j1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '6.1', 'aut_weyl_index': 10368, 'centralizer': '324.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['108.l1', '108.n1', '162.b1'], 'contains': ['648.d1', '972.c1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 108, 'diagramx': [3124, -1, 7287, -1], 'generators': [37, 1800], 'label': '1944.3492.324.j1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.a1', 'old_label': '324.j1', 'projective_image': '1944.3492', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.j1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 107638028
    {'ambient': '1944.3492', 'aut_centralizer_order': 12, 'aut_label': '324.k1', 'aut_quo_index': None, 'aut_stab_index': 864, 'aut_weyl_group': '6.1', 'aut_weyl_index': 10368, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['108.m1', '108.n1', '108.o1'], 'contains': ['648.e1', '972.c1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 864, 'diagramx': [936, -1, 7974, -1], 'generators': [37, 1802], 'label': '1944.3492.324.k1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.m1', 'old_label': '324.k1', 'projective_image': '1944.3492', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '324.k1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 107638029
    {'ambient': '1944.3492', 'aut_centralizer_order': 768, 'aut_label': '486.a1', 'aut_quo_index': None, 'aut_stab_index': 81, 'aut_weyl_group': '1.1', 'aut_weyl_index': 62208, 'centralizer': '81.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['162.a1', '162.b1', '162.c1', '243.a1'], 'contains': ['972.a1', '972.b1', '972.c1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 81, 'diagramx': [6447, -1, 4863, -1], 'generators': [1, 36], 'label': '1944.3492.486.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1', 'old_label': '486.a1', 'projective_image': '1944.3492', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '486.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 107638030
    {'ambient': '1944.3492', 'aut_centralizer_order': 3456, 'aut_label': '486.b1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '2.1', 'aut_weyl_index': 31104, 'centralizer': '9.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['162.d1', '162.f1', '162.h1', '243.a1'], 'contains': ['972.b1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [8112, -1, 1416, -1], 'generators': [54], 'label': '1944.3492.486.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '18.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '486.b1', 'projective_image': '1944.3492', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '486.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 107638031
    {'ambient': '1944.3492', 'aut_centralizer_order': 384, 'aut_label': '486.c1', 'aut_quo_index': None, 'aut_stab_index': 81, 'aut_weyl_group': '2.1', 'aut_weyl_index': 31104, 'centralizer': '81.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['162.e1', '162.g1', '243.a1'], 'contains': ['972.b1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 81, 'diagramx': [8853, -1, 2261, -1], 'generators': [31], 'label': '1944.3492.486.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1', 'old_label': '486.c1', 'projective_image': '1944.3492', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '486.c1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 107638032
    {'ambient': '1944.3492', 'aut_centralizer_order': 31104, 'aut_label': '648.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 31104, 'centralizer': '1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['216.a1', '216.c1', '216.d1', '324.a1', '324.d1', '324.h1'], 'contains': ['1944.a1'], 'core': '648.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2836, 8435, 6887, 9403], 'generators': [648], 'label': '1944.3492.648.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '648.a1', 'normal_contained_in': ['72.b1', '216.a1'], 'normal_contains': ['1944.a1'], 'normalizer': '1.a1', 'old_label': '648.a1', 'projective_image': '648.715', 'quotient_action_image': '1.1', 'quotient_action_kernel': '648.715', 'quotient_action_kernel_order': 648, 'quotient_fusion': None, 'short_label': '648.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 107638033
    {'ambient': '1944.3492', 'aut_centralizer_order': 6, 'aut_label': '6.d1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '864.4662', 'aut_weyl_index': 72, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['2.c1', '3.a1'], 'contains': ['12.a1', '18.h1', '54.f1'], 'core': '12.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [8371, -1, 3781, -1], 'generators': [31, 648, 216, 36, 2, 936], 'label': '1944.3492.6.d1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '6.d1', 'projective_image': '648.715', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.d1', 'subgroup_fusion': None, 'weyl_group': '216.156'}
  • id: 107638034
    {'ambient': '1944.3492', 'aut_centralizer_order': 7776, 'aut_label': '648.b1', 'aut_quo_index': 1, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 31104, 'centralizer': '2.b1', 'complements': ['3.a1'], 'conjugacy_class_count': 4, 'contained_in': ['216.a1', '216.b1', '216.e1', '216.f1', '216.g1', '324.c1', '324.e1', '324.i1'], 'contains': ['1944.a1'], 'core': '648.b1', 'coset_action_label': None, 'count': 4, 'diagramx': [3018, 7598, 6566, 8559], 'generators': [2], 'label': '1944.3492.648.b1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '648.b1', 'normal_contained_in': ['216.a1', '216.b1'], 'normal_contains': ['1944.a1'], 'normalizer': '1.a1', 'old_label': '648.b1', 'projective_image': '1944.3492', 'quotient_action_image': '2.1', 'quotient_action_kernel': '324.110', 'quotient_action_kernel_order': 324, 'quotient_fusion': None, 'short_label': '648.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 107638035
    {'ambient': '1944.3492', 'aut_centralizer_order': 3888, 'aut_label': '648.c1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '2.1', 'aut_weyl_index': 31104, 'centralizer': '2.b1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['216.a1', '216.e1', '216.h1', '216.i1', '324.f1'], 'contains': ['1944.a1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [3318, -1, 6405, -1], 'generators': [650], 'label': '1944.3492.648.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '216.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1', 'old_label': '648.c1', 'projective_image': '1944.3492', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.c1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 107638036
    {'ambient': '1944.3492', 'aut_centralizer_order': 2592, 'aut_label': '648.d1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '2.1', 'aut_weyl_index': 31104, 'centralizer': '12.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['216.c1', '216.f1', '216.h1', '324.b1', '324.g1', '324.j1'], 'contains': ['1944.a1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [3748, -1, 6727, -1], 'generators': [1152], 'label': '1944.3492.648.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '72.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.c1', 'old_label': '648.d1', 'projective_image': '1944.3492', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.d1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 107638037
    {'ambient': '1944.3492', 'aut_centralizer_order': 324, 'aut_label': '648.e1', 'aut_quo_index': None, 'aut_stab_index': 96, 'aut_weyl_group': '2.1', 'aut_weyl_index': 31104, 'centralizer': '24.c1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['216.d1', '216.f1', '216.g1', '216.h1', '216.i1', '324.k1'], 'contains': ['1944.a1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 96, 'diagramx': [1341, -1, 7459, -1], 'generators': [1154], 'label': '1944.3492.648.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.g1', 'old_label': '648.e1', 'projective_image': '1944.3492', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '648.e1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 107638038
    {'ambient': '1944.3492', 'aut_centralizer_order': 6912, 'aut_label': '972.a1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '1.1', 'aut_weyl_index': 62208, 'centralizer': '9.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['324.a1', '324.b1', '324.c1', '486.a1'], 'contains': ['1944.a1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [5151, -1, 5691, -1], 'generators': [1], 'label': '1944.3492.972.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '108.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '972.a1', 'projective_image': '1944.3492', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 107638039
    {'ambient': '1944.3492', 'aut_centralizer_order': 6912, 'aut_label': '972.b1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '1.1', 'aut_weyl_index': 62208, 'centralizer': '9.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['324.d1', '324.e1', '324.f1', '324.g1', '486.a1', '486.b1', '486.c1'], 'contains': ['1944.a1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [7172, -1, 3652, -1], 'generators': [36], 'label': '1944.3492.972.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '972.b1', 'projective_image': '1944.3492', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 107638040
    {'ambient': '1944.3492', 'aut_centralizer_order': 768, 'aut_label': '972.c1', 'aut_quo_index': None, 'aut_stab_index': 81, 'aut_weyl_group': '1.1', 'aut_weyl_index': 62208, 'centralizer': '81.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['324.h1', '324.i1', '324.j1', '324.k1', '486.a1'], 'contains': ['1944.a1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 81, 'diagramx': [2425, -1, 7166, -1], 'generators': [37], 'label': '1944.3492.972.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1', 'old_label': '972.c1', 'projective_image': '1944.3492', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '972.c1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 107638041
