Abstract group data - 1728.34767

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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': '16.14', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 3, 'aut_exponent': 12, 'aut_gen_orders': [2, 4, 12, 6, 6, 4, 6, 2, 2, 6], 'aut_gens': [[1, 2, 12, 144], [5, 58, 636, 1584], [54, 53, 1192, 1656], [918, 993, 332, 144], [77, 122, 348, 1008], [945, 26, 1236, 216], [6, 53, 40, 792], [102, 97, 904, 1080], [945, 874, 1236, 792], [945, 946, 1164, 1656], [945, 26, 84, 1584]], 'aut_group': None, 'aut_hash': 7214043090240141899, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 110592, 'aut_permdeg': 40, 'aut_perms': [709979369774842847576604511590086135563423899222, 761601611040396596764831259211403316787327720283, 41410108889281508068580353050681315835909274323, 424167849300852069823472102349708414626437284912, 121476680672375753227938030096996211022622188990, 223793418295878241191928730688343871969558402632, 659894018634537844879589211446491437586343091582, 733344698777967944419604615237865187888101110768, 6695292109535124329982622180950296452040573825, 750848933792582221923010973771372605293620331980], 'aut_phi_ratio': 192.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [2, 6, 4, 1], [3, 2, 1, 1], [3, 2, 2, 1], [3, 4, 1, 1], [3, 4, 2, 1], [3, 8, 1, 1], [4, 4, 1, 1], [4, 6, 2, 1], [4, 12, 1, 1], [4, 12, 2, 1], [4, 18, 2, 2], [4, 36, 2, 2], [4, 54, 2, 1], [4, 108, 1, 1], [6, 2, 1, 3], [6, 2, 2, 3], [6, 4, 1, 3], [6, 4, 2, 3], [6, 8, 1, 3], [6, 12, 4, 2], [6, 24, 4, 1], [12, 4, 2, 1], [12, 8, 2, 2], [12, 8, 4, 2], [12, 12, 4, 2], [12, 18, 4, 1], [12, 24, 2, 4], [12, 24, 4, 1], [12, 36, 2, 1], [12, 36, 4, 1], [12, 72, 2, 1]], 'aut_supersolvable': False, 'aut_tex': 'C_2^2\\times C_3^3.C_2^6.C_2^4', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 2, 'autcent_group': '256.56092', 'autcent_hash': 56092, 'autcent_nilpotent': True, 'autcent_order': 256, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^8', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 12, 'autcentquo_group': '432.741', 'autcentquo_hash': 741, 'autcentquo_nilpotent': False, 'autcentquo_order': 432, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'S_3^3:C_2', 'cc_stats': [[1, 1, 1], [2, 1, 3], [2, 6, 4], [3, 2, 3], [3, 4, 3], [3, 8, 1], [4, 4, 1], [4, 6, 2], [4, 12, 3], [4, 18, 4], [4, 36, 4], [4, 54, 2], [4, 108, 1], [6, 2, 9], [6, 4, 9], [6, 8, 3], [6, 12, 8], [6, 24, 4], [12, 4, 2], [12, 8, 12], [12, 12, 8], [12, 18, 4], [12, 24, 12], [12, 36, 6], [12, 72, 2]], 'center_label': '4.2', 'center_order': 4, 'central_product': False, 'central_quotient': '432.759', 'commutator_count': 1, 'commutator_label': '108.45', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '3.1', '3.1', '3.1'], 'composition_length': 9, 'conjugacy_classes_known': True, 'counter': 34767, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [2, 6, 1, 4], [3, 2, 1, 3], [3, 4, 1, 3], [3, 8, 1, 1], [4, 4, 1, 1], [4, 6, 2, 1], [4, 12, 1, 3], [4, 18, 1, 2], [4, 18, 2, 1], [4, 36, 1, 4], [4, 54, 1, 2], [4, 108, 1, 1], [6, 2, 1, 9], [6, 4, 1, 9], [6, 8, 1, 3], [6, 12, 1, 8], [6, 24, 1, 4], [12, 4, 2, 1], [12, 8, 1, 4], [12, 8, 2, 4], [12, 12, 2, 4], [12, 18, 4, 1], [12, 24, 1, 4], [12, 24, 2, 4], [12, 36, 1, 2], [12, 36, 2, 2], [12, 72, 1, 2]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 22145760, 'exponent': 12, 'exponents_of_order': [6, 3], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [], 'familial': False, 'frattini_label': '4.2', 'frattini_quotient': '432.759', 'hash': 34767, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 6, 'inner_gen_orders': [2, 6, 6, 6], 'inner_gens': [[1, 946, 12, 1080], [941, 2, 60, 1080], [1, 98, 12, 1584], [937, 938, 300, 144]], 'inner_hash': 759, 'inner_nilpotent': False, 'inner_order': 432, 'inner_split': True, 'inner_tex': 'C_2\\times S_3^3', 'inner_used': [1, 2, 3, 4], 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': -1, 'irrep_stats': [[1, 16], [2, 40], [4, 41], [8, 14]], 'label': '1728.34767', 'linC_count': None, 'linC_degree': None, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': None, 'linQ_degree_count': None, 'linQ_dim': None, 'linQ_dim_count': None, 'linR_count': None, 'linR_degree': None, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': False, 'monomial': True, 'name': '(C2*C4).S3^3', 'ngens': 9, 'nilpotency_class': -1, 'nilpotent': False, 'normal_counts': [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 54, 'number_characteristic_subgroups': 58, 'number_conjugacy_classes': 111, 'number_divisions': 91, 'number_normal_subgroups': 194, 'number_subgroup_autclasses': 634, 'number_subgroup_classes': 1168, 'number_subgroups': 8356, 'old_label': None, 'order': 1728, 'order_factorization_type': 33, 'order_stats': [[1, 1], [2, 27], [3, 26], [4, 484], [6, 270], [12, 920]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 4, 'outer_gen_orders': [2, 2, 2, 2, 2, 2, 4], 'outer_gen_pows': [96, 584, 624, 4, 0, 676, 0], 'outer_gens': [[1, 898, 12, 720], [9, 2, 588, 1008], [1, 50, 1524, 1008], [941, 866, 1500, 1656], [869, 874, 948, 792], [77, 26, 588, 144], [102, 965, 976, 1584]], 'outer_group': '256.55643', 'outer_hash': 55643, 'outer_nilpotent': True, 'outer_order': 256, 'outer_permdeg': 64, 'outer_perms': [12257309289760343774605855458287405213698076116231869265937468697619720813973254821366121, 73831087184710904455939441741154406504506842877844678601083159089852749803360527546906393, 118465307525375087883419688714462959740646022452006035163261107839277225071770426936632564, 28453496941954504967169382965599332177989788091405576281442614978188062893975419221223127, 52866728992654941797193116356984683845200993163334619838458962509130021815571356789552991, 40161574247444892958827969444148661024489788135526272700405701746597403786759565019663472, 86109635487182336369671667448550370881728094034728774797973941769446814441087000109645145], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^5:D_4', 'pc_rank': 4, 'perfect': False, 'permutation_degree': 25, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 2, 2], 'quasisimple': False, 'rank': 4, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 16], [2, 28], [4, 23], [8, 22], [16, 2]], 'representations': {'PC': {'code': 19085572857874713721845307296823019314483703932644263148893257, 'gens': [1, 2, 4, 7], 'pres': [9, 2, 2, 3, 2, 2, 3, 2, 2, 3, 17029, 46, 218, 1092, 102, 2713, 130, 2606, 68046, 34035, 8349, 186, 8674, 214, 7811]}, 'Perm': {'d': 25, 'gens': [622798591475511783129121, 622798591475512259630064, 1319781461471106746319624, 1969307671116938609260344, 622798591475511779328000, 12176904, 6706022400, 3, 22230464256000]}}, 'schur_multiplier': [2, 2, 2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 2, 2], 'solvability_type': 7, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': '(C_2\\times C_4).S_3^3', 'transitive_degree': 192, '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: 129700576
    {'aut_label': '1A', 'centralizer': '1.a1.a1', 'counter': 1, 'group_counter': 34767, 'group_order': 1728, 'label': '1A', 'order': 1, 'powers': [1, 1], 'representative': 0, 'size': 1}
  • id: 129700599
    {'aut_label': '2A', 'centralizer': '1.a1.a1', 'counter': 2, 'group_counter': 34767, 'group_order': 1728, 'label': '2A', 'order': 2, 'powers': [1, 2], 'representative': 936, 'size': 1}
  • id: 129700610
    {'aut_label': '2B', 'centralizer': '1.a1.a1', 'counter': 3, 'group_counter': 34767, 'group_order': 1728, 'label': '2B', 'order': 2, 'powers': [1, 3], 'representative': 72, 'size': 1}
  • id: 129700621
    {'aut_label': '2C', 'centralizer': '1.a1.a1', 'counter': 4, 'group_counter': 34767, 'group_order': 1728, 'label': '2C', 'order': 2, 'powers': [1, 4], 'representative': 864, 'size': 1}
  • id: 129700632
    {'aut_label': '2D', 'centralizer': '6.e1.a1', 'counter': 5, 'group_counter': 34767, 'group_order': 1728, 'label': '2D', 'order': 2, 'powers': [1, 5], 'representative': 6, 'size': 6}
  • id: 129700643
    {'aut_label': '2D', 'centralizer': '6.e1.a1', 'counter': 6, 'group_counter': 34767, 'group_order': 1728, 'label': '2E', 'order': 2, 'powers': [1, 6], 'representative': 30, 'size': 6}
  • id: 129700654
    {'aut_label': '2D', 'centralizer': '6.e1.b1', 'counter': 7, 'group_counter': 34767, 'group_order': 1728, 'label': '2F', 'order': 2, 'powers': [1, 7], 'representative': 1, 'size': 6}
  • id: 129700665
    {'aut_label': '2D', 'centralizer': '6.e1.b1', 'counter': 8, 'group_counter': 34767, 'group_order': 1728, 'label': '2G', 'order': 2, 'powers': [1, 8], 'representative': 865, 'size': 6}
  • id: 129700676
    {'aut_label': '3A', 'centralizer': '2.a1.b1', 'counter': 9, 'group_counter': 34767, 'group_order': 1728, 'label': '3A', 'order': 3, 'powers': [9, 1], 'representative': 48, 'size': 2}
  • id: 129700577
    {'aut_label': '3A', 'centralizer': '2.a1.a1', 'counter': 10, 'group_counter': 34767, 'group_order': 1728, 'label': '3B', 'order': 3, 'powers': [10, 1], 'representative': 8, 'size': 2}
  • id: 129700588
    {'aut_label': '3C', 'centralizer': '2.e1.a1', 'counter': 11, 'group_counter': 34767, 'group_order': 1728, 'label': '3C', 'order': 3, 'powers': [11, 1], 'representative': 1152, 'size': 2}
  • id: 129700591
    {'aut_label': '3D', 'centralizer': '4.a1.b1', 'counter': 12, 'group_counter': 34767, 'group_order': 1728, 'label': '3D', 'order': 3, 'powers': [12, 1], 'representative': 624, 'size': 4}
  • id: 129700592
    {'aut_label': '3E', 'centralizer': '4.h1.a1', 'counter': 13, 'group_counter': 34767, 'group_order': 1728, 'label': '3E', 'order': 3, 'powers': [13, 1], 'representative': 56, 'size': 4}
  • id: 129700593
    {'aut_label': '3D', 'centralizer': '4.a1.a1', 'counter': 14, 'group_counter': 34767, 'group_order': 1728, 'label': '3F', 'order': 3, 'powers': [14, 1], 'representative': 584, 'size': 4}
  • id: 129700594
    {'aut_label': '3G', 'centralizer': '8.b1.a1', 'counter': 15, 'group_counter': 34767, 'group_order': 1728, 'label': '3G', 'order': 3, 'powers': [15, 1], 'representative': 1208, 'size': 8}
  • id: 129700595
    {'aut_label': '4A', 'centralizer': '4.i1.a1', 'counter': 16, 'group_counter': 34767, 'group_order': 1728, 'label': '4A', 'order': 4, 'powers': [4, 16], 'representative': 432, 'size': 4}
  • id: 129700596
    {'aut_label': '4B1', 'centralizer': '6.r1.a1', 'counter': 17, 'group_counter': 34767, 'group_order': 1728, 'label': '4B1', 'order': 4, 'powers': [3, 18], 'representative': 36, 'size': 6}
  • id: 129700597
    {'aut_label': '4B1', 'centralizer': '6.r1.a1', 'counter': 18, 'group_counter': 34767, 'group_order': 1728, 'label': '4B-1', 'order': 4, 'powers': [3, 17], 'representative': 108, 'size': 6}
  • id: 129700598
    {'aut_label': '4C', 'centralizer': '12.s1.a1', 'counter': 19, 'group_counter': 34767, 'group_order': 1728, 'label': '4C', 'order': 4, 'powers': [3, 19], 'representative': 1369, 'size': 12}
  • id: 129700600
    {'aut_label': '4C', 'centralizer': '12.s1.b1', 'counter': 20, 'group_counter': 34767, 'group_order': 1728, 'label': '4D', 'order': 4, 'powers': [3, 20], 'representative': 1374, 'size': 12}
  • id: 129700601
    {'aut_label': '4E', 'centralizer': '12.ci1.a1', 'counter': 21, 'group_counter': 34767, 'group_order': 1728, 'label': '4E', 'order': 4, 'powers': [3, 21], 'representative': 180, 'size': 12}
  • id: 129700602
    {'aut_label': '4F', 'centralizer': '18.x1.a1', 'counter': 22, 'group_counter': 34767, 'group_order': 1728, 'label': '4F', 'order': 4, 'powers': [2, 22], 'representative': 939, 'size': 18}
  • id: 129700603
    {'aut_label': '4F', 'centralizer': '18.x1.a1', 'counter': 23, 'group_counter': 34767, 'group_order': 1728, 'label': '4G', 'order': 4, 'powers': [2, 23], 'representative': 75, 'size': 18}
  • id: 129700604
    {'aut_label': '4H1', 'centralizer': '18.j1.a1', 'counter': 24, 'group_counter': 34767, 'group_order': 1728, 'label': '4H1', 'order': 4, 'powers': [3, 25], 'representative': 1371, 'size': 18}
  • id: 129700605
    {'aut_label': '4H1', 'centralizer': '18.j1.a1', 'counter': 25, 'group_counter': 34767, 'group_order': 1728, 'label': '4H-1', 'order': 4, 'powers': [3, 24], 'representative': 1299, 'size': 18}
  • id: 129700606
    {'aut_label': '4I', 'centralizer': '36.d1.a1', 'counter': 26, 'group_counter': 34767, 'group_order': 1728, 'label': '4I', 'order': 4, 'powers': [3, 26], 'representative': 90, 'size': 36}
  • id: 129700607
    {'aut_label': '4I', 'centralizer': '36.d1.b1', 'counter': 27, 'group_counter': 34767, 'group_order': 1728, 'label': '4J', 'order': 4, 'powers': [3, 27], 'representative': 37, 'size': 36}
  • id: 129700608
    {'aut_label': '4K', 'centralizer': '36.w1.a1', 'counter': 28, 'group_counter': 34767, 'group_order': 1728, 'label': '4K', 'order': 4, 'powers': [4, 28], 'representative': 761, 'size': 36}
  • id: 129700609
    {'aut_label': '4K', 'centralizer': '36.w1.b1', 'counter': 29, 'group_counter': 34767, 'group_order': 1728, 'label': '4L', 'order': 4, 'powers': [4, 29], 'representative': 1314, 'size': 36}
  • id: 129700611
    {'aut_label': '4M', 'centralizer': '54.g1.a1', 'counter': 30, 'group_counter': 34767, 'group_order': 1728, 'label': '4M', 'order': 4, 'powers': [4, 30], 'representative': 1603, 'size': 54}
  • id: 129700612
    {'aut_label': '4M', 'centralizer': '54.g1.a1', 'counter': 31, 'group_counter': 34767, 'group_order': 1728, 'label': '4N', 'order': 4, 'powers': [4, 31], 'representative': 1335, 'size': 54}
  • id: 129700613
    {'aut_label': '4O', 'centralizer': '108.m1.a1', 'counter': 32, 'group_counter': 34767, 'group_order': 1728, 'label': '4O', 'order': 4, 'powers': [4, 32], 'representative': 1527, 'size': 108}
  • id: 129700614
    {'aut_label': '6A', 'centralizer': '2.a1.b1', 'counter': 33, 'group_counter': 34767, 'group_order': 1728, 'label': '6A', 'order': 6, 'powers': [9, 2], 'representative': 888, 'size': 2}
  • id: 129700615
    {'aut_label': '6A', 'centralizer': '2.a1.a1', 'counter': 34, 'group_counter': 34767, 'group_order': 1728, 'label': '6B', 'order': 6, 'powers': [10, 2], 'representative': 940, 'size': 2}
  • id: 129700616
    {'aut_label': '6C', 'centralizer': '2.e1.a1', 'counter': 35, 'group_counter': 34767, 'group_order': 1728, 'label': '6C', 'order': 6, 'powers': [11, 4], 'representative': 288, 'size': 2}
  • id: 129700617
    {'aut_label': '6D', 'centralizer': '2.a1.b1', 'counter': 36, 'group_counter': 34767, 'group_order': 1728, 'label': '6D', 'order': 6, 'powers': [9, 4], 'representative': 960, 'size': 2}
  • id: 129700618
    {'aut_label': '6D', 'centralizer': '2.a1.a1', 'counter': 37, 'group_counter': 34767, 'group_order': 1728, 'label': '6E', 'order': 6, 'powers': [10, 4], 'representative': 872, 'size': 2}
  • id: 129700619
    {'aut_label': '6F', 'centralizer': '2.a1.b1', 'counter': 38, 'group_counter': 34767, 'group_order': 1728, 'label': '6F', 'order': 6, 'powers': [9, 3], 'representative': 24, 'size': 2}
  • id: 129700620
    {'aut_label': '6G', 'centralizer': '2.e1.a1', 'counter': 39, 'group_counter': 34767, 'group_order': 1728, 'label': '6G', 'order': 6, 'powers': [11, 3], 'representative': 1224, 'size': 2}
  • id: 129700622
    {'aut_label': '6F', 'centralizer': '2.a1.a1', 'counter': 40, 'group_counter': 34767, 'group_order': 1728, 'label': '6H', 'order': 6, 'powers': [10, 3], 'representative': 80, 'size': 2}
  • id: 129700623
    {'aut_label': '6I', 'centralizer': '2.e1.a1', 'counter': 41, 'group_counter': 34767, 'group_order': 1728, 'label': '6I', 'order': 6, 'powers': [11, 2], 'representative': 360, 'size': 2}
  • id: 129700624
    {'aut_label': '6J', 'centralizer': '4.a1.b1', 'counter': 42, 'group_counter': 34767, 'group_order': 1728, 'label': '6J', 'order': 6, 'powers': [12, 2], 'representative': 312, 'size': 4}
  • id: 129700625
    {'aut_label': '6K', 'centralizer': '4.h1.a1', 'counter': 43, 'group_counter': 34767, 'group_order': 1728, 'label': '6K', 'order': 6, 'powers': [13, 2], 'representative': 892, 'size': 4}
  • id: 129700626
    {'aut_label': '6J', 'centralizer': '4.a1.a1', 'counter': 44, 'group_counter': 34767, 'group_order': 1728, 'label': '6L', 'order': 6, 'powers': [14, 2], 'representative': 364, 'size': 4}
  • id: 129700627
    {'aut_label': '6M', 'centralizer': '4.h1.a1', 'counter': 45, 'group_counter': 34767, 'group_order': 1728, 'label': '6M', 'order': 6, 'powers': [13, 4], 'representative': 968, 'size': 4}
  • id: 129700628
    {'aut_label': '6N', 'centralizer': '4.a1.b1', 'counter': 46, 'group_counter': 34767, 'group_order': 1728, 'label': '6N', 'order': 6, 'powers': [12, 4], 'representative': 384, 'size': 4}
  • id: 129700629
    {'aut_label': '6N', 'centralizer': '4.a1.a1', 'counter': 47, 'group_counter': 34767, 'group_order': 1728, 'label': '6O', 'order': 6, 'powers': [14, 4], 'representative': 296, 'size': 4}
  • id: 129700630
    {'aut_label': '6P', 'centralizer': '4.h1.a1', 'counter': 48, 'group_counter': 34767, 'group_order': 1728, 'label': '6P', 'order': 6, 'powers': [13, 3], 'representative': 32, 'size': 4}
  • id: 129700631
    {'aut_label': '6Q', 'centralizer': '4.a1.a1', 'counter': 49, 'group_counter': 34767, 'group_order': 1728, 'label': '6Q', 'order': 6, 'powers': [14, 3], 'representative': 1228, 'size': 4}
  • id: 129700633
    {'aut_label': '6Q', 'centralizer': '4.a1.b1', 'counter': 50, 'group_counter': 34767, 'group_order': 1728, 'label': '6R', 'order': 6, 'powers': [12, 3], 'representative': 1176, 'size': 4}
  • id: 129700634
    {'aut_label': '6S', 'centralizer': '8.b1.a1', 'counter': 51, 'group_counter': 34767, 'group_order': 1728, 'label': '6S', 'order': 6, 'powers': [15, 3], 'representative': 604, 'size': 8}
  • id: 129700635
    {'aut_label': '6T', 'centralizer': '8.b1.a1', 'counter': 52, 'group_counter': 34767, 'group_order': 1728, 'label': '6T', 'order': 6, 'powers': [15, 2], 'representative': 316, 'size': 8}
  • id: 129700636
    {'aut_label': '6U', 'centralizer': '8.b1.a1', 'counter': 53, 'group_counter': 34767, 'group_order': 1728, 'label': '6U', 'order': 6, 'powers': [15, 4], 'representative': 392, 'size': 8}
  • id: 129700637
    {'aut_label': '6V', 'centralizer': '12.n1.a1', 'counter': 54, 'group_counter': 34767, 'group_order': 1728, 'label': '6V', 'order': 6, 'powers': [10, 5], 'representative': 2, 'size': 12}
  • id: 129700638
    {'aut_label': '6V', 'centralizer': '12.n1.a1', 'counter': 55, 'group_counter': 34767, 'group_order': 1728, 'label': '6W', 'order': 6, 'powers': [10, 6], 'representative': 26, 'size': 12}
  • id: 129700639
    {'aut_label': '6X', 'centralizer': '12.o1.b1', 'counter': 56, 'group_counter': 34767, 'group_order': 1728, 'label': '6X', 'order': 6, 'powers': [11, 7], 'representative': 577, 'size': 12}
  • id: 129700640
    {'aut_label': '6X', 'centralizer': '12.o1.b1', 'counter': 57, 'group_counter': 34767, 'group_order': 1728, 'label': '6Y', 'order': 6, 'powers': [11, 8], 'representative': 289, 'size': 12}
  • id: 129700641
    {'aut_label': '6V', 'centralizer': '12.n1.b1', 'counter': 58, 'group_counter': 34767, 'group_order': 1728, 'label': '6Z', 'order': 6, 'powers': [9, 7], 'representative': 49, 'size': 12}
  • id: 129700642
    {'aut_label': '6V', 'centralizer': '12.n1.b1', 'counter': 59, 'group_counter': 34767, 'group_order': 1728, 'label': '6AA', 'order': 6, 'powers': [9, 8], 'representative': 25, 'size': 12}
  • id: 129700644
    {'aut_label': '6X', 'centralizer': '12.o1.a1', 'counter': 60, 'group_counter': 34767, 'group_order': 1728, 'label': '6AB', 'order': 6, 'powers': [11, 5], 'representative': 582, 'size': 12}
  • id: 129700645
    {'aut_label': '6X', 'centralizer': '12.o1.a1', 'counter': 61, 'group_counter': 34767, 'group_order': 1728, 'label': '6AC', 'order': 6, 'powers': [11, 6], 'representative': 294, 'size': 12}
  • id: 129700646
    {'aut_label': '6AD', 'centralizer': '24.n1.a1', 'counter': 62, 'group_counter': 34767, 'group_order': 1728, 'label': '6AD', 'order': 6, 'powers': [14, 5], 'representative': 578, 'size': 24}
  • id: 129700647
    {'aut_label': '6AD', 'centralizer': '24.n1.a1', 'counter': 63, 'group_counter': 34767, 'group_order': 1728, 'label': '6AE', 'order': 6, 'powers': [14, 6], 'representative': 290, 'size': 24}
  • id: 129700648
    {'aut_label': '6AD', 'centralizer': '24.n1.b1', 'counter': 64, 'group_counter': 34767, 'group_order': 1728, 'label': '6AF', 'order': 6, 'powers': [12, 7], 'representative': 625, 'size': 24}
  • id: 129700649
    {'aut_label': '6AD', 'centralizer': '24.n1.b1', 'counter': 65, 'group_counter': 34767, 'group_order': 1728, 'label': '6AG', 'order': 6, 'powers': [12, 8], 'representative': 337, 'size': 24}
  • id: 129700650
    {'aut_label': '12A1', 'centralizer': '4.i1.a1', 'counter': 66, 'group_counter': 34767, 'group_order': 1728, 'label': '12A1', 'order': 12, 'powers': [35, 16], 'representative': 144, 'size': 4}
  • id: 129700651
    {'aut_label': '12A1', 'centralizer': '4.i1.a1', 'counter': 67, 'group_counter': 34767, 'group_order': 1728, 'label': '12A5', 'order': 12, 'powers': [35, 16], 'representative': 720, 'size': 4}
  • id: 129700652
    {'aut_label': '12B', 'centralizer': '8.b1.a1', 'counter': 68, 'group_counter': 34767, 'group_order': 1728, 'label': '12B', 'order': 12, 'powers': [36, 16], 'representative': 480, 'size': 8}
  • id: 129700653
    {'aut_label': '12B', 'centralizer': '8.b1.a1', 'counter': 69, 'group_counter': 34767, 'group_order': 1728, 'label': '12C', 'order': 12, 'powers': [37, 16], 'representative': 436, 'size': 8}
  • id: 129700655
    {'aut_label': '12D', 'centralizer': '8.b1.a1', 'counter': 70, 'group_counter': 34767, 'group_order': 1728, 'label': '12D', 'order': 12, 'powers': [45, 16], 'representative': 484, 'size': 8}
  • id: 129700656
    {'aut_label': '12D', 'centralizer': '8.b1.a1', 'counter': 71, 'group_counter': 34767, 'group_order': 1728, 'label': '12E', 'order': 12, 'powers': [45, 16], 'representative': 532, 'size': 8}
  • id: 129700657
    {'aut_label': '12F1', 'centralizer': '8.b1.a1', 'counter': 72, 'group_counter': 34767, 'group_order': 1728, 'label': '12F1', 'order': 12, 'powers': [46, 16], 'representative': 192, 'size': 8}
  • id: 129700658
    {'aut_label': '12F1', 'centralizer': '8.b1.a1', 'counter': 73, 'group_counter': 34767, 'group_order': 1728, 'label': '12F5', 'order': 12, 'powers': [46, 16], 'representative': 168, 'size': 8}
  • id: 129700659
    {'aut_label': '12F1', 'centralizer': '8.b1.a1', 'counter': 74, 'group_counter': 34767, 'group_order': 1728, 'label': '12G1', 'order': 12, 'powers': [47, 16], 'representative': 148, 'size': 8}
  • id: 129700660
    {'aut_label': '12F1', 'centralizer': '8.b1.a1', 'counter': 75, 'group_counter': 34767, 'group_order': 1728, 'label': '12G5', 'order': 12, 'powers': [47, 16], 'representative': 724, 'size': 8}
  • id: 129700661
    {'aut_label': '12H1', 'centralizer': '8.b1.a1', 'counter': 76, 'group_counter': 34767, 'group_order': 1728, 'label': '12H1', 'order': 12, 'powers': [53, 16], 'representative': 196, 'size': 8}
  • id: 129700662
    {'aut_label': '12H1', 'centralizer': '8.b1.a1', 'counter': 77, 'group_counter': 34767, 'group_order': 1728, 'label': '12H5', 'order': 12, 'powers': [53, 16], 'representative': 172, 'size': 8}
  • id: 129700663
    {'aut_label': '12H1', 'centralizer': '8.b1.a1', 'counter': 78, 'group_counter': 34767, 'group_order': 1728, 'label': '12I1', 'order': 12, 'powers': [53, 16], 'representative': 244, 'size': 8}
  • id: 129700664
    {'aut_label': '12H1', 'centralizer': '8.b1.a1', 'counter': 79, 'group_counter': 34767, 'group_order': 1728, 'label': '12I5', 'order': 12, 'powers': [53, 16], 'representative': 176, 'size': 8}
  • id: 129700666
    {'aut_label': '12J1', 'centralizer': '12.y1.b1', 'counter': 80, 'group_counter': 34767, 'group_order': 1728, 'label': '12J1', 'order': 12, 'powers': [38, 17], 'representative': 12, 'size': 12}
  • id: 129700667
    {'aut_label': '12J1', 'centralizer': '12.y1.b1', 'counter': 81, 'group_counter': 34767, 'group_order': 1728, 'label': '12J-1', 'order': 12, 'powers': [38, 18], 'representative': 84, 'size': 12}
  • id: 129700668
    {'aut_label': '12K1', 'centralizer': '12.s1.a1', 'counter': 82, 'group_counter': 34767, 'group_order': 1728, 'label': '12K1', 'order': 12, 'powers': [39, 19], 'representative': 145, 'size': 12}
  • id: 129700669
    {'aut_label': '12K1', 'centralizer': '12.s1.a1', 'counter': 83, 'group_counter': 34767, 'group_order': 1728, 'label': '12K5', 'order': 12, 'powers': [39, 19], 'representative': 721, 'size': 12}
  • id: 129700670
    {'aut_label': '12J1', 'centralizer': '12.y1.a1', 'counter': 84, 'group_counter': 34767, 'group_order': 1728, 'label': '12L1', 'order': 12, 'powers': [40, 18], 'representative': 40, 'size': 12}
  • id: 129700671
    {'aut_label': '12J1', 'centralizer': '12.y1.a1', 'counter': 85, 'group_counter': 34767, 'group_order': 1728, 'label': '12L-1', 'order': 12, 'powers': [40, 17], 'representative': 112, 'size': 12}
  • id: 129700672
    {'aut_label': '12K1', 'centralizer': '12.s1.b1', 'counter': 86, 'group_counter': 34767, 'group_order': 1728, 'label': '12M1', 'order': 12, 'powers': [39, 20], 'representative': 150, 'size': 12}
  • id: 129700673
    {'aut_label': '12K1', 'centralizer': '12.s1.b1', 'counter': 87, 'group_counter': 34767, 'group_order': 1728, 'label': '12M5', 'order': 12, 'powers': [39, 20], 'representative': 726, 'size': 12}
  • id: 129700674
    {'aut_label': '12N1', 'centralizer': '18.j1.a1', 'counter': 88, 'group_counter': 34767, 'group_order': 1728, 'label': '12N1', 'order': 12, 'powers': [39, 24], 'representative': 147, 'size': 18}
  • id: 129700675
    {'aut_label': '12N1', 'centralizer': '18.j1.a1', 'counter': 89, 'group_counter': 34767, 'group_order': 1728, 'label': '12N-1', 'order': 12, 'powers': [39, 25], 'representative': 747, 'size': 18}
  • id: 129700677
    {'aut_label': '12N1', 'centralizer': '18.j1.a1', 'counter': 90, 'group_counter': 34767, 'group_order': 1728, 'label': '12N5', 'order': 12, 'powers': [39, 24], 'representative': 723, 'size': 18}
  • id: 129700678
    {'aut_label': '12N1', 'centralizer': '18.j1.a1', 'counter': 91, 'group_counter': 34767, 'group_order': 1728, 'label': '12N-5', 'order': 12, 'powers': [39, 25], 'representative': 171, 'size': 18}
  • id: 129700679
    {'aut_label': '12O', 'centralizer': '24.bd1.a1', 'counter': 92, 'group_counter': 34767, 'group_order': 1728, 'label': '12O', 'order': 12, 'powers': [38, 21], 'representative': 156, 'size': 24}
  • id: 129700680
    {'aut_label': '12P', 'centralizer': '24.p1.b1', 'counter': 93, 'group_counter': 34767, 'group_order': 1728, 'label': '12P', 'order': 12, 'powers': [40, 20], 'representative': 434, 'size': 24}
  • id: 129700681
    {'aut_label': '12O', 'centralizer': '24.bd1.a1', 'counter': 94, 'group_counter': 34767, 'group_order': 1728, 'label': '12Q', 'order': 12, 'powers': [40, 21], 'representative': 184, 'size': 24}
  • id: 129700682
    {'aut_label': '12P', 'centralizer': '24.p1.a1', 'counter': 95, 'group_counter': 34767, 'group_order': 1728, 'label': '12R', 'order': 12, 'powers': [38, 19], 'representative': 481, 'size': 24}
  • id: 129700683
    {'aut_label': '12S1', 'centralizer': '24.bc1.a1', 'counter': 96, 'group_counter': 34767, 'group_order': 1728, 'label': '12S1', 'order': 12, 'powers': [48, 17], 'representative': 16, 'size': 24}
  • id: 129700684
    {'aut_label': '12S1', 'centralizer': '24.bc1.a1', 'counter': 97, 'group_counter': 34767, 'group_order': 1728, 'label': '12S-1', 'order': 12, 'powers': [48, 18], 'representative': 88, 'size': 24}
  • id: 129700685
    {'aut_label': '12T1', 'centralizer': '24.p1.b1', 'counter': 98, 'group_counter': 34767, 'group_order': 1728, 'label': '12T1', 'order': 12, 'powers': [49, 20], 'representative': 146, 'size': 24}
  • id: 129700686
    {'aut_label': '12T1', 'centralizer': '24.p1.b1', 'counter': 99, 'group_counter': 34767, 'group_order': 1728, 'label': '12T5', 'order': 12, 'powers': [49, 20], 'representative': 722, 'size': 24}
  • id: 129700578
    {'aut_label': '12U1', 'centralizer': '24.bd1.a1', 'counter': 100, 'group_counter': 34767, 'group_order': 1728, 'label': '12U1', 'order': 12, 'powers': [48, 21], 'representative': 160, 'size': 24}
  • id: 129700579
    {'aut_label': '12U1', 'centralizer': '24.bd1.a1', 'counter': 101, 'group_counter': 34767, 'group_order': 1728, 'label': '12U-1', 'order': 12, 'powers': [48, 21], 'representative': 164, 'size': 24}
  • id: 129700580
    {'aut_label': '12T1', 'centralizer': '24.p1.a1', 'counter': 102, 'group_counter': 34767, 'group_order': 1728, 'label': '12V1', 'order': 12, 'powers': [50, 19], 'representative': 193, 'size': 24}
  • id: 129700581
    {'aut_label': '12T1', 'centralizer': '24.p1.a1', 'counter': 103, 'group_counter': 34767, 'group_order': 1728, 'label': '12V5', 'order': 12, 'powers': [50, 19], 'representative': 169, 'size': 24}
  • id: 129700582
    {'aut_label': '12W', 'centralizer': '36.bu1.a1', 'counter': 104, 'group_counter': 34767, 'group_order': 1728, 'label': '12W', 'order': 12, 'powers': [41, 22], 'representative': 579, 'size': 36}
  • id: 129700583
    {'aut_label': '12W', 'centralizer': '36.bu1.a1', 'counter': 105, 'group_counter': 34767, 'group_order': 1728, 'label': '12X', 'order': 12, 'powers': [41, 23], 'representative': 291, 'size': 36}
  • id: 129700584
    {'aut_label': '12Y1', 'centralizer': '36.d1.a1', 'counter': 106, 'group_counter': 34767, 'group_order': 1728, 'label': '12Y1', 'order': 12, 'powers': [40, 26], 'representative': 14, 'size': 36}
  • id: 129700585
    {'aut_label': '12Y1', 'centralizer': '36.d1.a1', 'counter': 107, 'group_counter': 34767, 'group_order': 1728, 'label': '12Y-1', 'order': 12, 'powers': [40, 26], 'representative': 302, 'size': 36}
  • id: 129700586
    {'aut_label': '12Y1', 'centralizer': '36.d1.b1', 'counter': 108, 'group_counter': 34767, 'group_order': 1728, 'label': '12Z1', 'order': 12, 'powers': [38, 27], 'representative': 13, 'size': 36}
  • id: 129700587
    {'aut_label': '12Y1', 'centralizer': '36.d1.b1', 'counter': 109, 'group_counter': 34767, 'group_order': 1728, 'label': '12Z-1', 'order': 12, 'powers': [38, 27], 'representative': 301, 'size': 36}
  • id: 129700589
    {'aut_label': '12AA', 'centralizer': '72.q1.a1', 'counter': 110, 'group_counter': 34767, 'group_order': 1728, 'label': '12AA', 'order': 12, 'powers': [36, 28], 'representative': 1673, 'size': 72}
  • id: 129700590
    {'aut_label': '12AA', 'centralizer': '72.q1.b1', 'counter': 111, 'group_counter': 34767, 'group_order': 1728, 'label': '12AB', 'order': 12, 'powers': [37, 29], 'representative': 454, 'size': 72}
• gps_qchar •

  Column	Type
  cdim	integer
  counter	smallint
  faithful	boolean
  group	text
  group_order	numeric
  image	text
  label	text
  multiplicity	smallint
  nt	integer[]
  qdim	integer
  qvalues	integer[]
  schur_index	smallint

  
  