    {'ambient': '1944.3492', 'aut_centralizer_order': None, 'aut_label': '1944.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1.a1', 'complements': ['1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['648.a1', '648.b1', '648.c1', '648.d1', '648.e1', '972.a1', '972.b1', '972.c1'], 'contains': [], 'core': '1944.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3192, 8016, 6646, 8981], 'generators': [], 'label': '1944.3492.1944.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '1944.a1', 'normal_contained_in': ['648.a1', '648.b1'], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '1944.a1', 'projective_image': '1944.3492', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1944.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 107638042
    {'ambient': '1944.3492', 'aut_centralizer_order': 9, 'aut_label': '8.a1', 'aut_quo_index': 4, 'aut_stab_index': 1, 'aut_weyl_group': None, 'aut_weyl_index': 9, 'centralizer': '72.a1', 'complements': ['243.a1'], 'conjugacy_class_count': 1, 'contained_in': ['4.a1', '4.b1', '4.c1'], 'contains': ['24.a1', '24.b1', '24.c1'], 'core': '8.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3302, 5784, 7818, 3650], 'generators': [2, 24, 1152, 1512], 'label': '1944.3492.8.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': ['4.a1', '4.b1', '4.c1'], 'normal_contains': ['24.a1', '72.a1'], 'normalizer': '1.a1', 'old_label': '8.a1', 'projective_image': '648.715', 'quotient_action_image': '8.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '8.a1', 'subgroup_fusion': None, 'weyl_group': '72.45'}
  • id: 107638043
    {'ambient': '1944.3492', 'aut_centralizer_order': 48, 'aut_label': '9.a1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '144.182', 'aut_weyl_index': 432, 'centralizer': '324.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1'], 'contains': ['18.a1', '18.b1', '18.h1', '81.a1'], 'core': '18.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [7945, -1, 3277, -1], 'generators': [1, 648, 216, 54, 36, 936], 'label': '1944.3492.9.a1', 'mobius_quo': None, 'mobius_sub': 3, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '9.a1', 'projective_image': '648.715', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '9.a1', 'subgroup_fusion': None, 'weyl_group': '36.9'}
  • id: 107638044
    {'ambient': '1944.3492', 'aut_centralizer_order': 4, 'aut_label': '9.b1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '1728.47845', 'aut_weyl_index': 36, 'centralizer': '162.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1'], 'contains': ['18.d1', '18.f1', '18.g1', '27.a1', '27.b1'], 'core': '36.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [9310, -1, 2092, -1], 'generators': [1, 24, 2, 18, 648, 36], 'label': '1944.3492.9.b1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '9.b1', 'projective_image': '648.715', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '9.b1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 107638045
    {'ambient': '1944.3492', 'aut_centralizer_order': 54, 'aut_label': '12.a1', 'aut_quo_index': 2, 'aut_stab_index': 4, 'aut_weyl_group': '288.1027', 'aut_weyl_index': 216, 'centralizer': '72.a1', 'complements': [], 'conjugacy_class_count': 4, 'contained_in': ['4.b1', '6.a1', '6.b1', '6.d1'], 'contains': ['24.a1', '36.b1', '36.g1'], 'core': '12.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [6387, 3761, 4801, 6087], 'generators': [36, 648, 2, 1800, 1512], 'label': '1944.3492.12.a1', 'mobius_quo': 0, 'mobius_sub': -6, 'normal_closure': '12.a1', 'normal_contained_in': ['4.b1', '6.a1'], 'normal_contains': ['24.a1', '36.b1'], 'normalizer': '1.a1', 'old_label': '12.a1', 'projective_image': '648.715', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.a1', 'subgroup_fusion': None, 'weyl_group': '72.45'}
  • id: 107638046
    {'ambient': '1944.3492', 'aut_centralizer_order': 6, 'aut_label': '12.b1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '864.4662', 'aut_weyl_index': 72, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['4.a1', '6.b1'], 'contains': ['24.a1', '36.c1', '36.d1'], 'core': '24.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [4120, -1, 6410, -1], 'generators': [1, 2, 1152, 1512, 648], 'label': '1944.3492.12.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '12.b1', 'projective_image': '648.715', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.b1', 'subgroup_fusion': None, 'weyl_group': '216.156'}
  • id: 107638047
    {'ambient': '1944.3492', 'aut_centralizer_order': 3, 'aut_label': '12.c1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '5184.qr', 'aut_weyl_index': 12, 'centralizer': '216.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['4.a1', '6.c1'], 'contains': ['24.c1', '36.a1', '36.d1', '36.e1'], 'core': '36.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [3664, -1, 5986, -1], 'generators': [1, 24, 1152, 648, 2], 'label': '1944.3492.12.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '12.c1', 'projective_image': '648.715', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.c1', 'subgroup_fusion': None, 'weyl_group': '108.39'}
  • id: 107638048
    {'ambient': '1944.3492', 'aut_centralizer_order': 9, 'aut_label': '12.d1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '576.8325', 'aut_weyl_index': 108, 'centralizer': '72.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['4.b1', '6.c1'], 'contains': ['24.c1', '36.f1', '36.g1', '36.h1', '36.i1'], 'core': '72.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [5885, -1, 3678, -1], 'generators': [36, 1800, 2, 24, 648], 'label': '1944.3492.12.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.c1', 'old_label': '12.d1', 'projective_image': '648.715', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.d1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 107638049
    {'ambient': '1944.3492', 'aut_centralizer_order': 1, 'aut_label': '2.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': None, 'aut_weyl_index': 1, 'centralizer': '648.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['1.a1'], 'contains': ['4.a1', '4.b1', '4.c1', '6.b1', '6.c1'], 'core': '2.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5226, 6900, 5013, 2982], 'generators': [1, 1512, 1800, 36, 648, 2, 24], 'label': '1944.3492.2.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.a1', 'normal_contained_in': ['1.a1'], 'normal_contains': ['4.a1', '4.b1', '4.c1'], 'normalizer': '1.a1', 'old_label': '2.a1', 'projective_image': '648.715', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2.a1', 'subgroup_fusion': None, 'weyl_group': '648.715'}
  • id: 107638050
    {'ambient': '1944.3492', 'aut_centralizer_order': 1, 'aut_label': '12.e1', 'aut_quo_index': None, 'aut_stab_index': 96, 'aut_weyl_group': '648.555', 'aut_weyl_index': 96, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['4.c1'], 'contains': ['24.b1', '36.j1', '36.k1', '36.m1', '36.o1'], 'core': '216.a1', 'coset_action_label': None, 'count': 96, 'diagramx': [868, -1, 9103, -1], 'generators': [37, 648, 1514, 24, 1800], 'label': '1944.3492.12.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.e1', 'old_label': '12.e1', 'projective_image': '648.715', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.e1', 'subgroup_fusion': None, 'weyl_group': '54.14'}
  • id: 107638051
    {'ambient': '1944.3492', 'aut_centralizer_order': 6, 'aut_label': '12.f1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '864.4662', 'aut_weyl_index': 72, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['4.c1', '6.b1'], 'contains': ['24.a1', '36.j1', '36.m1', '36.n1'], 'core': '24.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [3199, -1, 8195, -1], 'generators': [37, 648, 2, 1800, 1512], 'label': '1944.3492.12.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '12.f1', 'projective_image': '648.715', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.f1', 'subgroup_fusion': None, 'weyl_group': '216.156'}
  • id: 107638052
    {'ambient': '1944.3492', 'aut_centralizer_order': 1, 'aut_label': '12.g1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '5184.qr', 'aut_weyl_index': 12, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['4.c1', '6.c1'], 'contains': ['24.c1', '36.j1', '36.k1', '36.l1', '36.p1'], 'core': '72.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [2651, -1, 7369, -1], 'generators': [37, 1800, 648, 2, 24], 'label': '1944.3492.12.g1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.c1', 'old_label': '12.g1', 'projective_image': '648.715', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.g1', 'subgroup_fusion': None, 'weyl_group': '108.39'}
  • id: 107638053
    {'ambient': '1944.3492', 'aut_centralizer_order': 432, 'aut_label': '18.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '144.182', 'aut_weyl_index': 432, 'centralizer': '36.a1', 'complements': ['108.a1', '108.p1', '108.o1'], 'conjugacy_class_count': 1, 'contained_in': ['6.a1', '9.a1'], 'contains': ['36.b1', '162.d1'], 'core': '18.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7664, 2529, 2938, 8301], 'generators': [54, 648, 36, 936, 216], 'label': '1944.3492.18.a1', 'mobius_quo': 0, 'mobius_sub': -27, 'normal_closure': '18.a1', 'normal_contained_in': ['6.a1'], 'normal_contains': ['36.b1'], 'normalizer': '1.a1', 'old_label': '18.a1', 'projective_image': '648.715', 'quotient_action_image': '1.1', 'quotient_action_kernel': '18.4', 'quotient_action_kernel_order': 18, 'quotient_fusion': None, 'short_label': '18.a1', 'subgroup_fusion': None, 'weyl_group': '36.9'}
  • id: 107638054
    {'ambient': '1944.3492', 'aut_centralizer_order': 48, 'aut_label': '18.b1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '144.182', 'aut_weyl_index': 432, 'centralizer': '324.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1', '9.a1'], 'contains': ['36.b1', '36.c1', '36.n1', '54.a1'], 'core': '36.b1', 'coset_action_label': None, 'count': 9, 'diagramx': [5658, -1, 5568, -1], 'generators': [1, 648, 36, 1800, 1512], 'label': '1944.3492.18.b1', 'mobius_quo': None, 'mobius_sub': -3, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '18.b1', 'projective_image': '648.715', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.b1', 'subgroup_fusion': None, 'weyl_group': '36.9'}
  • id: 107638055
    {'ambient': '1944.3492', 'aut_centralizer_order': 6, 'aut_label': '18.c1', 'aut_quo_index': None, 'aut_stab_index': 144, 'aut_weyl_group': '72.46', 'aut_weyl_index': 864, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['6.b1', '6.c1'], 'contains': ['36.d1', '36.g1', '36.j1', '54.a1', '54.b1', '54.c1'], 'core': '216.a1', 'coset_action_label': None, 'count': 144, 'diagramx': [4849, -1, 5185, -1], 'generators': [1, 1800, 36, 648, 2], 'label': '1944.3492.18.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.c1', 'old_label': '18.c1', 'projective_image': '648.715', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.c1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 107638056
    {'ambient': '1944.3492', 'aut_centralizer_order': 8, 'aut_label': '18.d1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '864.4661', 'aut_weyl_index': 72, 'centralizer': '162.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.c1', '9.b1'], 'contains': ['36.a1', '36.f1', '36.l1', '54.b1', '54.d1'], 'core': '36.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [7081, -1, 4038, -1], 'generators': [1, 24, 36, 648, 2], 'label': '1944.3492.18.d1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '18.d1', 'projective_image': '648.715', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.d1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 107638057
    {'ambient': '1944.3492', 'aut_centralizer_order': 2, 'aut_label': '18.e1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '2592.fv', 'aut_weyl_index': 24, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['6.c1'], 'contains': ['36.e1', '36.i1', '36.p1', '54.c1', '54.d1'], 'core': '108.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [5235, -1, 4408, -1], 'generators': [1, 1800, 36, 2, 24], 'label': '1944.3492.18.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.c1', 'old_label': '18.e1', 'projective_image': '1944.3492', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.e1', 'subgroup_fusion': None, 'weyl_group': '108.39'}
  • id: 107638058
    {'ambient': '1944.3492', 'aut_centralizer_order': 36, 'aut_label': '18.f1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '192.1475', 'aut_weyl_index': 324, 'centralizer': '18.f1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1', '9.b1'], 'contains': ['36.f1', '54.e1', '54.g1', '54.h1'], 'core': '72.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [8583, -1, 1070, -1], 'generators': [18, 36, 2, 24, 648], 'label': '1944.3492.18.f1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '18.f1', 'projective_image': '648.715', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.f1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 107638059
    {'ambient': '1944.3492', 'aut_centralizer_order': 4, 'aut_label': '18.g1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '1728.47845', 'aut_weyl_index': 36, 'centralizer': '162.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.c1', '9.b1'], 'contains': ['36.f1', '54.f1', '54.i1'], 'core': '72.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [9211, -1, 2567, -1], 'generators': [31, 24, 648, 36, 2], 'label': '1944.3492.18.g1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '18.g1', 'projective_image': '648.715', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.g1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 107638060
    {'ambient': '1944.3492', 'aut_centralizer_order': 9, 'aut_label': '2.b1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': None, 'aut_weyl_index': 9, 'centralizer': '72.a1', 'complements': ['972.a1', '972.c1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1'], 'contains': ['4.b1', '6.a1', '18.f1'], 'core': '2.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [7673, 1285, 2726, 8641], 'generators': [18, 216, 72, 2, 648, 24, 36], 'label': '1944.3492.2.b1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.b1', 'normal_contained_in': ['1.a1'], 'normal_contains': ['4.b1', '6.a1'], 'normalizer': '1.a1', 'old_label': '2.b1', 'projective_image': '648.715', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.b1', 'subgroup_fusion': None, 'weyl_group': '72.45'}
  • id: 107638061
    {'ambient': '1944.3492', 'aut_centralizer_order': 48, 'aut_label': '18.h1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '144.182', 'aut_weyl_index': 432, 'centralizer': '324.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.d1', '9.a1'], 'contains': ['36.b1', '162.e1'], 'core': '36.b1', 'coset_action_label': None, 'count': 9, 'diagramx': [8007, -1, 3344, -1], 'generators': [31, 648, 36, 936, 216], 'label': '1944.3492.18.h1', 'mobius_quo': None, 'mobius_sub': -3, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '18.h1', 'projective_image': '648.715', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.h1', 'subgroup_fusion': None, 'weyl_group': '36.9'}
  • id: 107638062
    {'ambient': '1944.3492', 'aut_centralizer_order': 54, 'aut_label': '24.a1', 'aut_quo_index': 2, 'aut_stab_index': 4, 'aut_weyl_group': '288.1027', 'aut_weyl_index': 216, 'centralizer': '72.a1', 'complements': ['81.b1'], 'conjugacy_class_count': 4, 'contained_in': ['8.a1', '12.a1', '12.b1', '12.f1'], 'contains': ['72.b1', '72.c1', '72.e1'], 'core': '24.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [3400, 5051, 7880, 5185], 'generators': [2, 1152, 1512], 'label': '1944.3492.24.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '24.a1', 'normal_contained_in': ['8.a1', '12.a1'], 'normal_contains': ['72.b1', '216.a1'], 'normalizer': '1.a1', 'old_label': '24.a1', 'projective_image': '648.715', 'quotient_action_image': '8.2', 'quotient_action_kernel': '3.1', 'quotient_action_kernel_order': 3, 'quotient_fusion': None, 'short_label': '24.a1', 'subgroup_fusion': None, 'weyl_group': '72.45'}
  • id: 107638063
    {'ambient': '1944.3492', 'aut_centralizer_order': 9, 'aut_label': '24.b1', 'aut_quo_index': None, 'aut_stab_index': 32, 'aut_weyl_group': '216.162', 'aut_weyl_index': 288, 'centralizer': '72.a1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['8.a1', '12.e1'], 'contains': ['72.c1', '72.d1', '72.e1', '72.f1'], 'core': '216.a1', 'coset_action_label': None, 'count': 32, 'diagramx': [638, -1, 9304, -1], 'generators': [1514, 24, 1152], 'label': '1944.3492.24.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1', 'old_label': '24.b1', 'projective_image': '648.715', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.b1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 107638064
    {'ambient': '1944.3492', 'aut_centralizer_order': 27, 'aut_label': '24.c1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '576.8325', 'aut_weyl_index': 108, 'centralizer': '24.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['8.a1', '12.c1', '12.d1', '12.g1'], 'contains': ['72.a1', '72.c1', '72.d1', '72.g1', '72.h1'], 'core': '72.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [2886, -1, 7320, -1], 'generators': [2, 24, 1152, 648], 'label': '1944.3492.24.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '24.c1', 'projective_image': '648.715', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.c1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 107638065
    {'ambient': '1944.3492', 'aut_centralizer_order': 24, 'aut_label': '27.a1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '24.14', 'aut_weyl_index': 2592, 'centralizer': '162.d1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['3.a1', '9.b1'], 'contains': ['54.b1', '54.e1', '54.f1', '81.a1', '81.b1'], 'core': '216.a1', 'coset_action_label': None, 'count': 108, 'diagramx': [9189, -1, 2092, -1], 'generators': [1, 2, 54, 648, 36], 'label': '1944.3492.27.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '27.a1', 'projective_image': '648.715', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '27.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 107638066
    {'ambient': '1944.3492', 'aut_centralizer_order': 8, 'aut_label': '27.b1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '864.4661', 'aut_weyl_index': 72, 'centralizer': '162.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['9.b1'], 'contains': ['54.d1', '54.h1', '54.i1', '81.b1'], 'core': '108.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [9818, -1, 1726, -1], 'generators': [1, 24, 18, 36, 2], 'label': '1944.3492.27.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '27.b1', 'projective_image': '1944.3492', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '27.b1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 107638067
    {'ambient': '1944.3492', 'aut_centralizer_order': 72, 'aut_label': '36.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '864.4661', 'aut_weyl_index': 72, 'centralizer': '18.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['12.c1', '18.d1'], 'contains': ['72.a1', '108.a1', '108.c1'], 'core': '36.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5439, 7633, 5522, 9133], 'generators': [1, 648, 2, 24], 'label': '1944.3492.36.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '36.a1', 'normal_contained_in': ['4.a1'], 'normal_contains': ['72.a1', '108.a1'], 'normalizer': '1.a1', 'old_label': '36.a1', 'projective_image': '648.715', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.a1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 107638068