  • id: 9837874
    {'cdim': 1, 'counter': 1, 'faithful': False, 'group': '1728.34767', 'group_order': 1728, 'image': None, 'label': '1728.34767.1a', 'multiplicity': 1, 'nt': [1, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 'schur_index': 1}
  • id: 9837885
    {'cdim': 1, 'counter': 2, 'faithful': False, 'group': '1728.34767', 'group_order': 1728, 'image': None, 'label': '1728.34767.1b', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, 1, 1, 1, 1, -1, 1, -1, -1, -1, 1, 1, 1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, -1, -1, 1, -1, 1, 1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1], 'schur_index': 1}
  • id: 9837896
    {'cdim': 1, 'counter': 3, 'faithful': False, 'group': '1728.34767', 'group_order': 1728, 'image': None, 'label': '1728.34767.1c', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, -1, 1, 1, 1, 1, -1, 1, -1, 1, -1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, -1, 1, -1, 1, -1, 1, 1, -1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1], 'schur_index': 1}
  • id: 9837907
    {'cdim': 1, 'counter': 4, 'faithful': False, 'group': '1728.34767', 'group_order': 1728, 'image': None, 'label': '1728.34767.1d', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1], 'schur_index': 1}
  • id: 9837918
    {'cdim': 1, 'counter': 5, 'faithful': False, 'group': '1728.34767', 'group_order': 1728, 'image': None, 'label': '1728.34767.1e', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 1, 1, -1, 1, -1, -1, 1, 1, 1, 1, 1, -1, 1, -1, 1, -1, 1, 1, -1, 1, -1, -1, 1, 1, -1, -1, -1, -1, -1, -1], 'schur_index': 1}
  • id: 9837929
    {'cdim': 1, 'counter': 6, 'faithful': False, 'group': '1728.34767', 'group_order': 1728, 'image': None, 'label': '1728.34767.1f', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, 1, -1, 1, -1, 1, -1, 1, 1, -1, 1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 1, -1, -1, 1, 1, -1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, -1, 1, 1, -1, 1, -1, 1, -1, 1, 1, 1, -1, -1, -1, -1, -1, 1, 1, -1, 1], 'schur_index': 1}
  • id: 9837940
    {'cdim': 1, 'counter': 7, 'faithful': False, 'group': '1728.34767', 'group_order': 1728, 'image': None, 'label': '1728.34767.1g', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 1, 1, 1, -1, -1, -1, 1, -1, 1, -1, 1, -1, 1, 1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 1, -1, -1, 1, 1, -1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, -1, 1, -1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, 1, 1, -1, 1, -1, -1, -1, 1, 1, -1, -1, 1, -1], 'schur_index': 1}
  • id: 9837951
    {'cdim': 1, 'counter': 8, 'faithful': False, 'group': '1728.34767', 'group_order': 1728, 'image': None, 'label': '1728.34767.1h', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, 1, -1, -1, -1, -1, -1, -1, 1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 1, -1, -1, 1, 1, -1, 1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, -1, 1, -1, -1, -1, -1, -1, -1, -1, -1, 1, -1, 1, -1, -1, -1, -1, -1, 1, -1, -1, -1, -1, 1, 1, 1, -1], 'schur_index': 1}
  • id: 9837962
    {'cdim': 1, 'counter': 9, 'faithful': False, 'group': '1728.34767', 'group_order': 1728, 'image': None, 'label': '1728.34767.1i', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 1, 1, -1, -1, -1, -1, 1, -1, -1, 1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 1, -1, -1, 1, 1, -1, 1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, 1, -1, 1, 1, 1, 1, 1, 1, -1, 1, -1, 1, -1, -1, 1, 1, -1, -1, -1, 1], 'schur_index': 1}
  • id: 9837875
    {'cdim': 1, 'counter': 10, 'faithful': False, 'group': '1728.34767', 'group_order': 1728, 'image': None, 'label': '1728.34767.1j', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 1, -1, 1, 1, -1, -1, 1, -1, -1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, -1, 1, -1, 1, 1, 1, 1, -1, -1, 1, 1, 1, 1, 1, -1, -1, 1, -1, 1, -1, -1, 1, 1, -1, -1, 1, -1], 'schur_index': 1}
  • id: 9837876
    {'cdim': 1, 'counter': 11, 'faithful': False, 'group': '1728.34767', 'group_order': 1728, 'image': None, 'label': '1728.34767.1k', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, -1, 1, 1, -1, 1, -1, -1, 1, -1, 1, 1, -1, 1, -1, 1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 1, -1, 1, 1, -1, -1, 1, -1, -1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, -1, 1, 1, 1, 1, 1, -1, 1, 1, 1, 1, 1, -1, -1, 1, -1, 1, -1, 1, -1, -1, -1, 1, -1, -1, -1, -1, 1, 1, -1, 1], 'schur_index': 1}
  • id: 9837877
    {'cdim': 1, 'counter': 12, 'faithful': False, 'group': '1728.34767', 'group_order': 1728, 'image': None, 'label': '1728.34767.1l', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, -1, -1, -1, -1, -1, -1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 1, -1, 1, 1, -1, -1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 1, -1, -1, -1, -1, -1, 1, -1, -1, -1, -1, -1, 1, -1, -1, -1, -1, -1, -1, 1, -1, 1, -1, -1, -1, 1, 1, -1, -1, -1, 1], 'schur_index': 1}
  • id: 9837878
    {'cdim': 1, 'counter': 13, 'faithful': False, 'group': '1728.34767', 'group_order': 1728, 'image': None, 'label': '1728.34767.1m', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 1, -1, -1, -1, -1, -1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 1, -1, 1, 1, -1, -1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 1, -1, 1, -1, -1, -1, -1, 1, 1, 1, -1, 1, -1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, 1, 1, 1, -1], 'schur_index': 1}
  • id: 9837879
    {'cdim': 1, 'counter': 14, 'faithful': False, 'group': '1728.34767', 'group_order': 1728, 'image': None, 'label': '1728.34767.1n', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, 1, 1, -1, 1, -1, 1, 1, -1, -1, 1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, -1, 1, -1, 1, -1, -1, 1, -1, -1, 1, 1, -1, -1, -1, -1, 1, 1], 'schur_index': 1}
  • id: 9837880
    {'cdim': 1, 'counter': 15, 'faithful': False, 'group': '1728.34767', 'group_order': 1728, 'image': None, 'label': '1728.34767.1o', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 1, 1, -1, -1, -1, 1, -1, 1, -1, -1, -1, 1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, -1, 1, 1, -1, 1, -1, -1, -1, -1, -1, -1, 1, -1, -1, -1, -1, -1, -1, 1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, -1, -1], 'schur_index': 1}
  • id: 9837881
    {'cdim': 1, 'counter': 16, 'faithful': False, 'group': '1728.34767', 'group_order': 1728, 'image': None, 'label': '1728.34767.1p', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, 1, -1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 1, -1, -1, 1, -1, 1, 1, 1, 1, 1, 1, -1, 1, -1, 1, -1, 1, -1, -1, 1, -1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1], 'schur_index': 1}
  • id: 9837882
    {'cdim': 2, 'counter': 17, 'faithful': False, 'group': '1728.34767', 'group_order': 1728, 'image': None, 'label': '1728.34767.2a', 'multiplicity': 1, 'nt': [3, 2], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 0, 0, 2, 2, 2, -1, 2, -1, 2, -1, -1, 2, 2, 2, 0, 2, 2, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 2, -1, 2, -1, 2, -1, 2, 2, 2, -1, -1, -1, 2, 2, -1, 2, -1, -1, -1, -1, -1, 2, 0, 2, 0, 0, -1, -1, 0, -1, -1, 0, 0, 2, 2, -1, -1, -1, -1, 2, 2, -1, 2, -1, -1, -1, -1, -1, 0, 2, -1, 2, 2, 2, 0, 0, 0, 0, 0, -1, 0, -1, -1, 2, -1, -1, -1, 0, -1, 0, -1, 0, 0, -1, -1, 0, 0, 0, -1], 'schur_index': 1}
  • id: 9837883
    {'cdim': 2, 'counter': 18, 'faithful': False, 'group': '1728.34767', 'group_order': 1728, 'image': None, 'label': '1728.34767.2b', 'multiplicity': 1, 'nt': [3, 2], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 2, 2, 0, 0, -1, 2, 2, 2, -1, -1, -1, 2, 2, 2, 2, 0, 2, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 2, 2, -1, 2, -1, 2, -1, 2, 2, -1, -1, 2, -1, -1, -1, -1, 2, 2, -1, -1, -1, 0, 2, 0, -1, 2, 0, 0, -1, 0, 0, -1, -1, 2, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, 2, 2, 2, 2, 2, -1, 2, 0, -1, 0, 2, 0, 0, 0, 0, -1, -1, -1, 0, -1, 0, -1, -1, -1, 2, -1, 0, 0, 0, 0, 0, -1, -1, -1, 0], 'schur_index': 1}
  • id: 9837884
    {'cdim': 2, 'counter': 19, 'faithful': False, 'group': '1728.34767', 'group_order': 1728, 'image': None, 'label': '1728.34767.2c', 'multiplicity': 1, 'nt': [3, 2], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -1, -1, -1, 2, -1, 2, 0, 0, 2, 2, 0, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, -1, 2, 2, 2, 2, 2, 2, -1, -1, 2, 2, -1, -1, -1, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, 2, -1, 2, 2, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, 2, -1, -1, 2, 2, -1, 2, -1, -1, 0, -1, 0, 0, -1, 0, -1, -1, -1, -1, -1, -1, 0, -1, 0, -1, 0, -1, 0, 0, 2, 0, -1, 2, -1, -1, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 9837886
    {'cdim': 2, 'counter': 20, 'faithful': False, 'group': '1728.34767', 'group_order': 1728, 'image': None, 'label': '1728.34767.2d', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, 2, 2, 2, -2, -2, -2, -2, 2, 2, -1, -1, -1, 2, -1, -2, 0, 0, 2, 2, 0, 2, -2, 2, -2, 0, 0, 0, 0, 0, 0, 0, -1, 2, 2, 2, 2, 2, 2, -1, -1, 2, 2, -1, -1, -1, 2, -1, -1, -1, -1, -1, -1, 1, 1, 1, -2, 1, -2, -2, -2, 1, 1, 1, 1, 1, 1, 1, 1, 1, -2, 1, 1, -2, -2, 1, -2, 1, 1, 0, -1, 0, 0, -1, 0, -1, -1, 1, 1, 1, 1, 0, -1, 0, -1, 0, -1, 0, 0, 2, 0, -1, 2, -1, -1, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 9837887
    {'cdim': 2, 'counter': 21, 'faithful': False, 'group': '1728.34767', 'group_order': 1728, 'image': None, 'label': '1728.34767.2e', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, 2, 2, 2, -2, -2, -2, -2, 2, 2, -1, -1, -1, 2, -1, 2, 0, 0, -2, -2, 0, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, -1, 2, 2, 2, 2, 2, 2, -1, -1, 2, 2, -1, -1, -1, 2, -1, -1, -1, -1, -1, -1, 1, 1, 1, -2, 1, -2, -2, -2, 1, 1, 1, 1, -1, -1, -1, -1, -1, 2, -1, -1, 2, 2, -1, 2, -1, -1, 0, 1, 0, 0, 1, 0, 1, 1, -1, -1, -1, -1, 0, 1, 0, 1, 0, 1, 0, 0, -2, 0, 1, -2, -1, -1, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 9837888
    {'cdim': 2, 'counter': 22, 'faithful': False, 'group': '1728.34767', 'group_order': 1728, 'image': None, 'label': '1728.34767.2f', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, 2, 2, 2, -2, -2, 0, 0, -1, 2, 2, 2, -1, -1, -1, -2, -2, -2, 2, 0, 2, 0, 0, 0, 0, 0, -2, 2, 0, 0, 0, 0, 2, 2, -1, 2, -1, 2, -1, 2, 2, -1, -1, 2, -1, -1, -1, -1, 2, 2, -1, -1, -1, 0, -2, 0, 1, -2, 0, 0, 1, 0, 0, 1, 1, -2, -2, 1, 1, 1, 1, 1, 1, 1, 1, 1, -2, -2, -2, -2, 2, 1, -2, 0, 1, 0, 2, 0, 0, 0, 0, 1, -1, -1, 0, -1, 0, -1, 1, -1, 2, -1, 0, 0, 0, 0, 0, -1, -1, 1, 0], 'schur_index': 1}
  • id: 9837889
    {'cdim': 2, 'counter': 23, 'faithful': False, 'group': '1728.34767', 'group_order': 1728, 'image': None, 'label': '1728.34767.2g', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, 2, 2, 2, -2, -2, 0, 0, -1, 2, 2, 2, -1, -1, -1, -2, 2, 2, 2, 0, -2, 0, 0, 0, 0, 0, 2, -2, 0, 0, 0, 0, 2, 2, -1, 2, -1, 2, -1, 2, 2, -1, -1, 2, -1, -1, -1, -1, 2, 2, -1, -1, -1, 0, -2, 0, 1, -2, 0, 0, 1, 0, 0, 1, 1, -2, -2, 1, 1, 1, 1, 1, 1, 1, 1, 1, -2, -2, -2, 2, 2, -1, 2, 0, -1, 0, 2, 0, 0, 0, 0, -1, -1, 1, 0, 1, 0, 1, -1, -1, -2, -1, 0, 0, 0, 0, 0, 1, 1, -1, 0], 'schur_index': 1}
  • id: 9837890
    {'cdim': 2, 'counter': 24, 'faithful': False, 'group': '1728.34767', 'group_order': 1728, 'image': None, 'label': '1728.34767.2h', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, 2, 2, 2, -2, -2, 0, 0, -1, 2, 2, 2, -1, -1, -1, 2, -2, -2, -2, 0, -2, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 2, 2, -1, 2, -1, 2, -1, 2, 2, -1, -1, 2, -1, -1, -1, -1, 2, 2, -1, -1, -1, 0, -2, 0, 1, -2, 0, 0, 1, 0, 0, 1, 1, 2, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, 2, 2, 2, -2, -2, 1, -2, 0, 1, 0, -2, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 1, 1, 1, -2, 1, 0, 0, 0, 0, 0, -1, -1, -1, 0], 'schur_index': 1}
  • id: 9837891
    {'cdim': 2, 'counter': 25, 'faithful': False, 'group': '1728.34767', 'group_order': 1728, 'image': None, 'label': '1728.34767.2i', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, 2, 2, 2, -2, -2, 0, 0, -1, 2, 2, 2, -1, -1, -1, 2, 2, 2, -2, 0, 2, 0, 0, 0, 0, 0, -2, -2, 0, 0, 0, 0, 2, 2, -1, 2, -1, 2, -1, 2, 2, -1, -1, 2, -1, -1, -1, -1, 2, 2, -1, -1, -1, 0, -2, 0, 1, -2, 0, 0, 1, 0, 0, 1, 1, 2, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, 2, 2, 2, 2, -2, -1, 2, 0, -1, 0, -2, 0, 0, 0, 0, -1, 1, -1, 0, -1, 0, -1, -1, 1, 2, 1, 0, 0, 0, 0, 0, 1, 1, 1, 0], 'schur_index': 1}
  • id: 9837892
    {'cdim': 2, 'counter': 26, 'faithful': False, 'group': '1728.34767', 'group_order': 1728, 'image': None, 'label': '1728.34767.2j', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, 2, 2, 2, -2, -2, 2, 2, 2, 2, -1, -1, -1, 2, -1, -2, 0, 0, 2, -2, 0, -2, 2, -2, 2, 0, 0, 0, 0, 0, 0, 0, -1, 2, 2, 2, 2, 2, 2, -1, -1, 2, 2, -1, -1, -1, 2, -1, -1, -1, -1, -1, -1, -1, 1, -1, -2, 1, 2, 2, -2, -1, -1, 1, 1, 1, 1, 1, 1, 1, -2, 1, 1, -2, -2, 1, -2, 1, 1, 0, -1, 0, 0, 1, 0, 1, -1, -1, -1, -1, -1, 0, -1, 0, 1, 0, 1, 0, 0, 2, 0, -1, -2, 1, 1, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 9837893
    {'cdim': 2, 'counter': 27, 'faithful': False, 'group': '1728.34767', 'group_order': 1728, 'image': None, 'label': '1728.34767.2k', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, 2, 2, 2, -2, -2, 2, 2, 2, 2, -1, -1, -1, 2, -1, 2, 0, 0, -2, 2, 0, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, -1, 2, 2, 2, 2, 2, 2, -1, -1, 2, 2, -1, -1, -1, 2, -1, -1, -1, -1, -1, -1, -1, 1, -1, -2, 1, 2, 2, -2, -1, -1, 1, 1, -1, -1, -1, -1, -1, 2, -1, -1, 2, 2, -1, 2, -1, -1, 0, 1, 0, 0, -1, 0, -1, 1, 1, 1, 1, 1, 0, 1, 0, -1, 0, -1, 0, 0, -2, 0, 1, 2, 1, 1, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 9837894
    {'cdim': 2, 'counter': 28, 'faithful': False, 'group': '1728.34767', 'group_order': 1728, 'image': None, 'label': '1728.34767.2l', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 0, 0, -2, -2, 2, -1, 2, -1, 2, -1, -1, -2, -2, -2, 0, 2, 2, 0, 0, 0, 0, -2, 0, 0, 2, 0, 0, 0, 2, -1, 2, -1, 2, -1, 2, 2, 2, -1, -1, -1, 2, 2, -1, 2, -1, -1, -1, -1, -1, -2, 0, -2, 0, 0, 1, 1, 0, 1, 1, 0, 0, -2, -2, 1, 1, 1, 1, -2, -2, 1, -2, 1, 1, 1, 1, 1, 0, -2, 1, 2, -2, 2, 0, 0, 0, 0, 0, 1, 0, -1, -1, 2, -1, -1, 1, 0, -1, 0, -1, 0, 0, -1, -1, 0, 0, 0, 1], 'schur_index': 1}
  • id: 9837895
    {'cdim': 2, 'counter': 29, 'faithful': False, 'group': '1728.34767', 'group_order': 1728, 'image': None, 'label': '1728.34767.2m', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 0, 0, -2, -2, 2, -1, 2, -1, 2, -1, -1, -2, 2, 2, 0, 2, -2, 0, 0, 0, 0, 2, 0, 0, -2, 0, 0, 0, 2, -1, 2, -1, 2, -1, 2, 2, 2, -1, -1, -1, 2, 2, -1, 2, -1, -1, -1, -1, -1, -2, 0, -2, 0, 0, 1, 1, 0, 1, 1, 0, 0, -2, -2, 1, 1, 1, 1, -2, -2, 1, -2, 1, 1, 1, 1, -1, 0, 2, -1, 2, 2, 2, 0, 0, 0, 0, 0, -1, 0, 1, -1, -2, -1, 1, -1, 0, 1, 0, -1, 0, 0, 1, 1, 0, 0, 0, -1], 'schur_index': 1}
  • id: 9837897
    {'cdim': 2, 'counter': 30, 'faithful': False, 'group': '1728.34767', 'group_order': 1728, 'image': None, 'label': '1728.34767.2n', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 0, 0, -2, -2, 2, -1, 2, -1, 2, -1, -1, 2, -2, -2, 0, -2, -2, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 2, -1, 2, -1, 2, -1, 2, 2, 2, -1, -1, -1, 2, 2, -1, 2, -1, -1, -1, -1, -1, -2, 0, -2, 0, 0, 1, 1, 0, 1, 1, 0, 0, 2, 2, -1, -1, -1, -1, 2, 2, -1, 2, -1, -1, -1, -1, 1, 0, -2, 1, -2, -2, -2, 0, 0, 0, 0, 0, 1, 0, 1, 1, -2, 1, 1, 1, 0, 1, 0, 1, 0, 0, -1, -1, 0, 0, 0, -1], 'schur_index': 1}
  • id: 9837898
    {'cdim': 2, 'counter': 31, 'faithful': False, 'group': '1728.34767', 'group_order': 1728, 'image': None, 'label': '1728.34767.2o', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 0, 0, -2, -2, 2, -1, 2, -1, 2, -1, -1, 2, 2, 2, 0, -2, 2, 0, 0, 0, 0, -2, 0, 0, -2, 0, 0, 0, 2, -1, 2, -1, 2, -1, 2, 2, 2, -1, -1, -1, 2, 2, -1, 2, -1, -1, -1, -1, -1, -2, 0, -2, 0, 0, 1, 1, 0, 1, 1, 0, 0, 2, 2, -1, -1, -1, -1, 2, 2, -1, 2, -1, -1, -1, -1, -1, 0, 2, -1, -2, 2, -2, 0, 0, 0, 0, 0, -1, 0, -1, 1, 2, 1, -1, -1, 0, -1, 0, 1, 0, 0, 1, 1, 0, 0, 0, 1], 'schur_index': 1}
  • id: 9837899
    {'cdim': 2, 'counter': 32, 'faithful': False, 'group': '1728.34767', 'group_order': 1728, 'image': None, 'label': '1728.34767.2p', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 0, 0, 2, 2, 2, -1, 2, -1, 2, -1, -1, -2, -2, -2, 0, -2, 2, 0, 0, 0, 0, 2, 0, 0, -2, 0, 0, 0, 2, -1, 2, -1, 2, -1, 2, 2, 2, -1, -1, -1, 2, 2, -1, 2, -1, -1, -1, -1, -1, 2, 0, 2, 0, 0, -1, -1, 0, -1, -1, 0, 0, -2, -2, 1, 1, 1, 1, -2, -2, 1, -2, 1, 1, 1, 1, 1, 0, -2, 1, -2, -2, -2, 0, 0, 0, 0, 0, 1, 0, -1, 1, 2, 1, -1, 1, 0, -1, 0, 1, 0, 0, 1, 1, 0, 0, 0, -1], 'schur_index': 1}
  • id: 9837900
    {'cdim': 2, 'counter': 33, 'faithful': False, 'group': '1728.34767', 'group_order': 1728, 'image': None, 'label': '1728.34767.2q', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 0, 0, 2, 2, 2, -1, 2, -1, 2, -1, -1, -2, 2, 2, 0, -2, -2, 0, 0, 0, 0, -2, 0, 0, 2, 0, 0, 0, 2, -1, 2, -1, 2, -1, 2, 2, 2, -1, -1, -1, 2, 2, -1, 2, -1, -1, -1, -1, -1, 2, 0, 2, 0, 0, -1, -1, 0, -1, -1, 0, 0, -2, -2, 1, 1, 1, 1, -2, -2, 1, -2, 1, 1, 1, 1, -1, 0, 2, -1, -2, 2, -2, 0, 0, 0, 0, 0, -1, 0, 1, 1, -2, 1, 1, -1, 0, 1, 0, 1, 0, 0, -1, -1, 0, 0, 0, 1], 'schur_index': 1}
  • id: 9837901
    {'cdim': 2, 'counter': 34, 'faithful': False, 'group': '1728.34767', 'group_order': 1728, 'image': None, 'label': '1728.34767.2r', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 0, 0, 2, 2, 2, -1, 2, -1, 2, -1, -1, 2, -2, -2, 0, 2, -2, 0, 0, 0, 0, -2, 0, 0, -2, 0, 0, 0, 2, -1, 2, -1, 2, -1, 2, 2, 2, -1, -1, -1, 2, 2, -1, 2, -1, -1, -1, -1, -1, 2, 0, 2, 0, 0, -1, -1, 0, -1, -1, 0, 0, 2, 2, -1, -1, -1, -1, 2, 2, -1, 2, -1, -1, -1, -1, 1, 0, -2, 1, 2, -2, 2, 0, 0, 0, 0, 0, 1, 0, 1, -1, -2, -1, 1, 1, 0, 1, 0, -1, 0, 0, 1, 1, 0, 0, 0, 1], 'schur_index': 1}
  • id: 9837902
    {'cdim': 2, 'counter': 35, 'faithful': False, 'group': '1728.34767', 'group_order': 1728, 'image': None, 'label': '1728.34767.2s', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 2, 2, -2, -2, 2, 2, -1, -1, -1, 2, -1, -2, 0, 0, -2, 2, 0, -2, 2, -2, 2, 0, 0, 0, 0, 0, 0, 0, -1, 2, 2, 2, 2, 2, 2, -1, -1, 2, 2, -1, -1, -1, 2, -1, -1, -1, -1, -1, -1, 1, -1, 1, 2, -1, -2, -2, 2, 1, 1, -1, -1, 1, 1, 1, 1, 1, -2, 1, 1, -2, -2, 1, -2, 1, 1, 0, 1, 0, 0, -1, 0, -1, 1, -1, -1, -1, -1, 0, 1, 0, -1, 0, -1, 0, 0, -2, 0, 1, 2, 1, 1, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 9837903
    {'cdim': 2, 'counter': 36, 'faithful': False, 'group': '1728.34767', 'group_order': 1728, 'image': None, 'label': '1728.34767.2t', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 2, 2, -2, -2, 2, 2, -1, -1, -1, 2, -1, 2, 0, 0, 2, -2, 0, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, -1, 2, 2, 2, 2, 2, 2, -1, -1, 2, 2, -1, -1, -1, 2, -1, -1, -1, -1, -1, -1, 1, -1, 1, 2, -1, -2, -2, 2, 1, 1, -1, -1, -1, -1, -1, -1, -1, 2, -1, -1, 2, 2, -1, 2, -1, -1, 0, -1, 0, 0, 1, 0, 1, -1, 1, 1, 1, 1, 0, -1, 0, 1, 0, 1, 0, 0, 2, 0, -1, -2, 1, 1, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 9837904
    {'cdim': 2, 'counter': 37, 'faithful': False, 'group': '1728.34767', 'group_order': 1728, 'image': None, 'label': '1728.34767.2u', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 2, 2, 0, 0, -1, 2, 2, 2, -1, -1, -1, -2, -2, -2, -2, 0, 2, 0, 0, 0, 0, 0, 2, -2, 0, 0, 0, 0, 2, 2, -1, 2, -1, 2, -1, 2, 2, -1, -1, 2, -1, -1, -1, -1, 2, 2, -1, -1, -1, 0, 2, 0, -1, 2, 0, 0, -1, 0, 0, -1, -1, -2, -2, 1, 1, 1, 1, 1, 1, 1, 1, 1, -2, -2, -2, -2, -2, 1, -2, 0, 1, 0, -2, 0, 0, 0, 0, 1, 1, -1, 0, -1, 0, -1, 1, 1, 2, 1, 0, 0, 0, 0, 0, 1, 1, -1, 0], 'schur_index': 1}
  • id: 9837905
    {'cdim': 2, 'counter': 38, 'faithful': False, 'group': '1728.34767', 'group_order': 1728, 'image': None, 'label': '1728.34767.2v', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 2, 2, 0, 0, -1, 2, 2, 2, -1, -1, -1, -2, 2, 2, -2, 0, -2, 0, 0, 0, 0, 0, -2, 2, 0, 0, 0, 0, 2, 2, -1, 2, -1, 2, -1, 2, 2, -1, -1, 2, -1, -1, -1, -1, 2, 2, -1, -1, -1, 0, 2, 0, -1, 2, 0, 0, -1, 0, 0, -1, -1, -2, -2, 1, 1, 1, 1, 1, 1, 1, 1, 1, -2, -2, -2, 2, -2, -1, 2, 0, -1, 0, -2, 0, 0, 0, 0, -1, 1, 1, 0, 1, 0, 1, -1, 1, -2, 1, 0, 0, 0, 0, 0, -1, -1, 1, 0], 'schur_index': 1}
  • id: 9837906
    {'cdim': 2, 'counter': 39, 'faithful': False, 'group': '1728.34767', 'group_order': 1728, 'image': None, 'label': '1728.34767.2w', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 2, 2, 0, 0, -1, 2, 2, 2, -1, -1, -1, 2, -2, -2, 2, 0, -2, 0, 0, 0, 0, 0, -2, -2, 0, 0, 0, 0, 2, 2, -1, 2, -1, 2, -1, 2, 2, -1, -1, 2, -1, -1, -1, -1, 2, 2, -1, -1, -1, 0, 2, 0, -1, 2, 0, 0, -1, 0, 0, -1, -1, 2, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, 2, 2, 2, -2, 2, 1, -2, 0, 1, 0, 2, 0, 0, 0, 0, 1, -1, 1, 0, 1, 0, 1, 1, -1, -2, -1, 0, 0, 0, 0, 0, 1, 1, 1, 0], 'schur_index': 1}
  • id: 9837908
    {'cdim': 2, 'counter': 40, 'faithful': False, 'group': '1728.34767', 'group_order': 1728, 'image': None, 'label': '1728.34767.2x', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -1, -1, -1, 2, -1, -2, 0, 0, -2, -2, 0, 2, -2, 2, -2, 0, 0, 0, 0, 0, 0, 0, -1, 2, 2, 2, 2, 2, 2, -1, -1, 2, 2, -1, -1, -1, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, 2, -1, 2, 2, 2, -1, -1, -1, -1, 1, 1, 1, 1, 1, -2, 1, 1, -2, -2, 1, -2, 1, 1, 0, 1, 0, 0, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 0, 1, 0, 0, -2, 0, 1, -2, -1, -1, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 9837909
    {'cdim': 2, 'counter': 41, 'faithful': False, 'group': '1728.34767', 'group_order': 1728, 'image': None, 'label': '1728.34767.2y', 'multiplicity': 1, 'nt': [8, 5], 'qdim': 2, 'qvalues': [2, 2, -2, -2, -2, 2, -2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, -2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, -2, 2, -2, -2, 2, -2, -2, -2, -2, 2, 2, 2, -2, -2, -2, -2, -2, -2, 2, -2, 2, -2, -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, 0, 0, 0, 0, 2, -2, 0, 0, 0, 0, 0, 0], 'schur_index': 2}
  • id: 9837910
    {'cdim': 2, 'counter': 42, 'faithful': False, 'group': '1728.34767', 'group_order': 1728, 'image': None, 'label': '1728.34767.2z', 'multiplicity': 1, 'nt': [8, 5], 'qdim': 2, 'qvalues': [2, 2, -2, -2, -2, 2, 2, -2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 2, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 2, -2, 2, -2, -2, 2, -2, -2, -2, -2, 2, 2, 2, -2, -2, -2, -2, -2, -2, 2, -2, -2, -2, 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, 0, 0, 0, 0, -2, 2, 0, 0, 0, 0, 0, 0], 'schur_index': 2}
  • id: 9837911
    {'cdim': 2, 'counter': 43, 'faithful': False, 'group': '1728.34767', 'group_order': 1728, 'image': None, 'label': '1728.34767.2aa', 'multiplicity': 1, 'nt': [8, 5], 'qdim': 2, 'qvalues': [2, 2, -2, -2, 2, -2, -2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 2, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 2, -2, 2, -2, -2, 2, -2, -2, -2, -2, 2, 2, 2, -2, -2, -2, -2, -2, -2, 2, -2, 2, 2, -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, 0, 0, 0, 0, -2, 2, 0, 0, 0, 0, 0, 0], 'schur_index': 2}
  • id: 9837912
    {'cdim': 2, 'counter': 44, 'faithful': False, 'group': '1728.34767', 'group_order': 1728, 'image': None, 'label': '1728.34767.2ab', 'multiplicity': 1, 'nt': [8, 5], 'qdim': 2, 'qvalues': [2, 2, -2, -2, 2, -2, 2, -2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, -2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, -2, 2, -2, -2, 2, -2, -2, -2, -2, 2, 2, 2, -2, -2, -2, -2, -2, -2, 2, -2, -2, 2, 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, 0, 0, 0, 0, 2, -2, 0, 0, 0, 0, 0, 0], 'schur_index': 2}
  • id: 9837913
    {'cdim': 2, 'counter': 45, 'faithful': False, 'group': '1728.34767', 'group_order': 1728, 'image': None, 'label': '1728.34767.2ac', 'multiplicity': 2, 'nt': [8, 11], 'qdim': 4, 'qvalues': [4, -4, -4, 4, 0, 0, 0, 0, 4, 4, 4, 4, 4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 4, 0, -4, 4, -4, -4, -4, -4, 4, -4, 4, -4, -4, -4, -4, 4, 4, -4, -4, 4, -4, -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, 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: 9837914
    {'cdim': 2, 'counter': 46, 'faithful': False, 'group': '1728.34767', 'group_order': 1728, 'image': None, 'label': '1728.34767.2ad', 'multiplicity': 2, 'nt': [8, 11], 'qdim': 4, 'qvalues': [4, -4, -4, 4, 0, 0, 0, 0, 4, 4, 4, 4, 4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, -4, 0, -4, 4, -4, -4, -4, -4, 4, -4, 4, -4, -4, -4, -4, 4, 4, -4, -4, 4, -4, -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, 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: 9837915
    {'cdim': 2, 'counter': 47, 'faithful': False, 'group': '1728.34767', 'group_order': 1728, 'image': None, 'label': '1728.34767.2ae', 'multiplicity': 2, 'nt': [24, 5], 'qdim': 4, 'qvalues': [4, 4, -4, -4, -4, 4, -4, 4, 4, 4, -2, -2, -2, 4, -2, 0, 0, 0, 0, 0, 0, -4, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, -2, -4, 4, -4, -4, 4, -4, 2, 2, -4, 4, -2, -2, 2, -4, 2, 2, 2, 2, -2, 2, -2, 2, 2, 4, -2, -4, 4, -4, 2, -2, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 2, 0, 0, 0, 0, 0, 0], 'schur_index': 2}
  • id: 9837916
    {'cdim': 2, 'counter': 48, 'faithful': False, 'group': '1728.34767', 'group_order': 1728, 'image': None, 'label': '1728.34767.2af', 'multiplicity': 2, 'nt': [24, 5], 'qdim': 4, 'qvalues': [4, 4, -4, -4, -4, 4, 4, -4, 4, 4, -2, -2, -2, 4, -2, 0, 0, 0, 0, 0, 0, 4, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, -2, -4, 4, -4, -4, 4, -4, 2, 2, -4, 4, -2, -2, 2, -4, 2, 2, 2, 2, -2, 2, 2, 2, -2, 4, -2, 4, -4, -4, -2, 2, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, -2, 0, 0, 0, 0, 0, 0], 'schur_index': 2}
  • id: 9837917
    {'cdim': 2, 'counter': 49, 'faithful': False, 'group': '1728.34767', 'group_order': 1728, 'image': None, 'label': '1728.34767.2ag', 'multiplicity': 2, 'nt': [24, 5], 'qdim': 4, 'qvalues': [4, 4, -4, -4, 4, -4, -4, 4, 4, 4, -2, -2, -2, 4, -2, 0, 0, 0, 0, 0, 0, 4, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, -2, -4, 4, -4, -4, 4, -4, 2, 2, -4, 4, -2, -2, 2, -4, 2, 2, 2, 2, -2, 2, -2, -2, 2, -4, 2, -4, 4, 4, 2, -2, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, -2, 0, 0, 0, 0, 0, 0], 'schur_index': 2}
  • id: 9837919
    {'cdim': 2, 'counter': 50, 'faithful': False, 'group': '1728.34767', 'group_order': 1728, 'image': None, 'label': '1728.34767.2ah', 'multiplicity': 2, 'nt': [24, 5], 'qdim': 4, 'qvalues': [4, 4, -4, -4, 4, -4, 4, -4, 4, 4, -2, -2, -2, 4, -2, 0, 0, 0, 0, 0, 0, -4, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, -2, -4, 4, -4, -4, 4, -4, 2, 2, -4, 4, -2, -2, 2, -4, 2, 2, 2, 2, -2, 2, 2, -2, -2, -4, 2, 4, -4, 4, -2, 2, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 2, 0, 0, 0, 0, 0, 0], 'schur_index': 2}
  • id: 9837920
    {'cdim': 4, 'counter': 51, 'faithful': False, 'group': '1728.34767', 'group_order': 1728, 'image': None, 'label': '1728.34767.4a', 'multiplicity': 1, 'nt': [6, 9], 'qdim': 4, 'qvalues': [4, 4, 4, 4, 0, 0, 0, 0, -2, -2, 4, -2, -2, 1, 1, 4, 4, 4, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, -2, -2, -2, -2, -2, -2, 4, 4, 1, 1, -2, -2, -2, 1, -2, -2, -2, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 1, 1, 1, 1, -2, -2, 1, -2, 1, -2, -2, -2, -2, 0, -2, -2, 0, -2, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, -2, 0, 1, 1, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 9837921
    {'cdim': 4, 'counter': 52, 'faithful': False, 'group': '1728.34767', 'group_order': 1728, 'image': None, 'label': '1728.34767.4b', 'multiplicity': 1, 'nt': [6, 9], 'qdim': 4, 'qvalues': [4, 4, 4, 4, 0, 0, 4, 4, 4, -2, -2, 1, -2, -2, 1, 4, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, 4, -2, 4, -2, 4, -2, -2, -2, -2, 1, -2, -2, -2, -2, 1, 1, 1, 1, 1, -2, 0, -2, 0, 0, -2, -2, 0, 1, 1, 0, 0, -2, -2, 1, 1, 1, -2, -2, -2, -2, 4, 1, -2, 1, 1, 0, 0, 0, 0, -2, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 9837922
    {'cdim': 4, 'counter': 53, 'faithful': False, 'group': '1728.34767', 'group_order': 1728, 'image': None, 'label': '1728.34767.4c', 'multiplicity': 1, 'nt': [6, 9], 'qdim': 4, 'qvalues': [4, 4, 4, 4, 4, 4, 0, 0, -2, 4, -2, -2, 1, -2, 1, 4, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 4, -2, 4, -2, 4, -2, -2, -2, -2, -2, -2, 1, 1, -2, 1, -2, -2, 1, 1, 1, 0, -2, 0, -2, -2, 0, 0, -2, 0, 0, 1, 1, -2, -2, 1, 1, 1, -2, 1, 1, -2, -2, 1, 4, -2, -2, 0, -2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, -2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 9837923
    {'cdim': 4, 'counter': 54, 'faithful': False, 'group': '1728.34767', 'group_order': 1728, 'image': None, 'label': '1728.34767.4d', 'multiplicity': 1, 'nt': [8, 22], 'qdim': 4, 'qvalues': [4, -4, 4, -4, 0, 0, 0, 0, 4, 4, 4, 4, 4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, -4, -4, 4, 4, -4, -4, 4, -4, 4, -4, -4, -4, -4, -4, 4, 4, -4, 4, -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, 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: 9837924
    {'cdim': 4, 'counter': 55, 'faithful': False, 'group': '1728.34767', 'group_order': 1728, 'image': None, 'label': '1728.34767.4e', 'multiplicity': 1, 'nt': [12, 37], 'qdim': 4, 'qvalues': [4, 4, 4, 4, -4, -4, 0, 0, -2, 4, -2, -2, 1, -2, 1, -4, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 4, -2, 4, -2, 4, -2, -2, -2, -2, -2, -2, 1, 1, -2, 1, -2, -2, 1, 1, 1, 0, 2, 0, 2, 2, 0, 0, 2, 0, 0, -1, -1, 2, 2, -1, -1, -1, 2, -1, -1, 2, 2, -1, -4, 2, 2, 0, -2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, -2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 9837925
    {'cdim': 4, 'counter': 56, 'faithful': False, 'group': '1728.34767', 'group_order': 1728, 'image': None, 'label': '1728.34767.4f', 'multiplicity': 1, 'nt': [12, 37], 'qdim': 4, 'qvalues': [4, 4, 4, 4, -4, -4, 0, 0, -2, 4, -2, -2, 1, -2, 1, 4, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 4, -2, 4, -2, 4, -2, -2, -2, -2, -2, -2, 1, 1, -2, 1, -2, -2, 1, 1, 1, 0, 2, 0, 2, 2, 0, 0, 2, 0, 0, -1, -1, -2, -2, 1, 1, 1, -2, 1, 1, -2, -2, 1, 4, -2, -2, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 2, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 9837926
    {'cdim': 4, 'counter': 57, 'faithful': False, 'group': '1728.34767', 'group_order': 1728, 'image': None, 'label': '1728.34767.4g', 'multiplicity': 1, 'nt': [12, 37], 'qdim': 4, 'qvalues': [4, 4, 4, 4, 0, 0, -4, -4, 4, -2, -2, 1, -2, -2, 1, -4, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, 4, -2, 4, -2, 4, -2, -2, -2, -2, 1, -2, -2, -2, -2, 1, 1, 1, 1, 1, 2, 0, 2, 0, 0, 2, 2, 0, -1, -1, 0, 0, 2, 2, -1, -1, -1, 2, 2, 2, 2, -4, -1, 2, -1, -1, 0, 0, 0, 0, -2, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 9837927
    {'cdim': 4, 'counter': 58, 'faithful': False, 'group': '1728.34767', 'group_order': 1728, 'image': None, 'label': '1728.34767.4h', 'multiplicity': 1, 'nt': [12, 37], 'qdim': 4, 'qvalues': [4, 4, 4, 4, 0, 0, -4, -4, 4, -2, -2, 1, -2, -2, 1, 4, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, 4, -2, 4, -2, 4, -2, -2, -2, -2, 1, -2, -2, -2, -2, 1, 1, 1, 1, 1, 2, 0, 2, 0, 0, 2, 2, 0, -1, -1, 0, 0, -2, -2, 1, 1, 1, -2, -2, -2, -2, 4, 1, -2, 1, 1, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, -1, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 9837928