    {'ambient': '1944.3492', 'aut_centralizer_order': 432, 'aut_label': '36.b1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '144.182', 'aut_weyl_index': 432, 'centralizer': '36.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['12.a1', '18.a1', '18.b1', '18.h1'], 'contains': ['72.b1', '108.h1'], 'core': '36.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [7078, 3703, 4727, 6977], 'generators': [36, 1800, 1512, 648], 'label': '1944.3492.36.b1', 'mobius_quo': 0, 'mobius_sub': 54, 'normal_closure': '36.b1', 'normal_contained_in': ['12.a1', '18.a1'], 'normal_contains': ['72.b1'], 'normalizer': '1.a1', 'old_label': '36.b1', 'projective_image': '648.715', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.b1', 'subgroup_fusion': None, 'weyl_group': '36.9'}
  • id: 107638069
    {'ambient': '1944.3492', 'aut_centralizer_order': 48, 'aut_label': '36.c1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '144.182', 'aut_weyl_index': 432, 'centralizer': '324.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.b1', '18.b1'], 'contains': ['72.b1', '108.b1'], 'core': '72.b1', 'coset_action_label': None, 'count': 9, 'diagramx': [4643, -1, 6642, -1], 'generators': [1, 1152, 1512, 648], 'label': '1944.3492.36.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '36.c1', 'projective_image': '648.715', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.c1', 'subgroup_fusion': None, 'weyl_group': '36.9'}
  • id: 107638070
    {'ambient': '1944.3492', 'aut_centralizer_order': 18, 'aut_label': '36.d1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '72.46', 'aut_weyl_index': 864, 'centralizer': '216.c1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['12.b1', '12.c1', '18.c1'], 'contains': ['72.c1', '108.b1', '108.c1', '108.d1'], 'core': '216.a1', 'coset_action_label': None, 'count': 48, 'diagramx': [2975, -1, 6251, -1], 'generators': [1, 1152, 648, 2], 'label': '1944.3492.36.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1', 'old_label': '36.d1', 'projective_image': '648.715', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.d1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 107638071
    {'ambient': '1944.3492', 'aut_centralizer_order': 1, 'aut_label': '2.c1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': None, 'aut_weyl_index': 1, 'centralizer': '648.a1', 'complements': ['972.a1', '972.c1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1'], 'contains': ['4.b1', '6.d1', '18.g1'], 'core': '2.c1', 'coset_action_label': None, 'count': 1, 'diagramx': [8374, 4157, 3781, 5747], 'generators': [31, 216, 936, 36, 648, 2, 24], 'label': '1944.3492.2.c1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.c1', 'normal_contained_in': ['1.a1'], 'normal_contains': ['4.b1'], 'normalizer': '1.a1', 'old_label': '2.c1', 'projective_image': '648.715', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.c1', 'subgroup_fusion': None, 'weyl_group': '648.715'}
  • id: 107638072
    {'ambient': '1944.3492', 'aut_centralizer_order': 6, 'aut_label': '36.e1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '864.4661', 'aut_weyl_index': 72, 'centralizer': '216.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.c1', '18.e1'], 'contains': ['72.h1', '108.a1', '108.d1'], 'core': '108.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [3361, -1, 5892, -1], 'generators': [1, 1152, 2, 24], 'label': '1944.3492.36.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.c1', 'old_label': '36.e1', 'projective_image': '1944.3492', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.e1', 'subgroup_fusion': None, 'weyl_group': '36.13'}
  • id: 107638073
    {'ambient': '1944.3492', 'aut_centralizer_order': 72, 'aut_label': '36.f1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '96.189', 'aut_weyl_index': 648, 'centralizer': '18.f1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.d1', '18.d1', '18.f1', '18.g1'], 'contains': ['72.a1', '108.e1', '108.f1', '108.g1'], 'core': '72.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [7585, -1, 2708, -1], 'generators': [36, 2, 24, 648], 'label': '1944.3492.36.f1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '36.f1', 'projective_image': '648.715', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.f1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 107638074
    {'ambient': '1944.3492', 'aut_centralizer_order': 54, 'aut_label': '36.g1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '24.14', 'aut_weyl_index': 2592, 'centralizer': '72.a1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['12.a1', '12.d1', '18.c1'], 'contains': ['72.c1', '108.e1', '108.h1', '108.i1', '108.j1'], 'core': '216.a1', 'coset_action_label': None, 'count': 48, 'diagramx': [5826, -1, 4125, -1], 'generators': [36, 2, 648, 1800], 'label': '1944.3492.36.g1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.c1', 'old_label': '36.g1', 'projective_image': '648.715', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.g1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 107638075
    {'ambient': '1944.3492', 'aut_centralizer_order': 9, 'aut_label': '36.h1', 'aut_quo_index': None, 'aut_stab_index': 96, 'aut_weyl_group': '72.46', 'aut_weyl_index': 864, 'centralizer': '72.a1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['12.d1'], 'contains': ['72.g1', '108.f1', '108.i1', '108.j1'], 'core': '648.b1', 'coset_action_label': None, 'count': 96, 'diagramx': [6574, -1, 3058, -1], 'generators': [36, 650, 24, 1800], 'label': '1944.3492.36.h1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.d1', 'old_label': '36.h1', 'projective_image': '1944.3492', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.h1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 107638076
    {'ambient': '1944.3492', 'aut_centralizer_order': 18, 'aut_label': '36.i1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '288.851', 'aut_weyl_index': 216, 'centralizer': '72.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.d1', '18.e1'], 'contains': ['72.h1', '108.g1', '108.i1'], 'core': '216.b1', 'coset_action_label': None, 'count': 12, 'diagramx': [6200, -1, 3777, -1], 'generators': [36, 2, 24, 1800], 'label': '1944.3492.36.i1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.c1', 'old_label': '36.i1', 'projective_image': '1944.3492', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.i1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 107638077
    {'ambient': '1944.3492', 'aut_centralizer_order': 6, 'aut_label': '36.j1', 'aut_quo_index': None, 'aut_stab_index': 144, 'aut_weyl_group': '72.46', 'aut_weyl_index': 864, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['12.e1', '12.f1', '12.g1', '18.c1'], 'contains': ['72.c1', '108.k1', '108.l1', '108.m1', '108.n1'], 'core': '216.a1', 'coset_action_label': None, 'count': 144, 'diagramx': [1922, -1, 8532, -1], 'generators': [37, 648, 2, 1800], 'label': '1944.3492.36.j1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.c1', 'old_label': '36.j1', 'projective_image': '648.715', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.j1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 107638078
    {'ambient': '1944.3492', 'aut_centralizer_order': 1, 'aut_label': '36.k1', 'aut_quo_index': None, 'aut_stab_index': 288, 'aut_weyl_group': '216.102', 'aut_weyl_index': 288, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['12.e1', '12.g1'], 'contains': ['72.d1', '108.k1', '108.m1', '108.o1'], 'core': '216.a1', 'coset_action_label': None, 'count': 288, 'diagramx': [1341, -1, 8902, -1], 'generators': [37, 648, 1802, 24], 'label': '1944.3492.36.k1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.k1', 'old_label': '36.k1', 'projective_image': '648.715', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.k1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 107638079
    {'ambient': '1944.3492', 'aut_centralizer_order': 8, 'aut_label': '36.l1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '864.4661', 'aut_weyl_index': 72, 'centralizer': '162.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.g1', '18.d1'], 'contains': ['72.a1', '108.k1', '108.p1'], 'core': '72.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [3851, -1, 7043, -1], 'generators': [37, 648, 2, 24], 'label': '1944.3492.36.l1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '36.l1', 'projective_image': '648.715', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.l1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 107638080
    {'ambient': '1944.3492', 'aut_centralizer_order': 6, 'aut_label': '36.m1', 'aut_quo_index': None, 'aut_stab_index': 288, 'aut_weyl_group': '36.10', 'aut_weyl_index': 1728, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['12.e1', '12.f1'], 'contains': ['72.e1', '108.l1', '108.m1'], 'core': '648.a1', 'coset_action_label': None, 'count': 288, 'diagramx': [917, -1, 9645, -1], 'generators': [37, 1514, 1800, 648], 'label': '1944.3492.36.m1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.m1', 'old_label': '36.m1', 'projective_image': '648.715', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.m1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 107638081
    {'ambient': '1944.3492', 'aut_centralizer_order': 48, 'aut_label': '36.n1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '144.182', 'aut_weyl_index': 432, 'centralizer': '324.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.f1', '18.b1'], 'contains': ['72.b1', '108.l1'], 'core': '72.b1', 'coset_action_label': None, 'count': 9, 'diagramx': [4184, -1, 8222, -1], 'generators': [37, 1800, 1512, 648], 'label': '1944.3492.36.n1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1', 'old_label': '36.n1', 'projective_image': '648.715', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.n1', 'subgroup_fusion': None, 'weyl_group': '36.9'}
  • id: 107638082
    {'ambient': '1944.3492', 'aut_centralizer_order': 6, 'aut_label': '3.a1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '864.4662', 'aut_weyl_index': 72, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['1.a1'], 'contains': ['6.a1', '6.b1', '6.d1', '9.a1', '27.a1'], 'core': '6.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [8066, -1, 3255, -1], 'generators': [1, 216, 936, 54, 648, 36, 2], 'label': '1944.3492.3.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '3.a1', 'projective_image': '648.715', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3.a1', 'subgroup_fusion': None, 'weyl_group': '216.156'}
  • id: 107638083
    {'ambient': '1944.3492', 'aut_centralizer_order': 1, 'aut_label': '36.o1', 'aut_quo_index': None, 'aut_stab_index': 432, 'aut_weyl_group': '144.182', 'aut_weyl_index': 432, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['12.e1'], 'contains': ['72.f1', '108.m1'], 'core': '648.a1', 'coset_action_label': None, 'count': 432, 'diagramx': [112, -1, 9895, -1], 'generators': [37, 1514, 1824, 648], 'label': '1944.3492.36.o1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.o1', 'old_label': '36.o1', 'projective_image': '648.715', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.o1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 107638084
    {'ambient': '1944.3492', 'aut_centralizer_order': 2, 'aut_label': '36.p1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '2592.fv', 'aut_weyl_index': 24, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['12.g1', '18.e1'], 'contains': ['72.h1', '108.n1', '108.o1', '108.p1'], 'core': '216.b1', 'coset_action_label': None, 'count': 12, 'diagramx': [2561, -1, 7539, -1], 'generators': [37, 2, 24, 1800], 'label': '1944.3492.36.p1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.c1', 'old_label': '36.p1', 'projective_image': '1944.3492', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.p1', 'subgroup_fusion': None, 'weyl_group': '108.39'}
  • id: 107638085
    {'ambient': '1944.3492', 'aut_centralizer_order': 48, 'aut_label': '54.a1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '12.4', 'aut_weyl_index': 5184, 'centralizer': '324.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['18.b1', '18.c1'], 'contains': ['108.b1', '108.h1', '108.l1', '162.a1', '162.b1'], 'core': '648.a1', 'coset_action_label': None, 'count': 108, 'diagramx': [5151, -1, 5185, -1], 'generators': [1, 36, 648, 1800], 'label': '1944.3492.54.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.a1', 'old_label': '54.a1', 'projective_image': '648.715', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 107638086
    {'ambient': '1944.3492', 'aut_centralizer_order': 48, 'aut_label': '54.b1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '12.4', 'aut_weyl_index': 5184, 'centralizer': '162.d1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['18.c1', '18.d1', '27.a1'], 'contains': ['108.c1', '108.e1', '108.k1', '162.a1', '162.c1'], 'core': '216.a1', 'coset_action_label': None, 'count': 108, 'diagramx': [6701, -1, 4450, -1], 'generators': [1, 36, 648, 2], 'label': '1944.3492.54.b1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '54.b1', 'projective_image': '648.715', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 107638087
    {'ambient': '1944.3492', 'aut_centralizer_order': 12, 'aut_label': '54.c1', 'aut_quo_index': None, 'aut_stab_index': 144, 'aut_weyl_group': '36.10', 'aut_weyl_index': 1728, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['18.c1', '18.e1'], 'contains': ['108.d1', '108.i1', '108.n1', '162.b1', '162.c1'], 'core': '648.b1', 'coset_action_label': None, 'count': 144, 'diagramx': [4892, -1, 4944, -1], 'generators': [1, 36, 2, 1800], 'label': '1944.3492.54.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.c1', 'old_label': '54.c1', 'projective_image': '1944.3492', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.c1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 107638088
    {'ambient': '1944.3492', 'aut_centralizer_order': 16, 'aut_label': '54.d1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '432.734', 'aut_weyl_index': 144, 'centralizer': '162.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.d1', '18.e1', '27.b1'], 'contains': ['108.a1', '108.g1', '108.p1', '162.c1'], 'core': '108.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [7246, -1, 3417, -1], 'generators': [1, 36, 2, 24], 'label': '1944.3492.54.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '54.d1', 'projective_image': '1944.3492', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.d1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 107638089
    {'ambient': '1944.3492', 'aut_centralizer_order': 216, 'aut_label': '54.e1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '8.5', 'aut_weyl_index': 7776, 'centralizer': '18.f1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['6.a1', '18.f1', '27.a1'], 'contains': ['108.e1', '162.d1', '162.f1', '162.h1'], 'core': '216.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [8583, -1, 889, -1], 'generators': [54, 2, 648, 36], 'label': '1944.3492.54.e1', 'mobius_quo': None, 'mobius_sub': -3, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '54.e1', 'projective_image': '648.715', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.e1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 107638090
    {'ambient': '1944.3492', 'aut_centralizer_order': 24, 'aut_label': '54.f1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '24.14', 'aut_weyl_index': 2592, 'centralizer': '162.d1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['6.d1', '18.g1', '27.a1'], 'contains': ['108.e1', '162.e1', '162.g1'], 'core': '216.a1', 'coset_action_label': None, 'count': 108, 'diagramx': [8978, -1, 2261, -1], 'generators': [31, 648, 36, 2], 'label': '1944.3492.54.f1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '54.f1', 'projective_image': '648.715', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.f1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 107638091
    {'ambient': '1944.3492', 'aut_centralizer_order': 36, 'aut_label': '54.g1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '24.14', 'aut_weyl_index': 2592, 'centralizer': '18.f1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['18.f1'], 'contains': ['108.f1', '162.f1', '162.h1'], 'core': '648.b1', 'coset_action_label': None, 'count': 72, 'diagramx': [8007, -1, 162, -1], 'generators': [18, 2, 672, 36], 'label': '1944.3492.54.g1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.f1', 'old_label': '54.g1', 'projective_image': '1944.3492', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.g1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 107638092
    {'ambient': '1944.3492', 'aut_centralizer_order': 72, 'aut_label': '54.h1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '96.189', 'aut_weyl_index': 648, 'centralizer': '18.f1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.f1', '27.b1'], 'contains': ['108.g1', '162.f1'], 'core': '216.b1', 'coset_action_label': None, 'count': 9, 'diagramx': [9557, -1, 525, -1], 'generators': [18, 2, 24, 36], 'label': '1944.3492.54.h1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '54.h1', 'projective_image': '1944.3492', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.h1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 107638093
    {'ambient': '1944.3492', 'aut_centralizer_order': 1, 'aut_label': '4.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': None, 'aut_weyl_index': 1, 'centralizer': '648.a1', 'complements': ['486.b1', '486.c1'], 'conjugacy_class_count': 1, 'contained_in': ['2.a1'], 'contains': ['8.a1', '12.b1', '12.c1'], 'core': '4.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3695, 6318, 6198, 3415], 'generators': [1, 24, 2, 1152, 1512, 648], 'label': '1944.3492.4.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': ['2.a1'], 'normal_contains': ['8.a1', '36.a1'], 'normalizer': '1.a1', 'old_label': '4.a1', 'projective_image': '648.715', 'quotient_action_image': '4.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.a1', 'subgroup_fusion': None, 'weyl_group': '648.715'}
  • id: 107638094
    {'ambient': '1944.3492', 'aut_centralizer_order': 8, 'aut_label': '54.i1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '864.4661', 'aut_weyl_index': 72, 'centralizer': '162.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.g1', '27.b1'], 'contains': ['108.g1', '162.g1'], 'core': '216.b1', 'coset_action_label': None, 'count': 9, 'diagramx': [9888, -1, 1949, -1], 'generators': [31, 36, 2, 24], 'label': '1944.3492.54.i1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '54.i1', 'projective_image': '1944.3492', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.i1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 107638095
    {'ambient': '1944.3492', 'aut_centralizer_order': 648, 'aut_label': '72.a1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '96.189', 'aut_weyl_index': 648, 'centralizer': '2.b1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['24.c1', '36.a1', '36.f1', '36.l1'], 'contains': ['216.a1', '216.b1', '216.e1'], 'core': '72.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4105, 7993, 6378, 9403], 'generators': [2, 24, 648], 'label': '1944.3492.72.a1', 'mobius_quo': -3, 'mobius_sub': 0, 'normal_closure': '72.a1', 'normal_contained_in': ['8.a1', '36.a1'], 'normal_contains': ['216.a1', '216.b1'], 'normalizer': '1.a1', 'old_label': '72.a1', 'projective_image': '648.715', 'quotient_action_image': '2.1', 'quotient_action_kernel': '36.9', 'quotient_action_kernel_order': 36, 'quotient_fusion': None, 'short_label': '72.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 107638096