    {'cdim': 4, 'counter': 59, 'faithful': False, 'group': '1728.34767', 'group_order': 1728, 'image': None, 'label': '1728.34767.4i', 'multiplicity': 1, 'nt': [12, 37], 'qdim': 4, 'qvalues': [4, 4, 4, 4, 0, 0, 0, 0, -2, -2, 4, -2, -2, 1, 1, -4, -4, -4, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, -2, -2, -2, -2, -2, -2, 4, 4, 1, 1, -2, -2, -2, 1, -2, -2, -2, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, -4, -1, -1, -1, -1, 2, 2, -1, 2, -1, 2, 2, 2, 2, 0, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, -1, 0, 1, 0, -2, 0, 1, -1, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 9837930
    {'cdim': 4, 'counter': 60, 'faithful': False, 'group': '1728.34767', 'group_order': 1728, 'image': None, 'label': '1728.34767.4j', 'multiplicity': 1, 'nt': [12, 37], 'qdim': 4, 'qvalues': [4, 4, 4, 4, 0, 0, 0, 0, -2, -2, 4, -2, -2, 1, 1, -4, 4, 4, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, -2, -2, -2, -2, -2, -2, 4, 4, 1, 1, -2, -2, -2, 1, -2, -2, -2, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, -4, -1, -1, -1, -1, 2, 2, -1, 2, -1, 2, 2, 2, -2, 0, -2, -2, 0, -2, 0, 0, 0, 0, 0, 0, 1, 0, -1, 0, 2, 0, -1, 1, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 9837931
    {'cdim': 4, 'counter': 61, 'faithful': False, 'group': '1728.34767', 'group_order': 1728, 'image': None, 'label': '1728.34767.4k', 'multiplicity': 1, 'nt': [12, 37], 'qdim': 4, 'qvalues': [4, 4, 4, 4, 0, 0, 0, 0, -2, -2, 4, -2, -2, 1, 1, 4, -4, -4, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, -2, -2, -2, -2, -2, -2, 4, 4, 1, 1, -2, -2, -2, 1, -2, -2, -2, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 1, 1, 1, 1, -2, -2, 1, -2, 1, -2, -2, -2, 2, 0, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, -1, 0, -1, 0, 2, 0, -1, -1, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 9837932
    {'cdim': 4, 'counter': 62, 'faithful': False, 'group': '1728.34767', 'group_order': 1728, 'image': None, 'label': '1728.34767.4l', 'multiplicity': 1, 'nt': [12, 37], 'qdim': 4, 'qvalues': [4, 4, 4, 4, 0, 0, 4, 4, 4, -2, -2, 1, -2, -2, 1, -4, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, 4, -2, 4, -2, 4, -2, -2, -2, -2, 1, -2, -2, -2, -2, 1, 1, 1, 1, 1, -2, 0, -2, 0, 0, -2, -2, 0, 1, 1, 0, 0, 2, 2, -1, -1, -1, 2, 2, 2, 2, -4, -1, 2, -1, -1, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, -1, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 9837933
    {'cdim': 4, 'counter': 63, 'faithful': False, 'group': '1728.34767', 'group_order': 1728, 'image': None, 'label': '1728.34767.4m', 'multiplicity': 1, 'nt': [12, 37], 'qdim': 4, 'qvalues': [4, 4, 4, 4, 4, 4, 0, 0, -2, 4, -2, -2, 1, -2, 1, -4, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 4, -2, 4, -2, 4, -2, -2, -2, -2, -2, -2, 1, 1, -2, 1, -2, -2, 1, 1, 1, 0, -2, 0, -2, -2, 0, 0, -2, 0, 0, 1, 1, 2, 2, -1, -1, -1, 2, -1, -1, 2, 2, -1, -4, 2, 2, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 2, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 9837934
    {'cdim': 4, 'counter': 64, 'faithful': False, 'group': '1728.34767', 'group_order': 1728, 'image': None, 'label': '1728.34767.4n', 'multiplicity': 1, 'nt': [24, 26], 'qdim': 4, 'qvalues': [4, 4, -4, -4, -4, 4, 0, 0, -2, 4, 4, 4, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, -4, -2, -4, 2, 4, 2, -4, -4, 2, -2, 4, -2, 2, 2, 2, -4, -4, 2, -2, 2, 0, -4, 0, -2, 4, 0, 0, 2, 0, 0, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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': 2}
  • id: 9837935
    {'cdim': 4, 'counter': 65, 'faithful': False, 'group': '1728.34767', 'group_order': 1728, 'image': None, 'label': '1728.34767.4o', 'multiplicity': 1, 'nt': [24, 26], 'qdim': 4, 'qvalues': [4, 4, -4, -4, 0, 0, -4, 4, 4, -2, 4, -2, 4, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 2, 4, 2, -4, -2, -4, -4, -4, 2, -2, -2, 4, -4, 2, -4, 2, 2, 2, -2, 2, 4, 0, -4, 0, 0, 2, -2, 0, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 2}
  • id: 9837936
    {'cdim': 4, 'counter': 66, 'faithful': False, 'group': '1728.34767', 'group_order': 1728, 'image': None, 'label': '1728.34767.4p', 'multiplicity': 1, 'nt': [24, 26], 'qdim': 4, 'qvalues': [4, 4, -4, -4, 0, 0, 4, -4, 4, -2, 4, -2, 4, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 2, 4, 2, -4, -2, -4, -4, -4, 2, -2, -2, 4, -4, 2, -4, 2, 2, 2, -2, 2, -4, 0, 4, 0, 0, -2, 2, 0, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 2}
  • id: 9837937
    {'cdim': 4, 'counter': 67, 'faithful': False, 'group': '1728.34767', 'group_order': 1728, 'image': None, 'label': '1728.34767.4q', 'multiplicity': 1, 'nt': [24, 26], 'qdim': 4, 'qvalues': [4, 4, -4, -4, 4, -4, 0, 0, -2, 4, 4, 4, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, -4, -2, -4, 2, 4, 2, -4, -4, 2, -2, 4, -2, 2, 2, 2, -4, -4, 2, -2, 2, 0, 4, 0, 2, -4, 0, 0, -2, 0, 0, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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': 2}
  • id: 9837938
    {'cdim': 4, 'counter': 68, 'faithful': False, 'group': '1728.34767', 'group_order': 1728, 'image': None, 'label': '1728.34767.4r', 'multiplicity': 2, 'nt': [24, 95], 'qdim': 8, 'qvalues': [8, -8, 8, -8, 0, 0, 0, 0, -4, 8, 8, 8, -4, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -8, -8, 4, 8, -4, -8, 4, 8, -8, -4, 4, -8, 4, 4, 4, -4, 8, -8, -4, 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, 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: 9837939
    {'cdim': 4, 'counter': 69, 'faithful': False, 'group': '1728.34767', 'group_order': 1728, 'image': None, 'label': '1728.34767.4s', 'multiplicity': 2, 'nt': [24, 95], 'qdim': 8, 'qvalues': [8, -8, 8, -8, 0, 0, 0, 0, 8, -4, 8, -4, 8, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -8, 4, -8, -4, 8, 4, -8, 8, -8, -4, 4, 4, -8, -8, 4, 8, -4, 4, -4, 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, 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: 9837941
    {'cdim': 4, 'counter': 70, 'faithful': False, 'group': '1728.34767', 'group_order': 1728, 'image': None, 'label': '1728.34767.4t', 'multiplicity': 2, 'nt': [24, 95], 'qdim': 8, 'qvalues': [8, -8, 8, -8, 0, 0, 0, 0, 8, 8, -4, -4, -4, 8, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, -8, -8, 8, 8, -8, -8, -4, 4, 8, -8, 4, 4, 4, -8, -4, -4, 4, -4, 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, 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: 9837942
    {'cdim': 4, 'counter': 71, 'faithful': False, 'group': '1728.34767', 'group_order': 1728, 'image': None, 'label': '1728.34767.4u', 'multiplicity': 2, 'nt': [24, 101], 'qdim': 8, 'qvalues': [8, -8, -8, 8, 0, 0, 0, 0, -4, 8, 8, 8, -4, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -8, 8, 4, -8, 4, -8, -4, -8, 8, 4, 4, -8, 4, -4, -4, 4, -8, 8, 4, 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, 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: 9837943
    {'cdim': 4, 'counter': 72, 'faithful': False, 'group': '1728.34767', 'group_order': 1728, 'image': None, 'label': '1728.34767.4v', 'multiplicity': 2, 'nt': [24, 101], 'qdim': 8, 'qvalues': [8, -8, -8, 8, 0, 0, 0, 0, 8, -4, 8, -4, 8, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -8, -4, -8, 4, -8, 4, 8, -8, 8, 4, 4, 4, -8, 8, -4, -8, 4, -4, 4, 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, 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: 9837944
    {'cdim': 4, 'counter': 73, 'faithful': False, 'group': '1728.34767', 'group_order': 1728, 'image': None, 'label': '1728.34767.4w', 'multiplicity': 2, 'nt': [24, 101], 'qdim': 8, 'qvalues': [8, -8, -8, 8, 0, 0, 0, 0, 8, 8, -4, -4, -4, 8, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 8, -8, -8, -8, -8, 8, 4, -4, -8, -8, 4, 4, -4, 8, 4, 4, -4, 4, 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, 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: 9837945
    {'cdim': 4, 'counter': 74, 'faithful': False, 'group': '1728.34767', 'group_order': 1728, 'image': None, 'label': '1728.34767.4x', 'multiplicity': 2, 'nt': [24, 610], 'qdim': 8, 'qvalues': [8, -8, -8, 8, 0, 0, 0, 0, -4, -4, 8, -4, -4, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -8, -4, 4, 4, 4, 4, -4, -8, 8, -2, -2, 4, 4, -4, 2, 4, 4, -4, -2, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6, -6, 6, -6, 0, 0, 6, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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: 9837946
    {'cdim': 4, 'counter': 75, 'faithful': False, 'group': '1728.34767', 'group_order': 1728, 'image': None, 'label': '1728.34767.4y', 'multiplicity': 2, 'nt': [24, 610], 'qdim': 8, 'qvalues': [8, -8, -8, 8, 0, 0, 0, 0, -4, -4, 8, -4, -4, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -8, -4, 4, 4, 4, 4, -4, -8, 8, -2, -2, 4, 4, -4, 2, 4, 4, -4, -2, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 6, -6, 6, 0, 0, -6, 0, -6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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: 9837947
    {'cdim': 4, 'counter': 76, 'faithful': False, 'group': '1728.34767', 'group_order': 1728, 'image': None, 'label': '1728.34767.4z', 'multiplicity': 2, 'nt': [48, 0], 'qdim': 8, 'qvalues': [8, 8, -8, -8, -8, 8, 0, 0, -4, 8, -4, -4, 2, -4, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, -8, -4, -8, 4, 8, 4, 4, 4, 4, -4, -4, 2, -2, 4, -2, 4, 4, -2, 2, -2, 0, 4, 0, -4, -4, 0, 0, 4, 0, 0, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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': 2}
  • id: 9837948
    {'cdim': 4, 'counter': 77, 'faithful': False, 'group': '1728.34767', 'group_order': 1728, 'image': None, 'label': '1728.34767.4aa', 'multiplicity': 2, 'nt': [48, 0], 'qdim': 8, 'qvalues': [8, 8, -8, -8, 0, 0, -8, 8, 8, -4, -4, 2, -4, -4, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 4, 8, 4, -8, -4, -8, 4, 4, 4, -4, 2, -4, 4, 4, 4, -2, -2, -2, 2, -2, -4, 0, 4, 0, 0, 4, -4, 0, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 2}
  • id: 9837949
    {'cdim': 4, 'counter': 78, 'faithful': False, 'group': '1728.34767', 'group_order': 1728, 'image': None, 'label': '1728.34767.4ab', 'multiplicity': 2, 'nt': [48, 0], 'qdim': 8, 'qvalues': [8, 8, -8, -8, 0, 0, 8, -8, 8, -4, -4, 2, -4, -4, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 4, 8, 4, -8, -4, -8, 4, 4, 4, -4, 2, -4, 4, 4, 4, -2, -2, -2, 2, -2, 4, 0, -4, 0, 0, -4, 4, 0, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 2}
  • id: 9837950
    {'cdim': 4, 'counter': 79, 'faithful': False, 'group': '1728.34767', 'group_order': 1728, 'image': None, 'label': '1728.34767.4ac', 'multiplicity': 2, 'nt': [48, 0], 'qdim': 8, 'qvalues': [8, 8, -8, -8, 8, -8, 0, 0, -4, 8, -4, -4, 2, -4, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, -8, -4, -8, 4, 8, 4, 4, 4, 4, -4, -4, 2, -2, 4, -2, 4, 4, -2, 2, -2, 0, -4, 0, 4, 4, 0, 0, -4, 0, 0, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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': 2}
  • id: 9837952
    {'cdim': 8, 'counter': 80, 'faithful': False, 'group': '1728.34767', 'group_order': 1728, 'image': None, 'label': '1728.34767.8a', 'multiplicity': 1, 'nt': [12, 117], 'qdim': 8, 'qvalues': [8, 8, 8, 8, 0, 0, 0, 0, -4, -4, -4, 2, 2, 2, -1, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, -4, -4, -4, -4, -4, -4, -4, -4, 2, 2, 2, 2, 2, 2, 2, 2, 2, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, -4, -1, -1, -1, 2, 2, 2, 2, -4, -1, -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], 'schur_index': 1}
  • id: 9837953
    {'cdim': 8, 'counter': 81, 'faithful': False, 'group': '1728.34767', 'group_order': 1728, 'image': None, 'label': '1728.34767.8b', 'multiplicity': 1, 'nt': [24, 608], 'qdim': 8, 'qvalues': [8, -8, -8, 8, 0, 0, 0, 0, -4, 8, -4, -4, 2, -4, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 8, 4, -8, 4, -8, -4, 4, -4, 4, 4, 4, -2, 2, -4, -2, 4, -4, -2, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 9837954
    {'cdim': 8, 'counter': 82, 'faithful': False, 'group': '1728.34767', 'group_order': 1728, 'image': None, 'label': '1728.34767.8c', 'multiplicity': 1, 'nt': [24, 608], 'qdim': 8, 'qvalues': [8, -8, -8, 8, 0, 0, 0, 0, 8, -4, -4, 2, -4, -4, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, -4, -8, 4, -8, 4, 8, 4, -4, 4, 4, -2, 4, -4, -4, 4, -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, 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: 9837955
    {'cdim': 8, 'counter': 83, 'faithful': False, 'group': '1728.34767', 'group_order': 1728, 'image': None, 'label': '1728.34767.8d', 'multiplicity': 1, 'nt': [24, 1296], 'qdim': 8, 'qvalues': [8, 8, 8, 8, 0, 0, 0, 0, -4, -4, -4, 2, 2, 2, -1, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, -4, -4, -4, -4, -4, -4, -4, -4, 2, 2, 2, 2, 2, 2, 2, 2, 2, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 1, 1, 1, -2, -2, -2, -2, 4, 1, 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], 'schur_index': 1}
  • id: 9837956
    {'cdim': 8, 'counter': 84, 'faithful': False, 'group': '1728.34767', 'group_order': 1728, 'image': None, 'label': '1728.34767.8e', 'multiplicity': 1, 'nt': [24, 2624], 'qdim': 8, 'qvalues': [8, -8, -8, 8, 0, 0, 0, 0, -4, -4, -4, 2, 2, 2, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, -4, 4, 4, 4, 4, -4, 4, -4, -2, -2, -2, -2, 2, 2, -2, -2, 2, 1, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, -3, 3, 6, 0, 0, -6, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 9837957
    {'cdim': 8, 'counter': 85, 'faithful': False, 'group': '1728.34767', 'group_order': 1728, 'image': None, 'label': '1728.34767.8f', 'multiplicity': 1, 'nt': [24, 2624], 'qdim': 8, 'qvalues': [8, -8, -8, 8, 0, 0, 0, 0, -4, -4, -4, 2, 2, 2, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, -4, 4, 4, 4, 4, -4, 4, -4, -2, -2, -2, -2, 2, 2, -2, -2, 2, 1, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, -3, -6, 0, 0, 6, 0, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 9837958
    {'cdim': 8, 'counter': 86, 'faithful': False, 'group': '1728.34767', 'group_order': 1728, 'image': None, 'label': '1728.34767.8g', 'multiplicity': 1, 'nt': [48, 0], 'qdim': 8, 'qvalues': [8, -8, 8, -8, 0, 0, 0, 0, -4, -4, 8, -4, -4, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -8, 4, 4, -4, -4, 4, 4, 8, -8, 2, -2, 4, 4, 4, -2, -4, -4, 4, 2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 2}
  • id: 9837959
    {'cdim': 8, 'counter': 87, 'faithful': False, 'group': '1728.34767', 'group_order': 1728, 'image': None, 'label': '1728.34767.8h', 'multiplicity': 1, 'nt': [48, 0], 'qdim': 8, 'qvalues': [8, -8, 8, -8, 0, 0, 0, 0, -4, 8, -4, -4, 2, -4, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, -8, 4, 8, -4, -8, 4, -4, 4, -4, 4, 4, -2, -2, 4, 2, -4, 4, 2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 2}
  • id: 9837960
    {'cdim': 8, 'counter': 88, 'faithful': False, 'group': '1728.34767', 'group_order': 1728, 'image': None, 'label': '1728.34767.8i', 'multiplicity': 1, 'nt': [48, 0], 'qdim': 8, 'qvalues': [8, -8, 8, -8, 0, 0, 0, 0, 8, -4, -4, 2, -4, -4, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, -8, -4, 8, 4, -8, -4, 4, -4, 4, -2, 4, 4, 4, -4, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 2}
  • id: 9837961
    {'cdim': 8, 'counter': 89, 'faithful': False, 'group': '1728.34767', 'group_order': 1728, 'image': None, 'label': '1728.34767.8j', 'multiplicity': 1, 'nt': [48, 0], 'qdim': 8, 'qvalues': [8, 8, -8, -8, 0, 0, 0, 0, -4, -4, 8, -4, -4, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 4, -4, 4, 4, -4, 4, -8, -8, -2, 2, -4, -4, 4, -2, 4, 4, 4, -2, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 2}
  • id: 9837963
    {'cdim': 8, 'counter': 90, 'faithful': False, 'group': '1728.34767', 'group_order': 1728, 'image': None, 'label': '1728.34767.8k', 'multiplicity': 2, 'nt': [96, 0], 'qdim': 16, 'qvalues': [16, -16, 16, -16, 0, 0, 0, 0, -8, -8, -8, 4, 4, 4, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 8, 8, -8, -8, 8, 8, -8, 8, 4, -4, -4, -4, -4, -4, 4, 4, -4, -2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 2}
  • id: 9837964
    {'cdim': 8, 'counter': 91, 'faithful': False, 'group': '1728.34767', 'group_order': 1728, 'image': None, 'label': '1728.34767.8l', 'multiplicity': 2, 'nt': [96, 0], 'qdim': 16, 'qvalues': [16, 16, -16, -16, 0, 0, 0, 0, -8, -8, -8, 4, 4, 4, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -8, 8, -8, 8, 8, -8, 8, 8, 8, -4, 4, 4, 4, -4, -4, -4, -4, -4, 2, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 2}
• 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: 22376506
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 1728, 'counter': 1, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '1728.34767', 'group_counter': 34767, 'group_order': 1728, 'image': None, 'image_isoclass': '1.1', 'image_order': 1, 'indicator': 1, 'kernel': '1.a1.a1', 'kernel_order': 1728, 'label': '1728.34767.1a', 'nt': [1, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 22376529
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 1728, 'counter': 2, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '1728.34767', 'group_counter': 34767, 'group_order': 1728, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.k1.a1', 'kernel_order': 864, 'label': '1728.34767.1b', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 22376540
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 1728, 'counter': 3, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '1728.34767', 'group_counter': 34767, 'group_order': 1728, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.j1.a1', 'kernel_order': 864, 'label': '1728.34767.1c', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 22376551
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 1728, 'counter': 4, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '1728.34767', 'group_counter': 34767, 'group_order': 1728, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.i1.a1', 'kernel_order': 864, 'label': '1728.34767.1d', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 22376562
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 1728, 'counter': 5, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '1728.34767', 'group_counter': 34767, 'group_order': 1728, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.h1.a1', 'kernel_order': 864, 'label': '1728.34767.1e', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 22376573
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 1728, 'counter': 6, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '1728.34767', 'group_counter': 34767, 'group_order': 1728, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.d1.a1', 'kernel_order': 864, 'label': '1728.34767.1f', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]]]}
  • id: 22376584
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 1728, 'counter': 7, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '1728.34767', 'group_counter': 34767, 'group_order': 1728, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.c1.a1', 'kernel_order': 864, 'label': '1728.34767.1g', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]]]}
  • id: 22376595
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 1728, 'counter': 8, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '1728.34767', 'group_counter': 34767, 'group_order': 1728, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.b1.a1', 'kernel_order': 864, 'label': '1728.34767.1h', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]]]}
  • id: 22376606
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 1728, 'counter': 9, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '1728.34767', 'group_counter': 34767, 'group_order': 1728, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.a1.a1', 'kernel_order': 864, 'label': '1728.34767.1i', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]]]}
  • id: 22376507
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 1728, 'counter': 10, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '1728.34767', 'group_counter': 34767, 'group_order': 1728, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.d1.b1', 'kernel_order': 864, 'label': '1728.34767.1j', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]]]}
  • id: 22376518
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 1728, 'counter': 11, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '1728.34767', 'group_counter': 34767, 'group_order': 1728, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.c1.b1', 'kernel_order': 864, 'label': '1728.34767.1k', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]]]}
  • id: 22376521
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 1728, 'counter': 12, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '1728.34767', 'group_counter': 34767, 'group_order': 1728, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.b1.b1', 'kernel_order': 864, 'label': '1728.34767.1l', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]]]}
  • id: 22376522
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 1728, 'counter': 13, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '1728.34767', 'group_counter': 34767, 'group_order': 1728, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.a1.b1', 'kernel_order': 864, 'label': '1728.34767.1m', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]]]}
  • id: 22376523
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 1728, 'counter': 14, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '1728.34767', 'group_counter': 34767, 'group_order': 1728, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.g1.a1', 'kernel_order': 864, 'label': '1728.34767.1n', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]]]}
  • id: 22376524
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 1728, 'counter': 15, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '1728.34767', 'group_counter': 34767, 'group_order': 1728, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.f1.a1', 'kernel_order': 864, 'label': '1728.34767.1o', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 22376525
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 1728, 'counter': 16, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '1728.34767', 'group_counter': 34767, 'group_order': 1728, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.e1.a1', 'kernel_order': 864, 'label': '1728.34767.1p', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 22376526
    {'center': '6.a1.a1', 'center_index': 6, 'center_order': 288, 'counter': 17, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '1728.34767', 'group_counter': 34767, 'group_order': 1728, 'image': None, 'image_isoclass': '6.1', 'image_order': 6, 'indicator': 1, 'kernel': '6.a1.a1', 'kernel_order': 288, 'label': '1728.34767.2a', 'nt': [3, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]]]}
  • id: 22376555
    {'center': '4.g1.a1', 'center_index': 4, 'center_order': 432, 'counter': 43, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '1728.34767', 'group_counter': 34767, 'group_order': 1728, 'image': None, 'image_isoclass': '8.4', 'image_order': 8, 'indicator': -1, 'kernel': '8.l1.c1', 'kernel_order': 216, 'label': '1728.34767.2aa', 'nt': [8, 5], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 22376556
    {'center': '4.g1.a1', 'center_index': 4, 'center_order': 432, 'counter': 44, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '1728.34767', 'group_counter': 34767, 'group_order': 1728, 'image': None, 'image_isoclass': '8.4', 'image_order': 8, 'indicator': -1, 'kernel': '8.l1.a1', 'kernel_order': 216, 'label': '1728.34767.2ab', 'nt': [8, 5], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 22376557
    {'center': '4.n1.a1', 'center_index': 4, 'center_order': 432, 'counter': 45, 'cyclotomic_n': 4, 'dim': 2, 'faithful': False, 'field': [1, 0, 1], 'group': '1728.34767', 'group_counter': 34767, 'group_order': 1728, 'image': None, 'image_isoclass': '16.13', 'image_order': 16, 'indicator': 0, 'kernel': '16.d1.b1', 'kernel_order': 108, 'label': '1728.34767.2ac1', 'nt': [8, 11], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[-2, 1]], [[2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1]], [[0, 0]], [[2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1]], [[0, 0]], [[-2, 1]], [[-2, 1]], [[0, 0]], [[2, 1]], [[0, 0]], [[0, 0]], [[2, 1]], [[2, 1]], [[-2, 1]], [[-2, 1]], [[2, 1]], [[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]]]}
  • id: 22376558
    {'center': '4.n1.a1', 'center_index': 4, 'center_order': 432, 'counter': 46, 'cyclotomic_n': 4, 'dim': 2, 'faithful': False, 'field': [1, 0, 1], 'group': '1728.34767', 'group_counter': 34767, 'group_order': 1728, 'image': None, 'image_isoclass': '16.13', 'image_order': 16, 'indicator': 0, 'kernel': '16.d1.b1', 'kernel_order': 108, 'label': '1728.34767.2ac2', 'nt': [8, 2], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[2, 1]], [[-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1]], [[0, 0]], [[-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1]], [[0, 0]], [[2, 1]], [[2, 1]], [[0, 0]], [[-2, 1]], [[0, 0]], [[0, 0]], [[-2, 1]], [[-2, 1]], [[2, 1]], [[2, 1]], [[-2, 1]], [[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]]]}
  • id: 22376559
    {'center': '4.n1.a1', 'center_index': 4, 'center_order': 432, 'counter': 47, 'cyclotomic_n': 4, 'dim': 2, 'faithful': False, 'field': [1, 0, 1], 'group': '1728.34767', 'group_counter': 34767, 'group_order': 1728, 'image': None, 'image_isoclass': '16.13', 'image_order': 16, 'indicator': 0, 'kernel': '16.d1.a1', 'kernel_order': 108, 'label': '1728.34767.2ad1', 'nt': [8, 11], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[-2, 1]], [[2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1]], [[0, 0]], [[-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1]], [[0, 0]], [[-2, 1]], [[-2, 1]], [[0, 0]], [[2, 1]], [[0, 0]], [[0, 0]], [[-2, 1]], [[-2, 1]], [[2, 1]], [[2, 1]], [[2, 1]], [[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]]]}
  • id: 22376560
    {'center': '4.n1.a1', 'center_index': 4, 'center_order': 432, 'counter': 48, 'cyclotomic_n': 4, 'dim': 2, 'faithful': False, 'field': [1, 0, 1], 'group': '1728.34767', 'group_counter': 34767, 'group_order': 1728, 'image': None, 'image_isoclass': '16.13', 'image_order': 16, 'indicator': 0, 'kernel': '16.d1.a1', 'kernel_order': 108, 'label': '1728.34767.2ad2', 'nt': [8, 2], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[2, 1]], [[-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1]], [[0, 0]], [[2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1]], [[0, 0]], [[2, 1]], [[2, 1]], [[0, 0]], [[-2, 1]], [[0, 0]], [[0, 0]], [[2, 1]], [[2, 1]], [[-2, 1]], [[-2, 1]], [[-2, 1]], [[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]]]}
  • id: 22376561
    {'center': '12.f1.a1', 'center_index': 12, 'center_order': 144, 'counter': 49, 'cyclotomic_n': 12, 'dim': 2, 'faithful': False, 'field': [-3, 0, 1], 'group': '1728.34767', 'group_counter': 34767, 'group_order': 1728, 'image': None, 'image_isoclass': '24.4', 'image_order': 24, 'indicator': -1, 'kernel': '24.m1.d1', 'kernel_order': 72, 'label': '1728.34767.2ae1', 'nt': [24, 5], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[2, 0]], [[-1, 0]], [[-2, 0]], [[2, 0]], [[-2, 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]], [[0, 0]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[0, 0]], [[0, 0]], [[1, 1], [1, -1]], [[0, 0]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[0, 0]], [[1, 1], [1, -1]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, -1]], [[0, 0]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[0, 0]], [[-1, 1], [-1, -1]], [[0, 0]], [[1, 1], [1, -1]], [[0, 0]], [[-1, 1], [-1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, -1]], [[0, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 22376563
    {'center': '12.f1.a1', 'center_index': 12, 'center_order': 144, 'counter': 50, 'cyclotomic_n': 12, 'dim': 2, 'faithful': False, 'field': [-3, 0, 1], 'group': '1728.34767', 'group_counter': 34767, 'group_order': 1728, 'image': None, 'image_isoclass': '24.4', 'image_order': 24, 'indicator': -1, 'kernel': '24.m1.d1', 'kernel_order': 72, 'label': '1728.34767.2ae2', 'nt': [24, 5], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[2, 0]], [[-1, 0]], [[-2, 0]], [[2, 0]], [[-2, 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]], [[0, 0]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, -1]], [[0, 0]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[0, 0]], [[-1, 1], [-1, -1]], [[0, 0]], [[0, 0]], [[1, 1], [1, -1]], [[0, 0]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[0, 0]], [[1, 1], [1, -1]], [[0, 0]], [[-1, 1], [-1, -1]], [[0, 0]], [[1, 1], [1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, -1]], [[0, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 22376564
    {'center': '12.f1.a1', 'center_index': 12, 'center_order': 144, 'counter': 51, 'cyclotomic_n': 12, 'dim': 2, 'faithful': False, 'field': [-3, 0, 1], 'group': '1728.34767', 'group_counter': 34767, 'group_order': 1728, 'image': None, 'image_isoclass': '24.4', 'image_order': 24, 'indicator': -1, 'kernel': '24.m1.b1', 'kernel_order': 72, 'label': '1728.34767.2af1', 'nt': [24, 5], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-2, 0]], [[-2, 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]], [[0, 0]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[0, 0]], [[0, 0]], [[1, 1], [1, -1]], [[0, 0]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[0, 0]], [[1, 1], [1, -1]], [[0, 0]], [[0, 0]], [[1, 1], [1, -1]], [[0, 0]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[0, 0]], [[-1, 1], [-1, -1]], [[0, 0]], [[-1, 1], [-1, -1]], [[0, 0]], [[1, 1], [1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, -1]], [[0, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 22376565
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  • id: 22376566
    {'center': '12.f1.a1', 'center_index': 12, 'center_order': 144, 'counter': 53, 'cyclotomic_n': 12, 'dim': 2, 'faithful': False, 'field': [-3, 0, 1], 'group': '1728.34767', 'group_counter': 34767, 'group_order': 1728, 'image': None, 'image_isoclass': '24.4', 'image_order': 24, 'indicator': -1, 'kernel': '24.m1.c1', 'kernel_order': 72, 'label': '1728.34767.2ag1', 'nt': [24, 5], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[2, 0]], [[2, 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]], [[0, 0]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[0, 0]], [[0, 0]], [[1, 1], [1, -1]], [[0, 0]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[0, 0]], [[-1, 1], [-1, -1]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, -1]], [[0, 0]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[0, 0]], [[1, 1], [1, -1]], [[0, 0]], [[1, 1], [1, -1]], [[0, 0]], [[-1, 1], [-1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, -1]], [[0, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 22376567