    {'ambient': '1944.3492', 'aut_centralizer_order': 432, 'aut_label': '72.b1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '144.182', 'aut_weyl_index': 432, 'centralizer': '36.a1', 'complements': ['27.b1'], 'conjugacy_class_count': 1, 'contained_in': ['24.a1', '36.b1', '36.c1', '36.n1'], 'contains': ['216.c1'], 'core': '72.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [4290, 4144, 7121, 6708], 'generators': [1152, 1512], 'label': '1944.3492.72.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '72.b1', 'normal_contained_in': ['24.a1', '36.b1'], 'normal_contains': ['648.a1'], 'normalizer': '1.a1', 'old_label': '72.b1', 'projective_image': '648.715', 'quotient_action_image': '4.1', 'quotient_action_kernel': '18.4', 'quotient_action_kernel_order': 18, 'quotient_fusion': None, 'short_label': '72.b1', 'subgroup_fusion': None, 'weyl_group': '36.9'}
  • id: 107638097
    {'ambient': '1944.3492', 'aut_centralizer_order': 162, 'aut_label': '72.c1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '24.14', 'aut_weyl_index': 2592, 'centralizer': '24.c1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['24.a1', '24.b1', '24.c1', '36.d1', '36.g1', '36.j1'], 'contains': ['216.a1', '216.c1', '216.d1', '216.f1', '216.h1'], 'core': '216.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [2196, -1, 7293, -1], 'generators': [2, 1152, 648], 'label': '1944.3492.72.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '72.c1', 'projective_image': '648.715', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.c1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 107638098
    {'ambient': '1944.3492', 'aut_centralizer_order': 27, 'aut_label': '72.d1', 'aut_quo_index': None, 'aut_stab_index': 32, 'aut_weyl_group': '72.46', 'aut_weyl_index': 864, 'centralizer': '24.c1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['24.b1', '24.c1', '36.k1'], 'contains': ['216.a1', '216.d1', '216.g1', '216.i1'], 'core': '216.a1', 'coset_action_label': None, 'count': 32, 'diagramx': [1049, -1, 8284, -1], 'generators': [1154, 24, 648], 'label': '1944.3492.72.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1', 'old_label': '72.d1', 'projective_image': '648.715', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.d1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 107638099
    {'ambient': '1944.3492', 'aut_centralizer_order': 54, 'aut_label': '72.e1', 'aut_quo_index': None, 'aut_stab_index': 32, 'aut_weyl_group': '36.10', 'aut_weyl_index': 1728, 'centralizer': '72.a1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['24.a1', '24.b1', '36.m1'], 'contains': ['216.c1', '216.d1'], 'core': '648.a1', 'coset_action_label': None, 'count': 32, 'diagramx': [646, -1, 8661, -1], 'generators': [1514, 1152], 'label': '1944.3492.72.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1', 'old_label': '72.e1', 'projective_image': '648.715', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.e1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 107638100
    {'ambient': '1944.3492', 'aut_centralizer_order': 9, 'aut_label': '72.f1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '144.182', 'aut_weyl_index': 432, 'centralizer': '72.a1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['24.b1', '36.o1'], 'contains': ['216.d1'], 'core': '648.a1', 'coset_action_label': None, 'count': 48, 'diagramx': [161, -1, 9304, -1], 'generators': [1514, 1176], 'label': '1944.3492.72.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1', 'old_label': '72.f1', 'projective_image': '648.715', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.f1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 107638101
    {'ambient': '1944.3492', 'aut_centralizer_order': 27, 'aut_label': '72.g1', 'aut_quo_index': None, 'aut_stab_index': 96, 'aut_weyl_group': '24.14', 'aut_weyl_index': 2592, 'centralizer': '24.c1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['24.c1', '36.h1'], 'contains': ['216.e1', '216.f1', '216.g1', '216.h1', '216.i1'], 'core': '648.b1', 'coset_action_label': None, 'count': 96, 'diagramx': [2928, -1, 6767, -1], 'generators': [650, 24, 1152], 'label': '1944.3492.72.g1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.d1', 'old_label': '72.g1', 'projective_image': '1944.3492', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.g1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 107638102
    {'ambient': '1944.3492', 'aut_centralizer_order': 54, 'aut_label': '72.h1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '96.189', 'aut_weyl_index': 648, 'centralizer': '24.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['24.c1', '36.e1', '36.i1', '36.p1'], 'contains': ['216.b1', '216.f1', '216.g1'], 'core': '216.b1', 'coset_action_label': None, 'count': 12, 'diagramx': [2640, -1, 6950, -1], 'generators': [2, 24, 1152], 'label': '1944.3492.72.h1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.c1', 'old_label': '72.h1', 'projective_image': '1944.3492', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.h1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 107638103
    {'ambient': '1944.3492', 'aut_centralizer_order': 192, 'aut_label': '81.a1', 'aut_quo_index': None, 'aut_stab_index': 81, 'aut_weyl_group': '4.2', 'aut_weyl_index': 15552, 'centralizer': '81.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['9.a1', '27.a1'], 'contains': ['162.a1', '162.d1', '162.e1', '243.a1'], 'core': '648.a1', 'coset_action_label': None, 'count': 81, 'diagramx': [8765, -1, 1641, -1], 'generators': [1, 54, 648, 36], 'label': '1944.3492.81.a1', 'mobius_quo': None, 'mobius_sub': -3, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1', 'old_label': '81.a1', 'projective_image': '648.715', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '81.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 107638104
    {'ambient': '1944.3492', 'aut_centralizer_order': 9, 'aut_label': '4.b1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': None, 'aut_weyl_index': 9, 'centralizer': '72.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1', '2.b1', '2.c1'], 'contains': ['8.a1', '12.a1', '12.d1'], 'core': '4.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [6318, 3807, 4276, 5946], 'generators': [36, 648, 1512, 2, 24, 1800], 'label': '1944.3492.4.b1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.b1', 'normal_contained_in': ['2.a1', '2.b1', '2.c1'], 'normal_contains': ['8.a1', '12.a1'], 'normalizer': '1.a1', 'old_label': '4.b1', 'projective_image': '648.715', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.b1', 'subgroup_fusion': None, 'weyl_group': '72.45'}
  • id: 107638105
    {'ambient': '1944.3492', 'aut_centralizer_order': 48, 'aut_label': '81.b1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '12.4', 'aut_weyl_index': 5184, 'centralizer': '162.d1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['27.a1', '27.b1'], 'contains': ['162.c1', '162.f1', '162.g1', '243.a1'], 'core': '648.b1', 'coset_action_label': None, 'count': 108, 'diagramx': [9671, -1, 1222, -1], 'generators': [1, 54, 36, 2], 'label': '1944.3492.81.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '81.b1', 'projective_image': '1944.3492', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '81.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 107638106
    {'ambient': '1944.3492', 'aut_centralizer_order': 144, 'aut_label': '108.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '432.734', 'aut_weyl_index': 144, 'centralizer': '18.a1', 'complements': ['18.a1', '18.h1'], 'conjugacy_class_count': 1, 'contained_in': ['36.a1', '36.e1', '54.d1'], 'contains': ['216.b1', '324.c1'], 'core': '108.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5413, 7237, 5278, 8383], 'generators': [1, 2, 24], 'label': '1944.3492.108.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '108.a1', 'normal_contained_in': ['36.a1'], 'normal_contains': ['216.b1'], 'normalizer': '1.a1', 'old_label': '108.a1', 'projective_image': '1944.3492', 'quotient_action_image': '1.1', 'quotient_action_kernel': '108.15', 'quotient_action_kernel_order': 108, 'quotient_fusion': None, 'short_label': '108.a1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 107638107
    {'ambient': '1944.3492', 'aut_centralizer_order': 144, 'aut_label': '108.b1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '12.4', 'aut_weyl_index': 5184, 'centralizer': '108.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.c1', '36.d1', '54.a1'], 'contains': ['216.c1', '324.a1', '324.b1'], 'core': '648.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [4634, -1, 6135, -1], 'generators': [1, 1152, 648], 'label': '1944.3492.108.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.b1', 'old_label': '108.b1', 'projective_image': '648.715', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 107638108
    {'ambient': '1944.3492', 'aut_centralizer_order': 432, 'aut_label': '108.c1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '12.4', 'aut_weyl_index': 5184, 'centralizer': '18.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['36.a1', '36.d1', '54.b1'], 'contains': ['216.a1', '324.a1', '324.c1'], 'core': '216.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [5142, -1, 5531, -1], 'generators': [1, 648, 2], 'label': '1944.3492.108.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '108.c1', 'projective_image': '648.715', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.c1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 107638109
    {'ambient': '1944.3492', 'aut_centralizer_order': 36, 'aut_label': '108.d1', 'aut_quo_index': None, 'aut_stab_index': 144, 'aut_weyl_group': '12.4', 'aut_weyl_index': 5184, 'centralizer': '216.c1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['36.d1', '36.e1', '54.c1'], 'contains': ['216.f1', '324.b1', '324.c1'], 'core': '648.b1', 'coset_action_label': None, 'count': 144, 'diagramx': [3772, -1, 5832, -1], 'generators': [1, 1152, 2], 'label': '1944.3492.108.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.c1', 'old_label': '108.d1', 'projective_image': '1944.3492', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.d1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 107638110
    {'ambient': '1944.3492', 'aut_centralizer_order': 432, 'aut_label': '108.e1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '4.2', 'aut_weyl_index': 15552, 'centralizer': '18.f1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['36.f1', '36.g1', '54.b1', '54.e1', '54.f1'], 'contains': ['216.a1', '324.d1', '324.e1', '324.f1'], 'core': '216.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [7140, -1, 3491, -1], 'generators': [36, 2, 648], 'label': '1944.3492.108.e1', 'mobius_quo': None, 'mobius_sub': 6, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '108.e1', 'projective_image': '648.715', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.e1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 107638111
    {'ambient': '1944.3492', 'aut_centralizer_order': 72, 'aut_label': '108.f1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '12.4', 'aut_weyl_index': 5184, 'centralizer': '18.f1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['36.f1', '36.h1', '54.g1'], 'contains': ['216.e1', '324.e1', '324.f1'], 'core': '648.b1', 'coset_action_label': None, 'count': 72, 'diagramx': [7466, -1, 2884, -1], 'generators': [36, 650, 24], 'label': '1944.3492.108.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.f1', 'old_label': '108.f1', 'projective_image': '1944.3492', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.f1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 107638112
    {'ambient': '1944.3492', 'aut_centralizer_order': 144, 'aut_label': '108.g1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '48.29', 'aut_weyl_index': 1296, 'centralizer': '18.f1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.f1', '36.i1', '54.d1', '54.h1', '54.i1'], 'contains': ['216.b1', '324.e1'], 'core': '216.b1', 'coset_action_label': None, 'count': 9, 'diagramx': [7793, -1, 3188, -1], 'generators': [36, 2, 24], 'label': '1944.3492.108.g1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '108.g1', 'projective_image': '1944.3492', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.g1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 107638113
    {'ambient': '1944.3492', 'aut_centralizer_order': 432, 'aut_label': '108.h1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '12.4', 'aut_weyl_index': 5184, 'centralizer': '36.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.b1', '36.g1', '54.a1'], 'contains': ['216.c1', '324.d1', '324.g1'], 'core': '648.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [5685, -1, 4560, -1], 'generators': [36, 648, 1800], 'label': '1944.3492.108.h1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.c1', 'old_label': '108.h1', 'projective_image': '648.715', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.h1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 107638114
    {'ambient': '1944.3492', 'aut_centralizer_order': 108, 'aut_label': '108.i1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '12.4', 'aut_weyl_index': 5184, 'centralizer': '72.a1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['36.g1', '36.h1', '36.i1', '54.c1'], 'contains': ['216.f1', '324.e1', '324.g1'], 'core': '648.b1', 'coset_action_label': None, 'count': 48, 'diagramx': [6193, -1, 4096, -1], 'generators': [36, 2, 1800], 'label': '1944.3492.108.i1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.c1', 'old_label': '108.i1', 'projective_image': '1944.3492', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.i1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 107638115
    {'ambient': '1944.3492', 'aut_centralizer_order': 1, 'aut_label': '4.c1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': None, 'aut_weyl_index': 1, 'centralizer': '648.a1', 'complements': ['486.b1', '486.c1'], 'conjugacy_class_count': 1, 'contained_in': ['2.a1'], 'contains': ['8.a1', '12.e1', '12.f1', '12.g1'], 'core': '4.c1', 'coset_action_label': None, 'count': 1, 'diagramx': [2999, 8715, 7818, 1002], 'generators': [37, 648, 1512, 2, 24, 1800], 'label': '1944.3492.4.c1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '4.c1', 'normal_contained_in': ['2.a1'], 'normal_contains': ['8.a1'], 'normalizer': '1.a1', 'old_label': '4.c1', 'projective_image': '648.715', 'quotient_action_image': '4.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.c1', 'subgroup_fusion': None, 'weyl_group': '648.715'}
  • id: 107638116
    {'ambient': '1944.3492', 'aut_centralizer_order': 54, 'aut_label': '108.j1', 'aut_quo_index': None, 'aut_stab_index': 96, 'aut_weyl_group': '12.4', 'aut_weyl_index': 5184, 'centralizer': '72.a1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['36.g1', '36.h1'], 'contains': ['216.h1', '324.f1', '324.g1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 96, 'diagramx': [6516, -1, 3794, -1], 'generators': [36, 650, 1800], 'label': '1944.3492.108.j1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.d1', 'old_label': '108.j1', 'projective_image': '1944.3492', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.j1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 107638117
    {'ambient': '1944.3492', 'aut_centralizer_order': 48, 'aut_label': '108.k1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '12.4', 'aut_weyl_index': 5184, 'centralizer': '162.d1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['36.j1', '36.k1', '36.l1', '54.b1'], 'contains': ['216.a1', '324.h1', '324.i1'], 'core': '216.a1', 'coset_action_label': None, 'count': 108, 'diagramx': [1805, -1, 7537, -1], 'generators': [37, 648, 2], 'label': '1944.3492.108.k1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '108.k1', 'projective_image': '648.715', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.k1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 107638118
    {'ambient': '1944.3492', 'aut_centralizer_order': 48, 'aut_label': '108.l1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '12.4', 'aut_weyl_index': 5184, 'centralizer': '324.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['36.j1', '36.m1', '36.n1', '54.a1'], 'contains': ['216.c1', '324.h1', '324.j1'], 'core': '648.a1', 'coset_action_label': None, 'count': 108, 'diagramx': [3080, -1, 8041, -1], 'generators': [37, 648, 1800], 'label': '1944.3492.108.l1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.a1', 'old_label': '108.l1', 'projective_image': '648.715', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.l1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 107638119
    {'ambient': '1944.3492', 'aut_centralizer_order': 6, 'aut_label': '108.m1', 'aut_quo_index': None, 'aut_stab_index': 864, 'aut_weyl_group': '12.4', 'aut_weyl_index': 5184, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['36.j1', '36.k1', '36.m1', '36.o1'], 'contains': ['216.d1', '324.h1', '324.k1'], 'core': '648.a1', 'coset_action_label': None, 'count': 864, 'diagramx': [389, -1, 8893, -1], 'generators': [37, 648, 1802], 'label': '1944.3492.108.m1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '108.m1', 'old_label': '108.m1', 'projective_image': '648.715', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.m1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 107638120
    {'ambient': '1944.3492', 'aut_centralizer_order': 12, 'aut_label': '108.n1', 'aut_quo_index': None, 'aut_stab_index': 144, 'aut_weyl_group': '36.10', 'aut_weyl_index': 1728, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['36.j1', '36.p1', '54.c1'], 'contains': ['216.f1', '324.i1', '324.j1', '324.k1'], 'core': '648.b1', 'coset_action_label': None, 'count': 144, 'diagramx': [2260, -1, 7789, -1], 'generators': [37, 2, 1800], 'label': '1944.3492.108.n1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.c1', 'old_label': '108.n1', 'projective_image': '1944.3492', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.n1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 107638121
    {'ambient': '1944.3492', 'aut_centralizer_order': 2, 'aut_label': '108.o1', 'aut_quo_index': None, 'aut_stab_index': 288, 'aut_weyl_group': '108.17', 'aut_weyl_index': 576, 'centralizer': '648.a1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['36.k1', '36.p1'], 'contains': ['216.g1', '324.i1', '324.k1'], 'core': '648.b1', 'coset_action_label': None, 'count': 288, 'diagramx': [1257, -1, 8478, -1], 'generators': [37, 1802, 24], 'label': '1944.3492.108.o1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.k1', 'old_label': '108.o1', 'projective_image': '1944.3492', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.o1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 107638122
    {'ambient': '1944.3492', 'aut_centralizer_order': 16, 'aut_label': '108.p1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '432.734', 'aut_weyl_index': 144, 'centralizer': '162.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.l1', '36.p1', '54.d1'], 'contains': ['216.b1', '324.i1'], 'core': '216.b1', 'coset_action_label': None, 'count': 9, 'diagramx': [4043, -1, 6573, -1], 'generators': [37, 2, 24], 'label': '1944.3492.108.p1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '108.p1', 'projective_image': '1944.3492', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.p1', 'subgroup_fusion': None, 'weyl_group': '18.4'}
  • id: 107638123