    {'center': '12.f1.a1', 'center_index': 12, 'center_order': 144, 'counter': 54, 'cyclotomic_n': 12, 'dim': 2, 'faithful': False, 'field': [-3, 0, 1], 'group': '1728.34767', 'group_counter': 34767, 'group_order': 1728, 'image': None, 'image_isoclass': '24.4', 'image_order': 24, 'indicator': -1, 'kernel': '24.m1.c1', 'kernel_order': 72, 'label': '1728.34767.2ag2', 'nt': [24, 5], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[2, 0]], [[2, 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]], [[0, 0]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, -1]], [[0, 0]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[0, 0]], [[1, 1], [1, -1]], [[0, 0]], [[0, 0]], [[1, 1], [1, -1]], [[0, 0]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[0, 0]], [[-1, 1], [-1, -1]], [[0, 0]], [[-1, 1], [-1, -1]], [[0, 0]], [[1, 1], [1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, -1]], [[0, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 22376568
    {'center': '12.f1.a1', 'center_index': 12, 'center_order': 144, 'counter': 55, 'cyclotomic_n': 12, 'dim': 2, 'faithful': False, 'field': [-3, 0, 1], 'group': '1728.34767', 'group_counter': 34767, 'group_order': 1728, 'image': None, 'image_isoclass': '24.4', 'image_order': 24, 'indicator': -1, 'kernel': '24.m1.a1', 'kernel_order': 72, 'label': '1728.34767.2ah1', 'nt': [24, 5], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-2, 0]], [[1, 0]], [[2, 0]], [[-2, 0]], [[2, 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]], [[0, 0]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[0, 0]], [[0, 0]], [[1, 1], [1, -1]], [[0, 0]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[0, 0]], [[-1, 1], [-1, -1]], [[0, 0]], [[0, 0]], [[1, 1], [1, -1]], [[0, 0]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[0, 0]], [[1, 1], [1, -1]], [[0, 0]], [[-1, 1], [-1, -1]], [[0, 0]], [[1, 1], [1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, -1]], [[0, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 22376569
    {'center': '12.f1.a1', 'center_index': 12, 'center_order': 144, 'counter': 56, 'cyclotomic_n': 12, 'dim': 2, 'faithful': False, 'field': [-3, 0, 1], 'group': '1728.34767', 'group_counter': 34767, 'group_order': 1728, 'image': None, 'image_isoclass': '24.4', 'image_order': 24, 'indicator': -1, 'kernel': '24.m1.a1', 'kernel_order': 72, 'label': '1728.34767.2ah2', 'nt': [24, 5], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-2, 0]], [[1, 0]], [[2, 0]], [[-2, 0]], [[2, 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]], [[0, 0]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, -1]], [[0, 0]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[0, 0]], [[1, 1], [1, -1]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, -1]], [[0, 0]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[0, 0]], [[-1, 1], [-1, -1]], [[0, 0]], [[1, 1], [1, -1]], [[0, 0]], [[-1, 1], [-1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, -1]], [[0, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 22376527
    {'center': '6.a1.b1', 'center_index': 6, 'center_order': 288, 'counter': 18, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '1728.34767', 'group_counter': 34767, 'group_order': 1728, 'image': None, 'image_isoclass': '6.1', 'image_order': 6, 'indicator': 1, 'kernel': '6.a1.b1', 'kernel_order': 288, 'label': '1728.34767.2b', 'nt': [3, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 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]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]]]}
  • id: 22376528
    {'center': '6.b1.a1', 'center_index': 6, 'center_order': 288, 'counter': 19, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '1728.34767', 'group_counter': 34767, 'group_order': 1728, 'image': None, 'image_isoclass': '6.1', 'image_order': 6, 'indicator': 1, 'kernel': '6.b1.a1', 'kernel_order': 288, 'label': '1728.34767.2c', 'nt': [3, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 22376530
    {'center': '6.b1.a1', 'center_index': 6, 'center_order': 288, 'counter': 20, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '1728.34767', 'group_counter': 34767, 'group_order': 1728, 'image': None, 'image_isoclass': '12.4', 'image_order': 12, 'indicator': 1, 'kernel': '12.l1.a1', 'kernel_order': 144, 'label': '1728.34767.2d', 'nt': [6, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 22376531
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  • id: 22376532
    {'center': '6.a1.b1', 'center_index': 6, 'center_order': 288, 'counter': 22, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '1728.34767', 'group_counter': 34767, 'group_order': 1728, 'image': None, 'image_isoclass': '12.4', 'image_order': 12, 'indicator': 1, 'kernel': '12.j1.b1', 'kernel_order': 144, 'label': '1728.34767.2f', 'nt': [6, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[1, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 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]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[1, 0]], [[-2, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]]]}
  • id: 22376533
    {'center': '6.a1.b1', 'center_index': 6, 'center_order': 288, 'counter': 23, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '1728.34767', 'group_counter': 34767, 'group_order': 1728, 'image': None, 'image_isoclass': '12.4', 'image_order': 12, 'indicator': 1, 'kernel': '12.i1.b1', 'kernel_order': 144, 'label': '1728.34767.2g', 'nt': [6, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[1, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 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]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-2, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]]]}
  • id: 22376534
    {'center': '6.a1.b1', 'center_index': 6, 'center_order': 288, 'counter': 24, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '1728.34767', 'group_counter': 34767, 'group_order': 1728, 'image': None, 'image_isoclass': '12.4', 'image_order': 12, 'indicator': 1, 'kernel': '12.h1.b1', 'kernel_order': 144, 'label': '1728.34767.2h', 'nt': [6, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[1, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 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]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]]]}
  • id: 22376535
    {'center': '6.a1.b1', 'center_index': 6, 'center_order': 288, 'counter': 25, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '1728.34767', 'group_counter': 34767, 'group_order': 1728, 'image': None, 'image_isoclass': '12.4', 'image_order': 12, 'indicator': 1, 'kernel': '12.g1.b1', 'kernel_order': 144, 'label': '1728.34767.2i', 'nt': [6, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[1, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 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]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-1, 0]], [[2, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[2, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]]]}
  • id: 22376536
    {'center': '6.b1.a1', 'center_index': 6, 'center_order': 288, 'counter': 26, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '1728.34767', 'group_counter': 34767, 'group_order': 1728, 'image': None, 'image_isoclass': '12.4', 'image_order': 12, 'indicator': 1, 'kernel': '12.e1.a1', 'kernel_order': 144, 'label': '1728.34767.2j', 'nt': [6, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-2, 0]], [[1, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-1, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 22376537
    {'center': '6.b1.a1', 'center_index': 6, 'center_order': 288, 'counter': 27, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '1728.34767', 'group_counter': 34767, 'group_order': 1728, 'image': None, 'image_isoclass': '12.4', 'image_order': 12, 'indicator': 1, 'kernel': '12.d1.a1', 'kernel_order': 144, 'label': '1728.34767.2k', 'nt': [6, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-2, 0]], [[1, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[1, 0]], [[2, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 22376538
    {'center': '6.a1.a1', 'center_index': 6, 'center_order': 288, 'counter': 28, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '1728.34767', 'group_counter': 34767, 'group_order': 1728, 'image': None, 'image_isoclass': '12.4', 'image_order': 12, 'indicator': 1, 'kernel': '12.j1.a1', 'kernel_order': 144, 'label': '1728.34767.2l', 'nt': [6, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[-2, 0]], [[1, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]]]}
  • id: 22376539
    {'center': '6.a1.a1', 'center_index': 6, 'center_order': 288, 'counter': 29, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '1728.34767', 'group_counter': 34767, 'group_order': 1728, 'image': None, 'image_isoclass': '12.4', 'image_order': 12, 'indicator': 1, 'kernel': '12.i1.a1', 'kernel_order': 144, 'label': '1728.34767.2m', 'nt': [6, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[-2, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]]]}
  • id: 22376541
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  • id: 22376542
    {'center': '6.a1.a1', 'center_index': 6, 'center_order': 288, 'counter': 31, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '1728.34767', 'group_counter': 34767, 'group_order': 1728, 'image': None, 'image_isoclass': '12.4', 'image_order': 12, 'indicator': 1, 'kernel': '12.g1.a1', 'kernel_order': 144, 'label': '1728.34767.2o', 'nt': [6, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[2, 0]], [[-1, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[2, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]]]}
  • id: 22376543
    {'center': '6.a1.a1', 'center_index': 6, 'center_order': 288, 'counter': 32, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '1728.34767', 'group_counter': 34767, 'group_order': 1728, 'image': None, 'image_isoclass': '12.4', 'image_order': 12, 'indicator': 1, 'kernel': '12.c1.a1', 'kernel_order': 144, 'label': '1728.34767.2p', 'nt': [6, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[2, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]]]}
  • id: 22376544
    {'center': '6.a1.a1', 'center_index': 6, 'center_order': 288, 'counter': 33, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '1728.34767', 'group_counter': 34767, 'group_order': 1728, 'image': None, 'image_isoclass': '12.4', 'image_order': 12, 'indicator': 1, 'kernel': '12.b1.a1', 'kernel_order': 144, 'label': '1728.34767.2q', 'nt': [6, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[2, 0]], [[-1, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]]]}
  • id: 22376545
    {'center': '6.a1.a1', 'center_index': 6, 'center_order': 288, 'counter': 34, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '1728.34767', 'group_counter': 34767, 'group_order': 1728, 'image': None, 'image_isoclass': '12.4', 'image_order': 12, 'indicator': 1, 'kernel': '12.a1.a1', 'kernel_order': 144, 'label': '1728.34767.2r', 'nt': [6, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[-2, 0]], [[1, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[-2, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]]]}
  • id: 22376546
    {'center': '6.b1.a1', 'center_index': 6, 'center_order': 288, 'counter': 35, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '1728.34767', 'group_counter': 34767, 'group_order': 1728, 'image': None, 'image_isoclass': '12.4', 'image_order': 12, 'indicator': 1, 'kernel': '12.e1.b1', 'kernel_order': 144, 'label': '1728.34767.2s', 'nt': [6, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[2, 0]], [[-1, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[1, 0]], [[2, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 22376547
    {'center': '6.b1.a1', 'center_index': 6, 'center_order': 288, 'counter': 36, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '1728.34767', 'group_counter': 34767, 'group_order': 1728, 'image': None, 'image_isoclass': '12.4', 'image_order': 12, 'indicator': 1, 'kernel': '12.d1.b1', 'kernel_order': 144, 'label': '1728.34767.2t', 'nt': [6, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[2, 0]], [[-1, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-1, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 22376548
    {'center': '6.a1.b1', 'center_index': 6, 'center_order': 288, 'counter': 37, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '1728.34767', 'group_counter': 34767, 'group_order': 1728, 'image': None, 'image_isoclass': '12.4', 'image_order': 12, 'indicator': 1, 'kernel': '12.c1.b1', 'kernel_order': 144, 'label': '1728.34767.2u', 'nt': [6, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 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]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[2, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]]]}
  • id: 22376549
    {'center': '6.a1.b1', 'center_index': 6, 'center_order': 288, 'counter': 38, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '1728.34767', 'group_counter': 34767, 'group_order': 1728, 'image': None, 'image_isoclass': '12.4', 'image_order': 12, 'indicator': 1, 'kernel': '12.b1.b1', 'kernel_order': 144, 'label': '1728.34767.2v', 'nt': [6, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 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]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-1, 0]], [[2, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]]]}
  • id: 22376550
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  • id: 22376552
    {'center': '6.b1.a1', 'center_index': 6, 'center_order': 288, 'counter': 40, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '1728.34767', 'group_counter': 34767, 'group_order': 1728, 'image': None, 'image_isoclass': '12.4', 'image_order': 12, 'indicator': 1, 'kernel': '12.f1.a1', 'kernel_order': 144, 'label': '1728.34767.2x', 'nt': [6, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[1, 0]], [[-2, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 22376553
    {'center': '4.g1.a1', 'center_index': 4, 'center_order': 432, 'counter': 41, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '1728.34767', 'group_counter': 34767, 'group_order': 1728, 'image': None, 'image_isoclass': '8.4', 'image_order': 8, 'indicator': -1, 'kernel': '8.l1.d1', 'kernel_order': 216, 'label': '1728.34767.2y', 'nt': [8, 5], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 22376554
    {'center': '4.g1.a1', 'center_index': 4, 'center_order': 432, 'counter': 42, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '1728.34767', 'group_counter': 34767, 'group_order': 1728, 'image': None, 'image_isoclass': '8.4', 'image_order': 8, 'indicator': -1, 'kernel': '8.l1.b1', 'kernel_order': 216, 'label': '1728.34767.2z', 'nt': [8, 5], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 22376570
    {'center': '36.b1.a1', 'center_index': 36, 'center_order': 48, 'counter': 57, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '1728.34767', 'group_counter': 34767, 'group_order': 1728, 'image': None, 'image_isoclass': '36.10', 'image_order': 36, 'indicator': 1, 'kernel': '36.b1.a1', 'kernel_order': 48, 'label': '1728.34767.4a', 'nt': [6, 9], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 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]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[4, 0]], [[4, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 22376609
    {'center': '72.a1.a1', 'center_index': 72, 'center_order': 24, 'counter': 92, 'cyclotomic_n': 12, 'dim': 4, 'faithful': False, 'field': [-3, 0, 1], 'group': '1728.34767', 'group_counter': 34767, 'group_order': 1728, 'image': None, 'image_isoclass': '144.137', 'image_order': 144, 'indicator': -1, 'kernel': '144.c1.b1', 'kernel_order': 12, 'label': '1728.34767.4aa1', 'nt': [48, 0], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[4, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[1, 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]], [[-2, 0]], [[2, 0]], [[4, 0]], [[2, 0]], [[-4, 0]], [[-2, 0]], [[-4, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-2, 1], [-2, -1]], [[2, 1], [2, -1]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[0, 0]], [[2, 1], [2, -1]], [[-2, 1], [-2, -1]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, -1]], [[0, 0]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1], [-2, -1]], [[0, 0]], [[2, 1], [2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, -1]], [[0, 0]], [[1, 1], [1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 22376610
    {'center': '72.a1.a1', 'center_index': 72, 'center_order': 24, 'counter': 93, 'cyclotomic_n': 12, 'dim': 4, 'faithful': False, 'field': [-3, 0, 1], 'group': '1728.34767', 'group_counter': 34767, 'group_order': 1728, 'image': None, 'image_isoclass': '144.137', 'image_order': 144, 'indicator': -1, 'kernel': '144.c1.b1', 'kernel_order': 12, 'label': '1728.34767.4aa2', 'nt': [48, 0], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[4, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[1, 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]], [[-2, 0]], [[2, 0]], [[4, 0]], [[2, 0]], [[-4, 0]], [[-2, 0]], [[-4, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[2, 1], [2, -1]], [[-2, 1], [-2, -1]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[0, 0]], [[-2, 1], [-2, -1]], [[2, 1], [2, -1]], [[0, 0]], [[0, 0]], [[1, 1], [1, -1]], [[0, 0]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1], [2, -1]], [[0, 0]], [[-2, 1], [-2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, -1]], [[0, 0]], [[-1, 1], [-1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 22376611
    {'center': '72.a1.a1', 'center_index': 72, 'center_order': 24, 'counter': 94, 'cyclotomic_n': 12, 'dim': 4, 'faithful': False, 'field': [-3, 0, 1], 'group': '1728.34767', 'group_counter': 34767, 'group_order': 1728, 'image': None, 'image_isoclass': '144.137', 'image_order': 144, 'indicator': -1, 'kernel': '144.c1.a1', 'kernel_order': 12, 'label': '1728.34767.4ab1', 'nt': [48, 0], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[-4, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[1, 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]], [[-2, 0]], [[2, 0]], [[4, 0]], [[2, 0]], [[-4, 0]], [[-2, 0]], [[-4, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-2, 1], [-2, -1]], [[2, 1], [2, -1]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[0, 0]], [[2, 1], [2, -1]], [[-2, 1], [-2, -1]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, -1]], [[0, 0]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1], [2, -1]], [[0, 0]], [[-2, 1], [-2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, -1]], [[0, 0]], [[-1, 1], [-1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 22376612
    {'center': '72.a1.a1', 'center_index': 72, 'center_order': 24, 'counter': 95, 'cyclotomic_n': 12, 'dim': 4, 'faithful': False, 'field': [-3, 0, 1], 'group': '1728.34767', 'group_counter': 34767, 'group_order': 1728, 'image': None, 'image_isoclass': '144.137', 'image_order': 144, 'indicator': -1, 'kernel': '144.c1.a1', 'kernel_order': 12, 'label': '1728.34767.4ab2', 'nt': [48, 0], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[-4, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[1, 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]], [[-2, 0]], [[2, 0]], [[4, 0]], [[2, 0]], [[-4, 0]], [[-2, 0]], [[-4, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[2, 1], [2, -1]], [[-2, 1], [-2, -1]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[0, 0]], [[-2, 1], [-2, -1]], [[2, 1], [2, -1]], [[0, 0]], [[0, 0]], [[1, 1], [1, -1]], [[0, 0]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1], [-2, -1]], [[0, 0]], [[2, 1], [2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, -1]], [[0, 0]], [[1, 1], [1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 22376613
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  • id: 22376614
    {'center': '72.a1.b1', 'center_index': 72, 'center_order': 24, 'counter': 97, 'cyclotomic_n': 12, 'dim': 4, 'faithful': False, 'field': [-3, 0, 1], 'group': '1728.34767', 'group_counter': 34767, 'group_order': 1728, 'image': None, 'image_isoclass': '144.137', 'image_order': 144, 'indicator': -1, 'kernel': '144.c1.c1', 'kernel_order': 12, 'label': '1728.34767.4ac2', 'nt': [48, 0], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[-2, 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]], [[-2, 0]], [[-4, 0]], [[-2, 0]], [[-4, 0]], [[2, 0]], [[4, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 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]], [[0, 0]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[0, 0]], [[0, 0]], [[1, 1], [1, -1]], [[0, 0]], [[2, 1], [2, -1]], [[-2, 1], [-2, -1]], [[0, 0]], [[2, 1], [2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1], [-2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 22376571
    {'center': '36.a1.a1', 'center_index': 36, 'center_order': 48, 'counter': 58, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '1728.34767', 'group_counter': 34767, 'group_order': 1728, 'image': None, 'image_isoclass': '36.10', 'image_order': 36, 'indicator': 1, 'kernel': '36.a1.a1', 'kernel_order': 48, 'label': '1728.34767.4b', 'nt': [6, 9], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 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]], [[-2, 0]], [[-2, 0]], [[4, 0]], [[-2, 0]], [[4, 0]], [[-2, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[4, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 22376572
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  • id: 22376574
    {'center': '16.a1.a1', 'center_index': 16, 'center_order': 108, 'counter': 60, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '1728.34767', 'group_counter': 34767, 'group_order': 1728, 'image': None, 'image_isoclass': '32.49', 'image_order': 32, 'indicator': 1, 'kernel': '32.b1.a1', 'kernel_order': 54, 'label': '1728.34767.4d', 'nt': [8, 22], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 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]], [[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]], [[-4, 0]], [[4, 0]], [[4, 0]], [[-4, 0]], [[4, 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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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: 22376575
    {'center': '36.a1.b1', 'center_index': 36, 'center_order': 48, 'counter': 61, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '1728.34767', 'group_counter': 34767, 'group_order': 1728, 'image': None, 'image_isoclass': '72.46', 'image_order': 72, 'indicator': 1, 'kernel': '72.c1.b1', 'kernel_order': 24, 'label': '1728.34767.4e', 'nt': [12, 37], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[-4, 0]], [[0, 0]], [[0, 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]], [[-2, 0]], [[4, 0]], [[-2, 0]], [[4, 0]], [[-2, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-4, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 22376576
    {'center': '36.a1.b1', 'center_index': 36, 'center_order': 48, 'counter': 62, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '1728.34767', 'group_counter': 34767, 'group_order': 1728, 'image': None, 'image_isoclass': '72.46', 'image_order': 72, 'indicator': 1, 'kernel': '72.b1.b1', 'kernel_order': 24, 'label': '1728.34767.4f', 'nt': [12, 37], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[4, 0]], [[0, 0]], [[0, 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]], [[-2, 0]], [[4, 0]], [[-2, 0]], [[4, 0]], [[-2, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 22376577
    {'center': '36.a1.a1', 'center_index': 36, 'center_order': 48, 'counter': 63, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '1728.34767', 'group_counter': 34767, 'group_order': 1728, 'image': None, 'image_isoclass': '72.46', 'image_order': 72, 'indicator': 1, 'kernel': '72.c1.a1', 'kernel_order': 24, 'label': '1728.34767.4g', 'nt': [12, 37], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 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]], [[-2, 0]], [[-2, 0]], [[4, 0]], [[-2, 0]], [[4, 0]], [[-2, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-4, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 22376578
    {'center': '36.a1.a1', 'center_index': 36, 'center_order': 48, 'counter': 64, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '1728.34767', 'group_counter': 34767, 'group_order': 1728, 'image': None, 'image_isoclass': '72.46', 'image_order': 72, 'indicator': 1, 'kernel': '72.b1.a1', 'kernel_order': 24, 'label': '1728.34767.4h', 'nt': [12, 37], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 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]], [[-2, 0]], [[-2, 0]], [[4, 0]], [[-2, 0]], [[4, 0]], [[-2, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[4, 0]], [[1, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 22376579
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  • id: 22376580
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  • id: 22376581
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  • id: 22376582
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  • id: 22376583
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  • id: 22376585
    {'center': '24.a1.b1', 'center_index': 24, 'center_order': 72, 'counter': 70, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '1728.34767', 'group_counter': 34767, 'group_order': 1728, 'image': None, 'image_isoclass': '48.40', 'image_order': 48, 'indicator': -1, 'kernel': '48.c1.d1', 'kernel_order': 36, 'label': '1728.34767.4n', 'nt': [24, 26], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[-4, 0]], [[-2, 0]], [[-4, 0]], [[2, 0]], [[4, 0]], [[2, 0]], [[-4, 0]], [[-4, 0]], [[2, 0]], [[-2, 0]], [[4, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-4, 0]], [[-4, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[-2, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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: 22376586
    {'center': '24.a1.a1', 'center_index': 24, 'center_order': 72, 'counter': 71, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '1728.34767', 'group_counter': 34767, 'group_order': 1728, 'image': None, 'image_isoclass': '48.40', 'image_order': 48, 'indicator': -1, 'kernel': '48.c1.b1', 'kernel_order': 36, 'label': '1728.34767.4o', 'nt': [24, 26], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[4, 0]], [[4, 0]], [[-2, 0]], [[4, 0]], [[-2, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[2, 0]], [[4, 0]], [[2, 0]], [[-4, 0]], [[-2, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[4, 0]], [[-4, 0]], [[2, 0]], [[-4, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[4, 0]], [[0, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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: 22376587
    {'center': '24.a1.a1', 'center_index': 24, 'center_order': 72, 'counter': 72, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '1728.34767', 'group_counter': 34767, 'group_order': 1728, 'image': None, 'image_isoclass': '48.40', 'image_order': 48, 'indicator': -1, 'kernel': '48.c1.a1', 'kernel_order': 36, 'label': '1728.34767.4p', 'nt': [24, 26], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[-4, 0]], [[4, 0]], [[-2, 0]], [[4, 0]], [[-2, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[2, 0]], [[4, 0]], [[2, 0]], [[-4, 0]], [[-2, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[4, 0]], [[-4, 0]], [[2, 0]], [[-4, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-4, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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: 22376588
    {'center': '24.a1.b1', 'center_index': 24, 'center_order': 72, 'counter': 73, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '1728.34767', 'group_counter': 34767, 'group_order': 1728, 'image': None, 'image_isoclass': '48.40', 'image_order': 48, 'indicator': -1, 'kernel': '48.c1.c1', 'kernel_order': 36, 'label': '1728.34767.4q', 'nt': [24, 26], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[-4, 0]], [[-2, 0]], [[-4, 0]], [[2, 0]], [[4, 0]], [[2, 0]], [[-4, 0]], [[-4, 0]], [[2, 0]], [[-2, 0]], [[4, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-4, 0]], [[-4, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[4, 0]], [[0, 0]], [[2, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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: 22376589
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  • id: 22376590
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  • id: 22376591
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  • id: 22376592
    {'center': '48.a1.a1', 'center_index': 48, 'center_order': 36, 'counter': 77, 'cyclotomic_n': 3, 'dim': 4, 'faithful': False, 'field': [1, -1, 1], 'group': '1728.34767', 'group_counter': 34767, 'group_order': 1728, 'image': None, 'image_isoclass': '96.211', 'image_order': 96, 'indicator': 0, 'kernel': '96.c1.a1', 'kernel_order': 18, 'label': '1728.34767.4s2', 'nt': [24, 2], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[-2, 0]], [[4, 0]], [[-2, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[2, 0]], [[-4, 0]], [[-2, 0]], [[4, 0]], [[2, 0]], [[-4, 0]], [[4, 0]], [[-4, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-4, 0]], [[-4, 0]], [[2, 0]], [[4, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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], [4, 1]], [[-2, 0], [-4, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 22376593
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  • id: 22376594
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  • id: 22376596
    {'center': '24.d1.b1', 'center_index': 24, 'center_order': 72, 'counter': 80, 'cyclotomic_n': 4, 'dim': 4, 'faithful': False, 'field': [1, 0, 1], 'group': '1728.34767', 'group_counter': 34767, 'group_order': 1728, 'image': None, 'image_isoclass': '96.215', 'image_order': 96, 'indicator': 0, 'kernel': '96.e1.b1', 'kernel_order': 18, 'label': '1728.34767.4u1', 'nt': [24, 101], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[-4, 1]], [[4, 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]], [[-4, 0]], [[4, 0]], [[2, 0]], [[-4, 0]], [[2, 0]], [[-4, 0]], [[-2, 0]], [[-4, 0]], [[4, 0]], [[2, 0]], [[2, 0]], [[-4, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-4, 0]], [[4, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 1]], [[0, 0]], [[2, 1]], [[-4, 1]], [[0, 0]], [[-2, 1]], [[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]], [[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]]]}
  • id: 22376597
    {'center': '24.d1.b1', 'center_index': 24, 'center_order': 72, 'counter': 81, 'cyclotomic_n': 4, 'dim': 4, 'faithful': False, 'field': [1, 0, 1], 'group': '1728.34767', 'group_counter': 34767, 'group_order': 1728, 'image': None, 'image_isoclass': '96.215', 'image_order': 96, 'indicator': 0, 'kernel': '96.e1.b1', 'kernel_order': 18, 'label': '1728.34767.4u2', 'nt': [24, 2], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[4, 1]], [[-4, 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]], [[-4, 0]], [[4, 0]], [[2, 0]], [[-4, 0]], [[2, 0]], [[-4, 0]], [[-2, 0]], [[-4, 0]], [[4, 0]], [[2, 0]], [[2, 0]], [[-4, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-4, 0]], [[4, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 1]], [[0, 0]], [[-2, 1]], [[4, 1]], [[0, 0]], [[2, 1]], [[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]], [[-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]]]}
  • id: 22376598
    {'center': '24.d1.a1', 'center_index': 24, 'center_order': 72, 'counter': 82, 'cyclotomic_n': 4, 'dim': 4, 'faithful': False, 'field': [1, 0, 1], 'group': '1728.34767', 'group_counter': 34767, 'group_order': 1728, 'image': None, 'image_isoclass': '96.215', 'image_order': 96, 'indicator': 0, 'kernel': '96.e1.a1', 'kernel_order': 18, 'label': '1728.34767.4v1', 'nt': [24, 101], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[-2, 0]], [[4, 0]], [[-2, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[-4, 1]], [[4, 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]], [[-4, 0]], [[-2, 0]], [[-4, 0]], [[2, 0]], [[-4, 0]], [[2, 0]], [[4, 0]], [[-4, 0]], [[4, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-4, 0]], [[4, 0]], [[-2, 0]], [[-4, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1]], [[0, 0]], [[-4, 1]], [[2, 1]], [[0, 0]], [[4, 1]], [[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]], [[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]]]}
  • id: 22376599
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  • id: 22376600
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  • id: 22376601
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  • id: 22376602
    {'center': '72.e1.a1', 'center_index': 72, 'center_order': 24, 'counter': 86, 'cyclotomic_n': 4, 'dim': 4, 'faithful': False, 'field': [1, 0, 1], 'group': '1728.34767', 'group_counter': 34767, 'group_order': 1728, 'image': None, 'image_isoclass': '288.954', 'image_order': 288, 'indicator': 0, 'kernel': '288.f1.a1', 'kernel_order': 6, 'label': '1728.34767.4x1', 'nt': [24, 610], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[-4, 1]], [[4, 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]], [[-4, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-4, 0]], [[4, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[1, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[0, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1]], [[0, 0]], [[2, 1]], [[2, 1]], [[0, 0]], [[-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1]], [[0, 0]], [[3, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 1]], [[-1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 22376603
    {'center': '72.e1.a1', 'center_index': 72, 'center_order': 24, 'counter': 87, 'cyclotomic_n': 4, 'dim': 4, 'faithful': False, 'field': [1, 0, 1], 'group': '1728.34767', 'group_counter': 34767, 'group_order': 1728, 'image': None, 'image_isoclass': '288.954', 'image_order': 288, 'indicator': 0, 'kernel': '288.f1.a1', 'kernel_order': 6, 'label': '1728.34767.4x2', 'nt': [24, 2], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[4, 1]], [[-4, 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]], [[-4, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-4, 0]], [[4, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[1, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[0, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1]], [[0, 0]], [[-2, 1]], [[-2, 1]], [[0, 0]], [[2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1]], [[0, 0]], [[-3, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 1]], [[1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 22376604
    {'center': '72.e1.a1', 'center_index': 72, 'center_order': 24, 'counter': 88, 'cyclotomic_n': 4, 'dim': 4, 'faithful': False, 'field': [1, 0, 1], 'group': '1728.34767', 'group_counter': 34767, 'group_order': 1728, 'image': None, 'image_isoclass': '288.954', 'image_order': 288, 'indicator': 0, 'kernel': '288.f1.a1', 'kernel_order': 6, 'label': '1728.34767.4y1', 'nt': [24, 610], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[-4, 1]], [[4, 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]], [[-4, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-4, 0]], [[4, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[1, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[3, 0]], [[-3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1]], [[0, 0]], [[2, 1]], [[2, 1]], [[0, 0]], [[-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1]], [[0, 0]], [[-3, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 1]], [[-1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 22376605
    {'center': '72.e1.a1', 'center_index': 72, 'center_order': 24, 'counter': 89, 'cyclotomic_n': 4, 'dim': 4, 'faithful': False, 'field': [1, 0, 1], 'group': '1728.34767', 'group_counter': 34767, 'group_order': 1728, 'image': None, 'image_isoclass': '288.954', 'image_order': 288, 'indicator': 0, 'kernel': '288.f1.a1', 'kernel_order': 6, 'label': '1728.34767.4y2', 'nt': [24, 2], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[4, 1]], [[-4, 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]], [[-4, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-4, 0]], [[4, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[1, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[3, 0]], [[-3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1]], [[0, 0]], [[-2, 1]], [[-2, 1]], [[0, 0]], [[2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1]], [[0, 0]], [[3, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 1]], [[1, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 22376607
    {'center': '72.a1.b1', 'center_index': 72, 'center_order': 24, 'counter': 90, 'cyclotomic_n': 12, 'dim': 4, 'faithful': False, 'field': [-3, 0, 1], 'group': '1728.34767', 'group_counter': 34767, 'group_order': 1728, 'image': None, 'image_isoclass': '144.137', 'image_order': 144, 'indicator': -1, 'kernel': '144.c1.d1', 'kernel_order': 12, 'label': '1728.34767.4z1', 'nt': [48, 0], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[-2, 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]], [[-2, 0]], [[-4, 0]], [[-2, 0]], [[-4, 0]], [[2, 0]], [[4, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 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]], [[0, 0]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, -1]], [[0, 0]], [[-2, 1], [-2, -1]], [[2, 1], [2, -1]], [[0, 0]], [[2, 1], [2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1], [-2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 22376608
    {'center': '72.a1.b1', 'center_index': 72, 'center_order': 24, 'counter': 91, 'cyclotomic_n': 12, 'dim': 4, 'faithful': False, 'field': [-3, 0, 1], 'group': '1728.34767', 'group_counter': 34767, 'group_order': 1728, 'image': None, 'image_isoclass': '144.137', 'image_order': 144, 'indicator': -1, 'kernel': '144.c1.d1', 'kernel_order': 12, 'label': '1728.34767.4z2', 'nt': [48, 0], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[-2, 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]], [[-2, 0]], [[-4, 0]], [[-2, 0]], [[-4, 0]], [[2, 0]], [[4, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 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]], [[0, 0]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[0, 0]], [[0, 0]], [[1, 1], [1, -1]], [[0, 0]], [[2, 1], [2, -1]], [[-2, 1], [-2, -1]], [[0, 0]], [[-2, 1], [-2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1], [2, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1], [1, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 22376615
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  • id: 22376616
    {'center': '144.a1.b1', 'center_index': 144, 'center_order': 12, 'counter': 99, 'cyclotomic_n': 1, 'dim': 8, 'faithful': False, 'field': [0, 1], 'group': '1728.34767', 'group_counter': 34767, 'group_order': 1728, 'image': None, 'image_isoclass': '288.960', 'image_order': 288, 'indicator': 1, 'kernel': '288.e1.b1', 'kernel_order': 6, 'label': '1728.34767.8b', 'nt': [24, 608], 'q_character': None, 'values': [[[8, 0]], [[-8, 0]], [[-8, 0]], [[8, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[8, 0]], [[-4, 0]], [[-4, 0]], [[2, 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]], [[4, 0]], [[8, 0]], [[4, 0]], [[-8, 0]], [[4, 0]], [[-8, 0]], [[-4, 0]], [[4, 0]], [[-4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[-2, 0]], [[2, 0]], [[-4, 0]], [[-2, 0]], [[4, 0]], [[-4, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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: 22376508
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  • id: 22376509
    {'center': '216.a1.a1', 'center_index': 216, 'center_order': 8, 'counter': 101, 'cyclotomic_n': 1, 'dim': 8, 'faithful': False, 'field': [0, 1], 'group': '1728.34767', 'group_counter': 34767, 'group_order': 1728, 'image': None, 'image_isoclass': '432.759', 'image_order': 432, 'indicator': 1, 'kernel': '432.a1.a1', 'kernel_order': 4, 'label': '1728.34767.8d', 'nt': [24, 1296], 'q_character': None, 'values': [[[8, 0]], [[8, 0]], [[8, 0]], [[8, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-8, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[4, 0]], [[1, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 22376510
    {'center': '432.a1.a1', 'center_index': 432, 'center_order': 4, 'counter': 102, 'cyclotomic_n': 1, 'dim': 8, 'faithful': False, 'field': [0, 1], 'group': '1728.34767', 'group_counter': 34767, 'group_order': 1728, 'image': None, 'image_isoclass': '864.4378', 'image_order': 864, 'indicator': 1, 'kernel': '864.c1.a1', 'kernel_order': 2, 'label': '1728.34767.8e', 'nt': [24, 2624], 'q_character': None, 'values': [[[8, 0]], [[-8, 0]], [[-8, 0]], [[8, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[2, 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]], [[4, 0]], [[-4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[-4, 0]], [[4, 0]], [[-4, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[3, 0]], [[6, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[0, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 22376511
    {'center': '432.a1.a1', 'center_index': 432, 'center_order': 4, 'counter': 103, 'cyclotomic_n': 1, 'dim': 8, 'faithful': False, 'field': [0, 1], 'group': '1728.34767', 'group_counter': 34767, 'group_order': 1728, 'image': None, 'image_isoclass': '864.4378', 'image_order': 864, 'indicator': 1, 'kernel': '864.c1.a1', 'kernel_order': 2, 'label': '1728.34767.8f', 'nt': [24, 2624], 'q_character': None, 'values': [[[8, 0]], [[-8, 0]], [[-8, 0]], [[8, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[2, 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]], [[4, 0]], [[-4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[-4, 0]], [[4, 0]], [[-4, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[3, 0]], [[-3, 0]], [[-6, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 22376512
    {'center': '144.b1.a1', 'center_index': 144, 'center_order': 12, 'counter': 104, 'cyclotomic_n': 1, 'dim': 8, 'faithful': False, 'field': [0, 1], 'group': '1728.34767', 'group_counter': 34767, 'group_order': 1728, 'image': None, 'image_isoclass': '288.961', 'image_order': 288, 'indicator': -1, 'kernel': '288.d1.a1', 'kernel_order': 6, 'label': '1728.34767.8g', 'nt': [48, 0], 'q_character': None, 'values': [[[8, 0]], [[-8, 0]], [[8, 0]], [[-8, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[-4, 0]], [[8, 0]], [[-4, 0]], [[-4, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-8, 0]], [[4, 0]], [[4, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[4, 0]], [[8, 0]], [[-8, 0]], [[2, 0]], [[-2, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[-2, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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: 22376513
    {'center': '144.a1.b1', 'center_index': 144, 'center_order': 12, 'counter': 105, 'cyclotomic_n': 1, 'dim': 8, 'faithful': False, 'field': [0, 1], 'group': '1728.34767', 'group_counter': 34767, 'group_order': 1728, 'image': None, 'image_isoclass': '288.961', 'image_order': 288, 'indicator': -1, 'kernel': '288.c1.b1', 'kernel_order': 6, 'label': '1728.34767.8h', 'nt': [48, 0], 'q_character': None, 'values': [[[8, 0]], [[-8, 0]], [[8, 0]], [[-8, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[8, 0]], [[-4, 0]], [[-4, 0]], [[2, 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]], [[4, 0]], [[-8, 0]], [[4, 0]], [[8, 0]], [[-4, 0]], [[-8, 0]], [[4, 0]], [[-4, 0]], [[4, 0]], [[-4, 0]], [[4, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[4, 0]], [[2, 0]], [[-4, 0]], [[4, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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: 22376514
    {'center': '144.a1.a1', 'center_index': 144, 'center_order': 12, 'counter': 106, 'cyclotomic_n': 1, 'dim': 8, 'faithful': False, 'field': [0, 1], 'group': '1728.34767', 'group_counter': 34767, 'group_order': 1728, 'image': None, 'image_isoclass': '288.961', 'image_order': 288, 'indicator': -1, 'kernel': '288.c1.a1', 'kernel_order': 6, 'label': '1728.34767.8i', 'nt': [48, 0], 'q_character': None, 'values': [[[8, 0]], [[-8, 0]], [[8, 0]], [[-8, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[8, 0]], [[-4, 0]], [[-4, 0]], [[2, 0]], [[-4, 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]], [[4, 0]], [[4, 0]], [[-8, 0]], [[-4, 0]], [[8, 0]], [[4, 0]], [[-8, 0]], [[-4, 0]], [[4, 0]], [[-4, 0]], [[4, 0]], [[-2, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[-4, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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: 22376515
    {'center': '144.b1.a1', 'center_index': 144, 'center_order': 12, 'counter': 107, 'cyclotomic_n': 1, 'dim': 8, 'faithful': False, 'field': [0, 1], 'group': '1728.34767', 'group_counter': 34767, 'group_order': 1728, 'image': None, 'image_isoclass': '288.965', 'image_order': 288, 'indicator': -1, 'kernel': '288.b1.a1', 'kernel_order': 6, 'label': '1728.34767.8j', 'nt': [48, 0], 'q_character': None, 'values': [[[8, 0]], [[8, 0]], [[-8, 0]], [[-8, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[-4, 0]], [[8, 0]], [[-4, 0]], [[-4, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[8, 0]], [[4, 0]], [[-4, 0]], [[4, 0]], [[4, 0]], [[-4, 0]], [[4, 0]], [[-8, 0]], [[-8, 0]], [[-2, 0]], [[2, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[-2, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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: 22376516
    {'center': '432.a1.a1', 'center_index': 432, 'center_order': 4, 'counter': 108, 'cyclotomic_n': 12, 'dim': 8, 'faithful': False, 'field': [-3, 0, 1], 'group': '1728.34767', 'group_counter': 34767, 'group_order': 1728, 'image': None, 'image_isoclass': '864.4349', 'image_order': 864, 'indicator': -1, 'kernel': '864.b1.a1', 'kernel_order': 2, 'label': '1728.34767.8k1', 'nt': [96, 0], 'q_character': None, 'values': [[[8, 0]], [[-8, 0]], [[8, 0]], [[-8, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[2, 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]], [[4, 0]], [[4, 0]], [[4, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[4, 0]], [[-4, 0]], [[4, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 1], [-3, -1]], [[3, 1], [3, -1]], [[3, 1], [3, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-3, 1], [-3, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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: 22376517
    {'center': '432.a1.a1', 'center_index': 432, 'center_order': 4, 'counter': 109, 'cyclotomic_n': 12, 'dim': 8, 'faithful': False, 'field': [-3, 0, 1], 'group': '1728.34767', 'group_counter': 34767, 'group_order': 1728, 'image': None, 'image_isoclass': '864.4349', 'image_order': 864, 'indicator': -1, 'kernel': '864.b1.a1', 'kernel_order': 2, 'label': '1728.34767.8k2', 'nt': [96, 0], 'q_character': None, 'values': [[[8, 0]], [[-8, 0]], [[8, 0]], [[-8, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[2, 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]], [[4, 0]], [[4, 0]], [[4, 0]], [[-4, 0]], [[-4, 0]], [[4, 0]], [[4, 0]], [[-4, 0]], [[4, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 1], [3, -1]], [[-3, 1], [-3, -1]], [[-3, 1], [-3, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[3, 1], [3, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[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: 22376519
    {'center': '432.a1.a1', 'center_index': 432, 'center_order': 4, 'counter': 110, 'cyclotomic_n': 12, 'dim': 8, 'faithful': False, 'field': [-3, 0, 1], 'group': '1728.34767', 'group_counter': 34767, 'group_order': 1728, 'image': None, 'image_isoclass': '864.4337', 'image_order': 864, 'indicator': -1, 'kernel': '864.a1.a1', 'kernel_order': 2, 'label': '1728.34767.8l1', 'nt': [96, 0], 'q_character': None, 'values': [[[8, 0]], [[8, 0]], [[-8, 0]], [[-8, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[2, 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]], [[-4, 0]], [[4, 0]], [[-4, 0]], [[4, 0]], [[4, 0]], [[-4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 1], [-4, -1]], [[4, 1], [4, -1]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[0, 0]], [[-2, 1], [-2, -1]], [[2, 1], [2, -1]], [[0, 0]], [[0, 0]], [[1, 1], [1, -1]], [[0, 0]], [[2, 1], [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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 22376520
    {'center': '432.a1.a1', 'center_index': 432, 'center_order': 4, 'counter': 111, 'cyclotomic_n': 12, 'dim': 8, 'faithful': False, 'field': [-3, 0, 1], 'group': '1728.34767', 'group_counter': 34767, 'group_order': 1728, 'image': None, 'image_isoclass': '864.4337', 'image_order': 864, 'indicator': -1, 'kernel': '864.a1.a1', 'kernel_order': 2, 'label': '1728.34767.8l2', 'nt': [96, 0], 'q_character': None, 'values': [[[8, 0]], [[8, 0]], [[-8, 0]], [[-8, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[-4, 0]], [[-4, 0]], [[2, 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]], [[-4, 0]], [[4, 0]], [[-4, 0]], [[4, 0]], [[4, 0]], [[-4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 1], [4, -1]], [[-4, 1], [-4, -1]], [[1, 1], [1, -1]], [[-1, 1], [-1, -1]], [[1, 1], [1, -1]], [[0, 0]], [[2, 1], [2, -1]], [[-2, 1], [-2, -1]], [[0, 0]], [[0, 0]], [[-1, 1], [-1, -1]], [[0, 0]], [[-2, 1], [-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]], [[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: 93301431
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 1728, 'counter': 1, 'cyclic': False, 'direct': True, 'hall': 6, 'label': '1728.34767.1.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '1.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': False, 'quotient': '1.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 1, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_1', 'simple': False, 'solvable': True, 'special_labels': ['R', 'L0', 'D0', 'C0'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '1728.34767', 'subgroup_hash': 34767, 'subgroup_order': 1728, 'subgroup_tex': '(C_2\\times C_4).S_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 93301711
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 864, 'counter': 2, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.34767.2.a1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '864.3191', 'subgroup_hash': 3191, 'subgroup_order': 864, 'subgroup_tex': '(C_3^2\\times D_6):Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 93301822
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 864, 'counter': 3, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.34767.2.a1.b1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.a1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '864.3191', 'subgroup_hash': 3191, 'subgroup_order': 864, 'subgroup_tex': '(C_3^2\\times D_6):Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 93301933
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 864, 'counter': 4, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.34767.2.b1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '864.3463', 'subgroup_hash': 3463, 'subgroup_order': 864, 'subgroup_tex': '(C_3^2\\times D_6):Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 93302044
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 864, 'counter': 5, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.34767.2.b1.b1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '864.3463', 'subgroup_hash': 3463, 'subgroup_order': 864, 'subgroup_tex': '(C_3^2\\times D_6):Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 93302155
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 864, 'counter': 6, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.34767.2.c1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '864.2876', 'subgroup_hash': 2876, 'subgroup_order': 864, 'subgroup_tex': 'C_2^2.S_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 93302266
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 864, 'counter': 7, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.34767.2.c1.b1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.c1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '864.2876', 'subgroup_hash': 2876, 'subgroup_order': 864, 'subgroup_tex': 'C_2^2.S_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 93302377
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 864, 'counter': 8, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.34767.2.d1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '864.2936', 'subgroup_hash': 2936, 'subgroup_order': 864, 'subgroup_tex': 'C_2^2.S_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 93302488
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 864, 'counter': 9, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.34767.2.d1.b1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.d1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '864.2936', 'subgroup_hash': 2936, 'subgroup_order': 864, 'subgroup_tex': 'C_2^2.S_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 93301432
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': True, 'core_order': 864, 'counter': 10, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.34767.2.e1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '864.3194', 'subgroup_hash': 3194, 'subgroup_order': 864, 'subgroup_tex': 'D_6:(S_3\\times C_{12})', 'supersolvable': True, 'sylow': 0}
  • id: 93301543
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 864, 'counter': 11, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.34767.2.f1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': ['C1'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '864.2890', 'subgroup_hash': 2890, 'subgroup_order': 864, 'subgroup_tex': 'C_2^2.S_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 93301623
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 864, 'counter': 12, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.34767.2.g1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '864.2892', 'subgroup_hash': 2892, 'subgroup_order': 864, 'subgroup_tex': 'C_2^2.S_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 93301634
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 864, 'counter': 13, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.34767.2.h1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '864.3373', 'subgroup_hash': 3373, 'subgroup_order': 864, 'subgroup_tex': '(C_6\\times C_{12}).D_6', 'supersolvable': True, 'sylow': 0}
  • id: 93301645
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 864, 'counter': 14, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.34767.2.i1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '864.3646', 'subgroup_hash': 3646, 'subgroup_order': 864, 'subgroup_tex': '(C_6\\times C_{12}).D_6', 'supersolvable': True, 'sylow': 0}
  • id: 93301656
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 864, 'counter': 15, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.34767.2.j1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '864.2985', 'subgroup_hash': 2985, 'subgroup_order': 864, 'subgroup_tex': 'C_2^2.S_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 93301667
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 864, 'counter': 16, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.34767.2.k1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '864.2999', 'subgroup_hash': 2999, 'subgroup_order': 864, 'subgroup_tex': 'C_2^2.S_3^3', 'supersolvable': True, 'sylow': 0}
  • id: 93301678
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 288, 'counter': 17, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.3.a1.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '576.6038', 'subgroup_hash': 6038, 'subgroup_order': 576, 'subgroup_tex': 'C_2^2.D_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 93301689
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 288, 'counter': 18, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.3.a1.b1', 'maximal': True, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3.a1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '576.6038', 'subgroup_hash': 6038, 'subgroup_order': 576, 'subgroup_tex': 'C_2^2.D_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 93301700
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 288, 'counter': 19, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.3.b1.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '576.6416', 'subgroup_hash': 6416, 'subgroup_order': 576, 'subgroup_tex': 'C_2^2.D_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 93301712
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 432, 'counter': 20, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.34767.4.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '432.474', 'subgroup_hash': 474, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 93301723
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 432, 'counter': 21, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.34767.4.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.a1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '432.474', 'subgroup_hash': 474, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 93301734
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 432, 'counter': 22, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.34767.4.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '432.651', 'subgroup_hash': 651, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 93301745
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 432, 'counter': 23, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.34767.4.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '432.651', 'subgroup_hash': 651, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 93301756
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 432, 'counter': 24, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.34767.4.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '432.651', 'subgroup_hash': 651, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 93301767
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 432, 'counter': 25, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.34767.4.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.c1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '432.651', 'subgroup_hash': 651, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 93301778
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 432, 'counter': 26, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.34767.4.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '432.426', 'subgroup_hash': 426, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 93301789
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 432, 'counter': 27, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.34767.4.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.d1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '432.426', 'subgroup_hash': 426, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 93301800
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 432, 'counter': 28, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.34767.4.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '432.449', 'subgroup_hash': 449, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 93301811
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 432, 'counter': 29, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.34767.4.e1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.e1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '432.449', 'subgroup_hash': 449, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 93301823
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 432, 'counter': 30, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.34767.4.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '432.674', 'subgroup_hash': 674, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 93301834
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 432, 'counter': 31, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.34767.4.f1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.f1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '432.674', 'subgroup_hash': 674, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 93301845
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': True, 'core_order': 432, 'counter': 32, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.34767.4.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': ['C2'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '432.655', 'subgroup_hash': 655, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 93301856
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': True, 'core_order': 432, 'counter': 33, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.34767.4.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '432.473', 'subgroup_hash': 473, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 93301867