    {'ambient': '1944.3492', 'aut_centralizer_order': 384, 'aut_label': '162.a1', 'aut_quo_index': None, 'aut_stab_index': 81, 'aut_weyl_group': '2.1', 'aut_weyl_index': 31104, 'centralizer': '81.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['54.a1', '54.b1', '81.a1'], 'contains': ['324.a1', '324.d1', '324.h1', '486.a1'], 'core': '648.a1', 'coset_action_label': None, 'count': 81, 'diagramx': [6474, -1, 4863, -1], 'generators': [1, 36, 648], 'label': '1944.3492.162.a1', 'mobius_quo': None, 'mobius_sub': 3, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1', 'old_label': '162.a1', 'projective_image': '648.715', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '162.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 107638124
    {'ambient': '1944.3492', 'aut_centralizer_order': 96, 'aut_label': '162.b1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '6.1', 'aut_weyl_index': 10368, 'centralizer': '324.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['54.a1', '54.c1'], 'contains': ['324.b1', '324.g1', '324.j1', '486.a1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 108, 'diagramx': [5353, -1, 5095, -1], 'generators': [1, 36, 1800], 'label': '1944.3492.162.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.a1', 'old_label': '162.b1', 'projective_image': '1944.3492', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '162.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 107638125
    {'ambient': '1944.3492', 'aut_centralizer_order': 96, 'aut_label': '162.c1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '6.1', 'aut_weyl_index': 10368, 'centralizer': '162.d1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['54.b1', '54.c1', '54.d1', '81.b1'], 'contains': ['324.c1', '324.e1', '324.i1', '486.a1'], 'core': '648.b1', 'coset_action_label': None, 'count': 108, 'diagramx': [6723, -1, 4328, -1], 'generators': [1, 36, 2], 'label': '1944.3492.162.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '162.c1', 'projective_image': '1944.3492', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '162.c1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 107638126
    {'ambient': '1944.3492', 'aut_centralizer_order': 54, 'aut_label': '6.a1', 'aut_quo_index': 1, 'aut_stab_index': 4, 'aut_weyl_group': '288.1027', 'aut_weyl_index': 216, 'centralizer': '72.a1', 'complements': ['324.c1', '324.i1', '324.k1'], 'conjugacy_class_count': 4, 'contained_in': ['2.b1', '3.a1'], 'contains': ['12.a1', '18.a1', '54.e1'], 'core': '6.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [7647, 2320, 2706, 8442], 'generators': [54, 648, 216, 2, 36, 936], 'label': '1944.3492.6.a1', 'mobius_quo': 0, 'mobius_sub': 3, 'normal_closure': '6.a1', 'normal_contained_in': ['2.b1'], 'normal_contains': ['12.a1', '18.a1'], 'normalizer': '1.a1', 'old_label': '6.a1', 'projective_image': '648.715', 'quotient_action_image': '2.1', 'quotient_action_kernel': '3.1', 'quotient_action_kernel_order': 3, 'quotient_fusion': None, 'short_label': '6.a1', 'subgroup_fusion': None, 'weyl_group': '72.45'}
  • id: 107638127
    {'ambient': '1944.3492', 'aut_centralizer_order': 1728, 'aut_label': '162.d1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '4.2', 'aut_weyl_index': 15552, 'centralizer': '9.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.a1', '54.e1', '81.a1'], 'contains': ['324.d1', '486.b1'], 'core': '648.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [8064, -1, 1416, -1], 'generators': [54, 648, 36], 'label': '1944.3492.162.d1', 'mobius_quo': None, 'mobius_sub': 27, 'normal_closure': '18.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '162.d1', 'projective_image': '648.715', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '162.d1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 107638128
    {'ambient': '1944.3492', 'aut_centralizer_order': 192, 'aut_label': '162.e1', 'aut_quo_index': None, 'aut_stab_index': 81, 'aut_weyl_group': '4.2', 'aut_weyl_index': 15552, 'centralizer': '81.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.h1', '54.f1', '81.a1'], 'contains': ['324.d1', '486.c1'], 'core': '648.a1', 'coset_action_label': None, 'count': 81, 'diagramx': [8734, -1, 2362, -1], 'generators': [31, 648, 36], 'label': '1944.3492.162.e1', 'mobius_quo': None, 'mobius_sub': 3, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '81.a1', 'old_label': '162.e1', 'projective_image': '648.715', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '162.e1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 107638129
    {'ambient': '1944.3492', 'aut_centralizer_order': 432, 'aut_label': '162.f1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '4.2', 'aut_weyl_index': 15552, 'centralizer': '18.f1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['54.e1', '54.g1', '54.h1', '81.b1'], 'contains': ['324.e1', '486.b1'], 'core': '648.b1', 'coset_action_label': None, 'count': 36, 'diagramx': [9130, -1, 1186, -1], 'generators': [54, 2, 36], 'label': '1944.3492.162.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1', 'old_label': '162.f1', 'projective_image': '1944.3492', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '162.f1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 107638130
    {'ambient': '1944.3492', 'aut_centralizer_order': 48, 'aut_label': '162.g1', 'aut_quo_index': None, 'aut_stab_index': 108, 'aut_weyl_group': '12.4', 'aut_weyl_index': 5184, 'centralizer': '162.d1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['54.f1', '54.i1', '81.b1'], 'contains': ['324.e1', '486.c1'], 'core': '648.b1', 'coset_action_label': None, 'count': 108, 'diagramx': [9660, -1, 2161, -1], 'generators': [31, 36, 2], 'label': '1944.3492.162.g1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1', 'old_label': '162.g1', 'projective_image': '1944.3492', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '162.g1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 107638131
    {'ambient': '1944.3492', 'aut_centralizer_order': 216, 'aut_label': '162.h1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '4.2', 'aut_weyl_index': 15552, 'centralizer': '18.f1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['54.e1', '54.g1'], 'contains': ['324.f1', '486.b1'], 'core': '1944.a1', 'coset_action_label': None, 'count': 72, 'diagramx': [8275, -1, 956, -1], 'generators': [54, 650, 36], 'label': '1944.3492.162.h1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.f1', 'old_label': '162.h1', 'projective_image': '1944.3492', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '162.h1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 107638132
    {'ambient': '1944.3492', 'aut_centralizer_order': 3888, 'aut_label': '216.a1', 'aut_quo_index': 1, 'aut_stab_index': 4, 'aut_weyl_group': '4.2', 'aut_weyl_index': 15552, 'centralizer': '2.b1', 'complements': [], 'conjugacy_class_count': 4, 'contained_in': ['72.a1', '72.c1', '72.d1', '108.c1', '108.e1', '108.k1'], 'contains': ['648.a1', '648.b1', '648.c1'], 'core': '216.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [2471, 8435, 6588, 9403], 'generators': [2, 648], 'label': '1944.3492.216.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '216.a1', 'normal_contained_in': ['24.a1', '72.a1'], 'normal_contains': ['648.a1', '648.b1'], 'normalizer': '1.a1', 'old_label': '216.a1', 'projective_image': '648.715', 'quotient_action_image': '2.1', 'quotient_action_kernel': '108.36', 'quotient_action_kernel_order': 108, 'quotient_fusion': None, 'short_label': '216.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 107638133
    {'ambient': '1944.3492', 'aut_centralizer_order': 1296, 'aut_label': '216.b1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '48.29', 'aut_weyl_index': 1296, 'centralizer': '2.b1', 'complements': ['9.a1'], 'conjugacy_class_count': 1, 'contained_in': ['72.a1', '72.h1', '108.a1', '108.g1', '108.p1'], 'contains': ['648.b1'], 'core': '216.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [4492, 7481, 6222, 8442], 'generators': [2, 24], 'label': '1944.3492.216.b1', 'mobius_quo': 3, 'mobius_sub': 0, 'normal_closure': '216.b1', 'normal_contained_in': ['72.a1', '108.a1'], 'normal_contains': ['648.b1'], 'normalizer': '1.a1', 'old_label': '216.b1', 'projective_image': '1944.3492', 'quotient_action_image': '2.1', 'quotient_action_kernel': '108.15', 'quotient_action_kernel_order': 108, 'quotient_fusion': None, 'short_label': '216.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 107638134
    {'ambient': '1944.3492', 'aut_centralizer_order': 1296, 'aut_label': '216.c1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '12.4', 'aut_weyl_index': 5184, 'centralizer': '12.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['72.b1', '72.c1', '72.e1', '108.b1', '108.h1', '108.l1'], 'contains': ['648.a1', '648.d1'], 'core': '648.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [3794, -1, 7115, -1], 'generators': [1152, 648], 'label': '1944.3492.216.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '72.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '216.c1', 'projective_image': '648.715', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.c1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 107638135
    {'ambient': '1944.3492', 'aut_centralizer_order': 162, 'aut_label': '216.d1', 'aut_quo_index': None, 'aut_stab_index': 32, 'aut_weyl_group': '12.4', 'aut_weyl_index': 5184, 'centralizer': '24.c1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['72.c1', '72.d1', '72.e1', '72.f1', '108.m1'], 'contains': ['648.a1', '648.e1'], 'core': '648.a1', 'coset_action_label': None, 'count': 32, 'diagramx': [616, -1, 8284, -1], 'generators': [1154, 648], 'label': '1944.3492.216.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1', 'old_label': '216.d1', 'projective_image': '648.715', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.d1', 'subgroup_fusion': None, 'weyl_group': '6.1'}