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': True, 'core_order': 432, 'counter': 34, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.34767.4.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '432.487', 'subgroup_hash': 487, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 93301878
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 432, 'counter': 35, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.34767.4.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '432.488', 'subgroup_hash': 488, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 93301889
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 432, 'counter': 36, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.34767.4.j1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.j1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '432.488', 'subgroup_hash': 488, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 93301900
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 432, 'counter': 37, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.34767.4.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '432.720', 'subgroup_hash': 720, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 93301911
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 432, 'counter': 38, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.34767.4.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.l1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '432.429', 'subgroup_hash': 429, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 93301922
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 432, 'counter': 39, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.34767.4.l1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.l1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '432.429', 'subgroup_hash': 429, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 93301934
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 432, 'counter': 40, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.34767.4.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.m1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '432.448', 'subgroup_hash': 448, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 93301945
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 432, 'counter': 41, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.34767.4.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.n1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '432.453', 'subgroup_hash': 453, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 93301956
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 432, 'counter': 42, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.34767.4.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.o1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '432.657', 'subgroup_hash': 657, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 93301967
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 432, 'counter': 43, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.34767.4.o1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.o1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '432.657', 'subgroup_hash': 657, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 93301978
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 432, 'counter': 44, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.34767.4.p1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.p1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '432.453', 'subgroup_hash': 453, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 93301989
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 432, 'counter': 45, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.34767.4.p1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.p1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '432.453', 'subgroup_hash': 453, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 93302000
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 432, 'counter': 46, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.34767.4.q1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.q1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '432.452', 'subgroup_hash': 452, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 93302011
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 432, 'counter': 47, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.34767.4.q1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.q1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '432.452', 'subgroup_hash': 452, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 93302022
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': True, 'core_order': 432, 'counter': 48, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.34767.4.r1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.r1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '432.429', 'subgroup_hash': 429, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 93302033
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 432, 'counter': 49, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.34767.4.s1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.s1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '432.448', 'subgroup_hash': 448, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 93302045
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 432, 'counter': 50, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.34767.4.t1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.t1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '432.453', 'subgroup_hash': 453, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 93302056
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 432, 'counter': 51, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.34767.4.u1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.u1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '432.462', 'subgroup_hash': 462, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 93302067
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 432, 'counter': 52, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.34767.4.v1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.v1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '432.462', 'subgroup_hash': 462, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 93302078
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 432, 'counter': 53, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.34767.4.w1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.w1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '432.462', 'subgroup_hash': 462, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 93302089
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 432, 'counter': 54, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.34767.4.w1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.w1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '432.462', 'subgroup_hash': 462, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 93302100
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 288, 'counter': 55, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.34767.6.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '6.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '6.1', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 6, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '288.547', 'subgroup_hash': 547, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2.C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 93302111
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 288, 'counter': 56, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.34767.6.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '6.a1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '6.1', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 6, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '288.547', 'subgroup_hash': 547, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2.C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 93302122
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': True, 'core_order': 288, 'counter': 57, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.34767.6.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '6.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '6.1', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 6, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '288.550', 'subgroup_hash': 550, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2.C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 93302133
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 144, 'counter': 58, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.6.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '288.649', 'subgroup_hash': 649, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 93302144
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 144, 'counter': 59, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.6.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.c1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '288.649', 'subgroup_hash': 649, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 93302156
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 144, 'counter': 60, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.6.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '288.735', 'subgroup_hash': 735, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 93302167
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 144, 'counter': 61, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.6.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.d1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '288.735', 'subgroup_hash': 735, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 93302178
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 144, 'counter': 62, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.6.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '288.615', 'subgroup_hash': 615, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 93302189
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 144, 'counter': 63, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.6.e1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.e1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '288.615', 'subgroup_hash': 615, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 93302200
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 144, 'counter': 64, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.6.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.612', 'subgroup_hash': 612, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 93302211
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 144, 'counter': 65, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.6.f1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.f1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '288.612', 'subgroup_hash': 612, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 93302222
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 144, 'counter': 66, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.6.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.544', 'subgroup_hash': 544, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2.C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 93302233
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 144, 'counter': 67, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.6.g1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.g1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '288.544', 'subgroup_hash': 544, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2.C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 93302244
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 144, 'counter': 68, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.6.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.524', 'subgroup_hash': 524, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2.C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 93302255
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 144, 'counter': 69, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.6.h1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.h1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '288.524', 'subgroup_hash': 524, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2.C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 93302267
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 144, 'counter': 70, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.6.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.504', 'subgroup_hash': 504, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2.C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 93302278
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 144, 'counter': 71, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.6.i1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.i1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '288.504', 'subgroup_hash': 504, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2.C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 93302289
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 48, 'counter': 72, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.6.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.544', 'subgroup_hash': 544, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2.C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 93302300
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 48, 'counter': 73, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.6.j1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.j1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '288.544', 'subgroup_hash': 544, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2.C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 93302311
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 144, 'counter': 74, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.6.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.667', 'subgroup_hash': 667, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2.C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 93302322
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 144, 'counter': 75, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.6.k1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.k1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '288.667', 'subgroup_hash': 667, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2.C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 93302333
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 144, 'counter': 76, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.6.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.l1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.544', 'subgroup_hash': 544, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2.C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 93302344
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 144, 'counter': 77, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.6.l1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.l1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '288.544', 'subgroup_hash': 544, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2.C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 93302355
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 144, 'counter': 78, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.6.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.m1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.524', 'subgroup_hash': 524, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2.C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 93302366
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 144, 'counter': 79, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.6.m1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.m1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '288.524', 'subgroup_hash': 524, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2.C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 93302378
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 144, 'counter': 80, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.6.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.n1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.535', 'subgroup_hash': 535, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2.C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 93302389
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 144, 'counter': 81, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.6.n1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.n1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '288.535', 'subgroup_hash': 535, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2.C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 93302400
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 144, 'counter': 82, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.6.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.o1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.652', 'subgroup_hash': 652, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2.C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 93302411
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 144, 'counter': 83, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.6.o1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.o1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '288.652', 'subgroup_hash': 652, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2.C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 93302422
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 144, 'counter': 84, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.6.p1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.p1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.620', 'subgroup_hash': 620, 'subgroup_order': 288, 'subgroup_tex': 'C_2^3.S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 93302433
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 144, 'counter': 85, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.6.p1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.p1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '288.620', 'subgroup_hash': 620, 'subgroup_order': 288, 'subgroup_tex': 'C_2^3.S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 93302444
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 144, 'counter': 86, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.6.q1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.q1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.621', 'subgroup_hash': 621, 'subgroup_order': 288, 'subgroup_tex': 'C_2^3.S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 93302455
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 144, 'counter': 87, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.6.q1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.q1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '288.621', 'subgroup_hash': 621, 'subgroup_order': 288, 'subgroup_tex': 'C_2^3.S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 93302466
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 144, 'counter': 88, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.6.r1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.r1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.549', 'subgroup_hash': 549, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2.C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 93302477
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 144, 'counter': 89, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.6.s1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.s1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.550', 'subgroup_hash': 550, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2.C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 93302489
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 144, 'counter': 90, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.6.t1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.t1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.492', 'subgroup_hash': 492, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2.C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 93302500
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 144, 'counter': 91, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.6.t1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.t1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '288.492', 'subgroup_hash': 492, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2.C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 93302511
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 144, 'counter': 92, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.6.u1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.u1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.515', 'subgroup_hash': 515, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2.C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 93302522
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 144, 'counter': 93, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.6.u1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.u1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '288.515', 'subgroup_hash': 515, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2.C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 93302533
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 144, 'counter': 94, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.6.v1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.v1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.493', 'subgroup_hash': 493, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2.C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 93302544
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 144, 'counter': 95, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.6.v1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.v1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '288.493', 'subgroup_hash': 493, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2.C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 93302555
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 144, 'counter': 96, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.6.w1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.w1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.487', 'subgroup_hash': 487, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2.C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 93302566
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 144, 'counter': 97, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.6.w1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.w1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '288.487', 'subgroup_hash': 487, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2.C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 93302577
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 144, 'counter': 98, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.6.x1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.x1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.744', 'subgroup_hash': 744, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2.C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 93302588
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 144, 'counter': 99, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.6.y1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.y1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.518', 'subgroup_hash': 518, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2.C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 93301433
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 144, 'counter': 100, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.6.z1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.z1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.518', 'subgroup_hash': 518, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2.C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 93301444
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 144, 'counter': 101, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.6.ba1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.ba1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.521', 'subgroup_hash': 521, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2.C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 93301455
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 48, 'counter': 102, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.6.bb1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.bb1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.492', 'subgroup_hash': 492, 'subgroup_order': 288, 'subgroup_tex': 'C_6^2.C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 93301466
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 216, 'counter': 103, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.34767.8.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '216.174', 'subgroup_hash': 174, 'subgroup_order': 216, 'subgroup_tex': 'S_3\\times C_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 93301477
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 216, 'counter': 104, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.34767.8.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.a1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': ['C3'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '216.174', 'subgroup_hash': 174, 'subgroup_order': 216, 'subgroup_tex': 'S_3\\times C_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 93301488
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 216, 'characteristic': True, 'core_order': 216, 'counter': 105, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.34767.8.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': ['F'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '216.150', 'subgroup_hash': 150, 'subgroup_order': 216, 'subgroup_tex': 'C_3\\times C_6\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 93301499
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': True, 'core_order': 216, 'counter': 106, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.34767.8.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '216.138', 'subgroup_hash': 138, 'subgroup_order': 216, 'subgroup_tex': 'C_6.C_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 93301510
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 216, 'counter': 107, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.34767.8.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '216.138', 'subgroup_hash': 138, 'subgroup_order': 216, 'subgroup_tex': 'C_6.C_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 93301521
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 216, 'counter': 108, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.34767.8.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.d1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '216.138', 'subgroup_hash': 138, 'subgroup_order': 216, 'subgroup_tex': 'C_6.C_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 93301532
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': True, 'core_order': 216, 'counter': 109, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.34767.8.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '216.138', 'subgroup_hash': 138, 'subgroup_order': 216, 'subgroup_tex': 'C_6.C_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 93301544
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': True, 'core_order': 216, 'counter': 110, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.34767.8.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '216.143', 'subgroup_hash': 143, 'subgroup_order': 216, 'subgroup_tex': 'C_6^2.C_6', 'supersolvable': True, 'sylow': 0}
  • id: 93301555
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': True, 'core_order': 216, 'counter': 111, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.34767.8.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '216.143', 'subgroup_hash': 143, 'subgroup_order': 216, 'subgroup_tex': 'C_6^2.C_6', 'supersolvable': True, 'sylow': 0}
  • id: 93301566
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 216, 'counter': 112, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.34767.8.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '216.143', 'subgroup_hash': 143, 'subgroup_order': 216, 'subgroup_tex': 'C_6^2.C_6', 'supersolvable': True, 'sylow': 0}
  • id: 93301577
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 216, 'counter': 113, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.34767.8.h1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.h1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '216.143', 'subgroup_hash': 143, 'subgroup_order': 216, 'subgroup_tex': 'C_6^2.C_6', 'supersolvable': True, 'sylow': 0}
  • id: 93301588
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 216, 'counter': 114, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.34767.8.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '216.143', 'subgroup_hash': 143, 'subgroup_order': 216, 'subgroup_tex': 'C_6^2.C_6', 'supersolvable': True, 'sylow': 0}
  • id: 93301599
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 216, 'counter': 115, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.34767.8.i1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.i1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '216.143', 'subgroup_hash': 143, 'subgroup_order': 216, 'subgroup_tex': 'C_6^2.C_6', 'supersolvable': True, 'sylow': 0}
  • id: 93301610
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 216, 'counter': 116, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.34767.8.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '216.148', 'subgroup_hash': 148, 'subgroup_order': 216, 'subgroup_tex': 'C_6^2.S_3', 'supersolvable': True, 'sylow': 0}
  • id: 93301620
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 216, 'counter': 117, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.34767.8.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '216.148', 'subgroup_hash': 148, 'subgroup_order': 216, 'subgroup_tex': 'C_6^2.S_3', 'supersolvable': True, 'sylow': 0}
  • id: 93301621
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 216, 'counter': 118, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.34767.8.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.l1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.4', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'Q_8', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '216.121', 'subgroup_hash': 121, 'subgroup_order': 216, 'subgroup_tex': 'C_3^3:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 93301622
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 216, 'counter': 119, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.34767.8.l1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.l1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.4', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'Q_8', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '216.121', 'subgroup_hash': 121, 'subgroup_order': 216, 'subgroup_tex': 'C_3^3:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 93301624
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 216, 'counter': 120, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.34767.8.l1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.l1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.4', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'Q_8', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '216.121', 'subgroup_hash': 121, 'subgroup_order': 216, 'subgroup_tex': 'C_3^3:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 93301625
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 216, 'counter': 121, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.34767.8.l1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.l1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.4', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'Q_8', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '216.121', 'subgroup_hash': 121, 'subgroup_order': 216, 'subgroup_tex': 'C_3^3:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 93301626
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 54, 'counter': 122, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.8.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.m1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.119', 'subgroup_hash': 119, 'subgroup_order': 216, 'subgroup_tex': 'C_6.S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 93301627
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 54, 'counter': 123, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.8.m1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.m1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.119', 'subgroup_hash': 119, 'subgroup_order': 216, 'subgroup_tex': 'C_6.S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 93301628
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 54, 'counter': 124, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.8.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.n1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.119', 'subgroup_hash': 119, 'subgroup_order': 216, 'subgroup_tex': 'C_6.S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 93301629
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 54, 'counter': 125, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.8.n1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.n1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.119', 'subgroup_hash': 119, 'subgroup_order': 216, 'subgroup_tex': 'C_6.S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 93301630
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 54, 'counter': 126, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.8.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.o1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.123', 'subgroup_hash': 123, 'subgroup_order': 216, 'subgroup_tex': 'C_3^3:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 93301631
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 54, 'counter': 127, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.8.o1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.o1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.123', 'subgroup_hash': 123, 'subgroup_order': 216, 'subgroup_tex': 'C_3^3:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 93301632
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 108, 'counter': 128, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.8.p1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.p1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.124', 'subgroup_hash': 124, 'subgroup_order': 216, 'subgroup_tex': 'C_6.S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 93301633
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 108, 'counter': 129, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.8.p1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.p1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.124', 'subgroup_hash': 124, 'subgroup_order': 216, 'subgroup_tex': 'C_6.S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 93301635
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 108, 'counter': 130, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.8.p1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.p1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.124', 'subgroup_hash': 124, 'subgroup_order': 216, 'subgroup_tex': 'C_6.S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 93301636
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 108, 'counter': 131, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.8.p1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.p1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.124', 'subgroup_hash': 124, 'subgroup_order': 216, 'subgroup_tex': 'C_6.S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 93301637
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 108, 'counter': 132, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.8.q1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.q1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.145', 'subgroup_hash': 145, 'subgroup_order': 216, 'subgroup_tex': 'C_3^3:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 93301638
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 108, 'counter': 133, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.8.q1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.q1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.145', 'subgroup_hash': 145, 'subgroup_order': 216, 'subgroup_tex': 'C_3^3:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 93301639
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 48, 'counter': 134, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.9.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '9.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 9, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.1098', 'subgroup_hash': 1098, 'subgroup_order': 192, 'subgroup_tex': 'C_4^2.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 93301640
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 48, 'counter': 135, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.9.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '9.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 9, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.1195', 'subgroup_hash': 1195, 'subgroup_order': 192, 'subgroup_tex': 'C_2.(Q_8\\times D_6)', 'supersolvable': True, 'sylow': 0}
  • id: 93301641
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 48, 'counter': 136, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.9.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '9.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '192.1195', 'subgroup_hash': 1195, 'subgroup_order': 192, 'subgroup_tex': 'C_2.(Q_8\\times D_6)', 'supersolvable': True, 'sylow': 0}
  • id: 93301642
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 144, 'counter': 137, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.34767.12.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '12.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '12.4', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '144.79', 'subgroup_hash': 79, 'subgroup_order': 144, 'subgroup_tex': 'D_6:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 93301643
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 144, 'counter': 138, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.34767.12.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '12.a1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '12.4', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '144.79', 'subgroup_hash': 79, 'subgroup_order': 144, 'subgroup_tex': 'D_6:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 93301644
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 144, 'counter': 139, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.34767.12.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '12.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '12.4', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '144.146', 'subgroup_hash': 146, 'subgroup_order': 144, 'subgroup_tex': 'D_6.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 93301646
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 144, 'counter': 140, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.34767.12.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '12.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '12.4', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '144.146', 'subgroup_hash': 146, 'subgroup_order': 144, 'subgroup_tex': 'D_6.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 93301647
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 144, 'counter': 141, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.34767.12.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '12.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '12.4', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '144.64', 'subgroup_hash': 64, 'subgroup_order': 144, 'subgroup_tex': 'C_6.D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 93301648
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 144, 'counter': 142, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.34767.12.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '12.c1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '12.4', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '144.64', 'subgroup_hash': 64, 'subgroup_order': 144, 'subgroup_tex': 'C_6.D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 93301649
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 144, 'counter': 143, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.34767.12.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '12.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '12.4', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '144.79', 'subgroup_hash': 79, 'subgroup_order': 144, 'subgroup_tex': 'D_6:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 93301650
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 144, 'counter': 144, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.34767.12.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '12.d1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '12.4', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '144.79', 'subgroup_hash': 79, 'subgroup_order': 144, 'subgroup_tex': 'D_6:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 93301651
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 144, 'counter': 145, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.34767.12.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '12.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '12.4', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '144.146', 'subgroup_hash': 146, 'subgroup_order': 144, 'subgroup_tex': 'D_6.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 93301652
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 144, 'counter': 146, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.34767.12.e1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '12.e1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '12.4', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '144.146', 'subgroup_hash': 146, 'subgroup_order': 144, 'subgroup_tex': 'D_6.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 93301653
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': True, 'core_order': 144, 'counter': 147, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.34767.12.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '12.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '12.4', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '144.150', 'subgroup_hash': 150, 'subgroup_order': 144, 'subgroup_tex': 'D_6:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 93301654
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 144, 'counter': 148, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.34767.12.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '12.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '12.4', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '144.78', 'subgroup_hash': 78, 'subgroup_order': 144, 'subgroup_tex': 'C_{12}:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 93301655
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 144, 'counter': 149, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.34767.12.g1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '12.g1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '12.4', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '144.78', 'subgroup_hash': 78, 'subgroup_order': 144, 'subgroup_tex': 'C_{12}:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 93301657
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 144, 'counter': 150, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.34767.12.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '12.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '12.4', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '144.93', 'subgroup_hash': 93, 'subgroup_order': 144, 'subgroup_tex': 'C_6^2.C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 93301658
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 144, 'counter': 151, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.34767.12.h1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '12.h1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '12.4', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '144.93', 'subgroup_hash': 93, 'subgroup_order': 144, 'subgroup_tex': 'C_6^2.C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 93301659
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 144, 'counter': 152, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.34767.12.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '12.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '12.4', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '144.67', 'subgroup_hash': 67, 'subgroup_order': 144, 'subgroup_tex': 'C_2^2.S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 93301660
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 144, 'counter': 153, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.34767.12.i1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '12.i1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '12.4', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '144.67', 'subgroup_hash': 67, 'subgroup_order': 144, 'subgroup_tex': 'C_2^2.S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 93301661
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 144, 'counter': 154, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.34767.12.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '12.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '12.4', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '144.152', 'subgroup_hash': 152, 'subgroup_order': 144, 'subgroup_tex': 'C_2^2.S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 93301662
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 144, 'counter': 155, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.34767.12.j1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '12.j1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '12.4', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '144.152', 'subgroup_hash': 152, 'subgroup_order': 144, 'subgroup_tex': 'C_2^2.S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 93301663
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': True, 'core_order': 144, 'counter': 156, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.34767.12.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '12.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '12.4', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '144.92', 'subgroup_hash': 92, 'subgroup_order': 144, 'subgroup_tex': 'C_3^2:C_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 93301664
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': True, 'core_order': 144, 'counter': 157, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.34767.12.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '12.l1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '12.4', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '144.67', 'subgroup_hash': 67, 'subgroup_order': 144, 'subgroup_tex': 'C_2^2.S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 93301665
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 72, 'counter': 158, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.12.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.m1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.102', 'subgroup_hash': 102, 'subgroup_order': 144, 'subgroup_tex': 'C_6^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 93301666
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 72, 'counter': 159, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.12.m1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.m1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.102', 'subgroup_hash': 102, 'subgroup_order': 144, 'subgroup_tex': 'C_6^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 93301668
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 72, 'counter': 160, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.12.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.n1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.166', 'subgroup_hash': 166, 'subgroup_order': 144, 'subgroup_tex': 'C_6^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 93301669
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 72, 'counter': 161, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.12.n1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.n1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.166', 'subgroup_hash': 166, 'subgroup_order': 144, 'subgroup_tex': 'C_6^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 93301670
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 72, 'counter': 162, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.12.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.o1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.166', 'subgroup_hash': 166, 'subgroup_order': 144, 'subgroup_tex': 'C_6^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 93301671
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 72, 'counter': 163, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.12.o1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.o1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.166', 'subgroup_hash': 166, 'subgroup_order': 144, 'subgroup_tex': 'C_6^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 93301672
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 72, 'counter': 164, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.12.p1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.p1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.84', 'subgroup_hash': 84, 'subgroup_order': 144, 'subgroup_tex': 'C_6^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 93301673
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 72, 'counter': 165, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.12.p1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.p1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.84', 'subgroup_hash': 84, 'subgroup_order': 144, 'subgroup_tex': 'C_6^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 93301674
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 72, 'counter': 166, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.12.q1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.q1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.100', 'subgroup_hash': 100, 'subgroup_order': 144, 'subgroup_tex': 'C_6^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 93301675
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 72, 'counter': 167, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.12.q1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.q1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '144.100', 'subgroup_hash': 100, 'subgroup_order': 144, 'subgroup_tex': 'C_6^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 93301676
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 72, 'counter': 168, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.12.r1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.r1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.176', 'subgroup_hash': 176, 'subgroup_order': 144, 'subgroup_tex': 'C_6^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 93301677
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 72, 'counter': 169, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.12.r1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.r1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '144.176', 'subgroup_hash': 176, 'subgroup_order': 144, 'subgroup_tex': 'C_6^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 93301679
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 72, 'counter': 170, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.12.s1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.s1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.159', 'subgroup_hash': 159, 'subgroup_order': 144, 'subgroup_tex': 'C_{12}\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 93301680
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 72, 'counter': 171, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.12.s1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.s1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '144.159', 'subgroup_hash': 159, 'subgroup_order': 144, 'subgroup_tex': 'C_{12}\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 93301681
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 72, 'counter': 172, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.12.t1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.t1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.64', 'subgroup_hash': 64, 'subgroup_order': 144, 'subgroup_tex': 'C_6.D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 93301682
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 72, 'counter': 173, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.12.t1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.t1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '144.64', 'subgroup_hash': 64, 'subgroup_order': 144, 'subgroup_tex': 'C_6.D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 93301683
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 72, 'counter': 174, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.12.u1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.u1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.146', 'subgroup_hash': 146, 'subgroup_order': 144, 'subgroup_tex': 'D_6.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 93301684
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 72, 'counter': 175, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.12.u1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.u1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '144.146', 'subgroup_hash': 146, 'subgroup_order': 144, 'subgroup_tex': 'D_6.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 93301685
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 48, 'counter': 176, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.12.v1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.v1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.79', 'subgroup_hash': 79, 'subgroup_order': 144, 'subgroup_tex': 'D_6:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 93301686
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 48, 'counter': 177, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.12.v1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.v1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '144.79', 'subgroup_hash': 79, 'subgroup_order': 144, 'subgroup_tex': 'D_6:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 93301687
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 178, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.12.w1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.w1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.64', 'subgroup_hash': 64, 'subgroup_order': 144, 'subgroup_tex': 'C_6.D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 93301688
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 179, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.12.w1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.w1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '144.64', 'subgroup_hash': 64, 'subgroup_order': 144, 'subgroup_tex': 'C_6.D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 93301690
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 180, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.12.x1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.x1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.146', 'subgroup_hash': 146, 'subgroup_order': 144, 'subgroup_tex': 'D_6.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 93301691
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 181, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.12.x1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.x1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.146', 'subgroup_hash': 146, 'subgroup_order': 144, 'subgroup_tex': 'D_6.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 93301692
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 72, 'counter': 182, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.12.y1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.y1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.159', 'subgroup_hash': 159, 'subgroup_order': 144, 'subgroup_tex': 'C_{12}\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 93301693
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 72, 'counter': 183, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.12.y1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.y1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.159', 'subgroup_hash': 159, 'subgroup_order': 144, 'subgroup_tex': 'C_{12}\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 93301694
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 72, 'counter': 184, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.12.z1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.z1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.79', 'subgroup_hash': 79, 'subgroup_order': 144, 'subgroup_tex': 'D_6:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 93301695
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 72, 'counter': 185, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.12.z1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.z1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.79', 'subgroup_hash': 79, 'subgroup_order': 144, 'subgroup_tex': 'D_6:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 93301696
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 72, 'counter': 186, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.12.ba1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.ba1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.64', 'subgroup_hash': 64, 'subgroup_order': 144, 'subgroup_tex': 'C_6.D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 93301697
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 72, 'counter': 187, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.12.ba1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.ba1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '144.64', 'subgroup_hash': 64, 'subgroup_order': 144, 'subgroup_tex': 'C_6.D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 93301698
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 72, 'counter': 188, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.12.bb1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.bb1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.146', 'subgroup_hash': 146, 'subgroup_order': 144, 'subgroup_tex': 'D_6.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 93301699
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 72, 'counter': 189, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.12.bb1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.bb1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.146', 'subgroup_hash': 146, 'subgroup_order': 144, 'subgroup_tex': 'D_6.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 93301701
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 72, 'counter': 190, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.12.bc1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.bc1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.167', 'subgroup_hash': 167, 'subgroup_order': 144, 'subgroup_tex': 'C_6^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 93301702
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 72, 'counter': 191, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.12.bc1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.bc1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.167', 'subgroup_hash': 167, 'subgroup_order': 144, 'subgroup_tex': 'C_6^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 93301703
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 72, 'counter': 192, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.12.bd1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.bd1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.76', 'subgroup_hash': 76, 'subgroup_order': 144, 'subgroup_tex': 'C_{12}:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 93301704
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 72, 'counter': 193, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.12.bd1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.bd1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '144.76', 'subgroup_hash': 76, 'subgroup_order': 144, 'subgroup_tex': 'C_{12}:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 93301705
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 72, 'counter': 194, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.12.be1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.be1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.77', 'subgroup_hash': 77, 'subgroup_order': 144, 'subgroup_tex': 'C_6^2.C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 93301706
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 72, 'counter': 195, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.12.be1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.be1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '144.77', 'subgroup_hash': 77, 'subgroup_order': 144, 'subgroup_tex': 'C_6^2.C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 93301707
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 72, 'counter': 196, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.12.bf1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.bf1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.168', 'subgroup_hash': 168, 'subgroup_order': 144, 'subgroup_tex': 'C_{12}.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 93301708
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 72, 'counter': 197, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.12.bf1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.bf1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.168', 'subgroup_hash': 168, 'subgroup_order': 144, 'subgroup_tex': 'C_{12}.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 93301709
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 72, 'counter': 198, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.12.bg1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.bg1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.77', 'subgroup_hash': 77, 'subgroup_order': 144, 'subgroup_tex': 'C_6^2.C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 93301710
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 72, 'counter': 199, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.12.bg1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.bg1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.77', 'subgroup_hash': 77, 'subgroup_order': 144, 'subgroup_tex': 'C_6^2.C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 93301713
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 72, 'counter': 200, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.12.bh1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.bh1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.63', 'subgroup_hash': 63, 'subgroup_order': 144, 'subgroup_tex': 'C_3^2:C_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 93301714
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 72, 'counter': 201, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.12.bh1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.bh1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '144.63', 'subgroup_hash': 63, 'subgroup_order': 144, 'subgroup_tex': 'C_3^2:C_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 93301715
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 72, 'counter': 202, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.12.bi1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.bi1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.67', 'subgroup_hash': 67, 'subgroup_order': 144, 'subgroup_tex': 'C_2^2.S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 93301716
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 72, 'counter': 203, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.12.bi1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.bi1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.67', 'subgroup_hash': 67, 'subgroup_order': 144, 'subgroup_tex': 'C_2^2.S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 93301717
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 72, 'counter': 204, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.12.bj1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.bj1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.158', 'subgroup_hash': 158, 'subgroup_order': 144, 'subgroup_tex': 'C_{12}.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 93301718
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 72, 'counter': 205, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.12.bj1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.bj1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.158', 'subgroup_hash': 158, 'subgroup_order': 144, 'subgroup_tex': 'C_{12}.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 93301719
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 72, 'counter': 206, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.12.bk1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.bk1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.93', 'subgroup_hash': 93, 'subgroup_order': 144, 'subgroup_tex': 'C_6^2.C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 93301720
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 72, 'counter': 207, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.12.bk1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.bk1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '144.93', 'subgroup_hash': 93, 'subgroup_order': 144, 'subgroup_tex': 'C_6^2.C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 93301721
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 72, 'counter': 208, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.12.bl1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.bl1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.94', 'subgroup_hash': 94, 'subgroup_order': 144, 'subgroup_tex': 'C_6.D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 93301722
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 72, 'counter': 209, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.12.bl1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.bl1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.94', 'subgroup_hash': 94, 'subgroup_order': 144, 'subgroup_tex': 'C_6.D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 93301724
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 72, 'counter': 210, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.12.bm1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.bm1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.67', 'subgroup_hash': 67, 'subgroup_order': 144, 'subgroup_tex': 'C_2^2.S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 93301725
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 72, 'counter': 211, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.12.bm1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.bm1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.67', 'subgroup_hash': 67, 'subgroup_order': 144, 'subgroup_tex': 'C_2^2.S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 93301726
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 72, 'counter': 212, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.12.bn1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.bn1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.66', 'subgroup_hash': 66, 'subgroup_order': 144, 'subgroup_tex': 'C_6.D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 93301727
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 72, 'counter': 213, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.12.bn1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.bn1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '144.66', 'subgroup_hash': 66, 'subgroup_order': 144, 'subgroup_tex': 'C_6.D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 93301728
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 72, 'counter': 214, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.12.bo1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.bo1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.77', 'subgroup_hash': 77, 'subgroup_order': 144, 'subgroup_tex': 'C_6^2.C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 93301729
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 72, 'counter': 215, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.12.bo1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.bo1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '144.77', 'subgroup_hash': 77, 'subgroup_order': 144, 'subgroup_tex': 'C_6^2.C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 93301730
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 72, 'counter': 216, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.12.bp1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.bp1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.63', 'subgroup_hash': 63, 'subgroup_order': 144, 'subgroup_tex': 'C_3^2:C_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 93301731
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 72, 'counter': 217, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.12.bp1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.bp1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '144.63', 'subgroup_hash': 63, 'subgroup_order': 144, 'subgroup_tex': 'C_3^2:C_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 93301732
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 72, 'counter': 218, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.12.bq1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.bq1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.67', 'subgroup_hash': 67, 'subgroup_order': 144, 'subgroup_tex': 'C_2^2.S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 93301733
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 72, 'counter': 219, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.12.bq1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.bq1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '144.67', 'subgroup_hash': 67, 'subgroup_order': 144, 'subgroup_tex': 'C_2^2.S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 93301735
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 72, 'counter': 220, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.12.br1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.br1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.66', 'subgroup_hash': 66, 'subgroup_order': 144, 'subgroup_tex': 'C_6.D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 93301736
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 72, 'counter': 221, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.12.br1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.br1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '144.66', 'subgroup_hash': 66, 'subgroup_order': 144, 'subgroup_tex': 'C_6.D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 93301737
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 72, 'counter': 222, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.12.bs1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.bs1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.66', 'subgroup_hash': 66, 'subgroup_order': 144, 'subgroup_tex': 'C_6.D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 93301738
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 72, 'counter': 223, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.12.bs1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.bs1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '144.66', 'subgroup_hash': 66, 'subgroup_order': 144, 'subgroup_tex': 'C_6.D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 93301739
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 72, 'counter': 224, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.12.bt1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.bt1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.67', 'subgroup_hash': 67, 'subgroup_order': 144, 'subgroup_tex': 'C_2^2.S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 93301740
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 72, 'counter': 225, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.12.bt1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.bt1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '144.67', 'subgroup_hash': 67, 'subgroup_order': 144, 'subgroup_tex': 'C_2^2.S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 93301741
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 72, 'counter': 226, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.12.bu1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.bu1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.66', 'subgroup_hash': 66, 'subgroup_order': 144, 'subgroup_tex': 'C_6.D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 93301742
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 72, 'counter': 227, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.12.bu1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.bu1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '144.66', 'subgroup_hash': 66, 'subgroup_order': 144, 'subgroup_tex': 'C_6.D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 93301743
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 24, 'counter': 228, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.12.bv1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.bv1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.77', 'subgroup_hash': 77, 'subgroup_order': 144, 'subgroup_tex': 'C_6^2.C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 93301744
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 24, 'counter': 229, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.12.bv1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.bv1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '144.77', 'subgroup_hash': 77, 'subgroup_order': 144, 'subgroup_tex': 'C_6^2.C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 93301746
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 230, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.12.bw1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.bw1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.168', 'subgroup_hash': 168, 'subgroup_order': 144, 'subgroup_tex': 'C_{12}.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 93301747
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 231, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.12.bw1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.bw1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '144.168', 'subgroup_hash': 168, 'subgroup_order': 144, 'subgroup_tex': 'C_{12}.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 93301748
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 232, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.12.bx1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.bx1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.67', 'subgroup_hash': 67, 'subgroup_order': 144, 'subgroup_tex': 'C_2^2.S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 93301749
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 233, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.12.bx1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.bx1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '144.67', 'subgroup_hash': 67, 'subgroup_order': 144, 'subgroup_tex': 'C_2^2.S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 93301750
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 234, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.12.by1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.by1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.66', 'subgroup_hash': 66, 'subgroup_order': 144, 'subgroup_tex': 'C_6.D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 93301751
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 235, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.12.by1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.by1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.66', 'subgroup_hash': 66, 'subgroup_order': 144, 'subgroup_tex': 'C_6.D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 93301752
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 72, 'counter': 236, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.12.bz1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.bz1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.103', 'subgroup_hash': 103, 'subgroup_order': 144, 'subgroup_tex': 'C_{12}:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 93301753
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 72, 'counter': 237, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.12.ca1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.ca1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.77', 'subgroup_hash': 77, 'subgroup_order': 144, 'subgroup_tex': 'C_6^2.C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 93301754
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 72, 'counter': 238, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.12.ca1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.ca1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.77', 'subgroup_hash': 77, 'subgroup_order': 144, 'subgroup_tex': 'C_6^2.C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 93301755
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 72, 'counter': 239, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.12.cb1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.cb1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.168', 'subgroup_hash': 168, 'subgroup_order': 144, 'subgroup_tex': 'C_{12}.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 93301757
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 72, 'counter': 240, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.12.cc1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.cc1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.77', 'subgroup_hash': 77, 'subgroup_order': 144, 'subgroup_tex': 'C_6^2.C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 93301758
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 72, 'counter': 241, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.12.cc1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.cc1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.77', 'subgroup_hash': 77, 'subgroup_order': 144, 'subgroup_tex': 'C_6^2.C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 93301759
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 72, 'counter': 242, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.12.cd1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.cd1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.92', 'subgroup_hash': 92, 'subgroup_order': 144, 'subgroup_tex': 'C_3^2:C_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 93301760
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 72, 'counter': 243, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.12.ce1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.ce1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.93', 'subgroup_hash': 93, 'subgroup_order': 144, 'subgroup_tex': 'C_6^2.C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 93301761
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 72, 'counter': 244, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.12.cf1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.cf1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.158', 'subgroup_hash': 158, 'subgroup_order': 144, 'subgroup_tex': 'C_{12}.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 93301762
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 72, 'counter': 245, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.12.cf1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.cf1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.158', 'subgroup_hash': 158, 'subgroup_order': 144, 'subgroup_tex': 'C_{12}.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 93301763
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 72, 'counter': 246, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.12.cg1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.cg1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.67', 'subgroup_hash': 67, 'subgroup_order': 144, 'subgroup_tex': 'C_2^2.S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 93301764
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 72, 'counter': 247, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.12.cg1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.cg1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.67', 'subgroup_hash': 67, 'subgroup_order': 144, 'subgroup_tex': 'C_2^2.S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 93301765
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 72, 'counter': 248, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.12.ch1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.ch1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.66', 'subgroup_hash': 66, 'subgroup_order': 144, 'subgroup_tex': 'C_6.D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 93301766
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 72, 'counter': 249, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.12.ch1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.ch1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.66', 'subgroup_hash': 66, 'subgroup_order': 144, 'subgroup_tex': 'C_6.D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 93301768
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 72, 'counter': 250, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.12.ci1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.ci1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '144.92', 'subgroup_hash': 92, 'subgroup_order': 144, 'subgroup_tex': 'C_3^2:C_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 93301769
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 72, 'counter': 251, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.12.cj1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.cj1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '144.93', 'subgroup_hash': 93, 'subgroup_order': 144, 'subgroup_tex': 'C_6^2.C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 93301770
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 72, 'counter': 252, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.12.ck1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.ck1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '144.67', 'subgroup_hash': 67, 'subgroup_order': 144, 'subgroup_tex': 'C_2^2.S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 93301771
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 72, 'counter': 253, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.12.cl1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.cl1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '144.67', 'subgroup_hash': 67, 'subgroup_order': 144, 'subgroup_tex': 'C_2^2.S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 93301772
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 72, 'counter': 254, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.12.cm1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.cm1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '144.66', 'subgroup_hash': 66, 'subgroup_order': 144, 'subgroup_tex': 'C_6.D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 93301773
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 72, 'counter': 255, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.12.cm1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.cm1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '144.66', 'subgroup_hash': 66, 'subgroup_order': 144, 'subgroup_tex': 'C_6.D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 93301774
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 48, 'counter': 256, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.12.cn1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.cn1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '144.78', 'subgroup_hash': 78, 'subgroup_order': 144, 'subgroup_tex': 'C_{12}:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 93301775
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 24, 'counter': 257, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.12.co1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.co1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '144.76', 'subgroup_hash': 76, 'subgroup_order': 144, 'subgroup_tex': 'C_{12}:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 93301776
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 258, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.12.cp1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.cp1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '144.168', 'subgroup_hash': 168, 'subgroup_order': 144, 'subgroup_tex': 'C_{12}.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 93301777
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 259, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.12.cq1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.cq1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '144.63', 'subgroup_hash': 63, 'subgroup_order': 144, 'subgroup_tex': 'C_3^2:C_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 93301779
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 260, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.12.cr1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.cr1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '144.67', 'subgroup_hash': 67, 'subgroup_order': 144, 'subgroup_tex': 'C_2^2.S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 93301780
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 261, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.12.cs1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.cs1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '144.63', 'subgroup_hash': 63, 'subgroup_order': 144, 'subgroup_tex': 'C_3^2:C_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 93301781
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 262, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.12.ct1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.ct1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '144.67', 'subgroup_hash': 67, 'subgroup_order': 144, 'subgroup_tex': 'C_2^2.S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 93301782
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 263, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.12.cu1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.cu1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '144.168', 'subgroup_hash': 168, 'subgroup_order': 144, 'subgroup_tex': 'C_{12}.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 93301783
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 216, 'characteristic': True, 'core_order': 108, 'counter': 264, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.34767.16.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.14', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 14, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^4', 'simple': False, 'solvable': True, 'special_labels': ['D', 'S', 'L1', 'D1', 'C4'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '108.45', 'subgroup_hash': 45, 'subgroup_order': 108, 'subgroup_tex': 'C_3\\times C_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 93301784
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 108, 'counter': 265, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.34767.16.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '16.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.12', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 12, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times Q_8', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '108.42', 'subgroup_hash': 42, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 93301785
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 108, 'counter': 266, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.34767.16.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '16.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.12', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 12, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times Q_8', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '108.42', 'subgroup_hash': 42, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 93301786
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 108, 'counter': 267, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.34767.16.b1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '16.b1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.12', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 12, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times Q_8', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '108.42', 'subgroup_hash': 42, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 93301787
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 108, 'counter': 268, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.34767.16.b1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '16.b1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.12', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 12, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times Q_8', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '108.42', 'subgroup_hash': 42, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 93301788
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 108, 'counter': 269, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.34767.16.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '16.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.12', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 12, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times Q_8', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, '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: 93301790
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 108, 'counter': 270, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.34767.16.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '16.c1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.12', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 12, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times Q_8', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, '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: 93301791
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 108, 'counter': 271, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.34767.16.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '16.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.13', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 13, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4:C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '108.34', 'subgroup_hash': 34, 'subgroup_order': 108, 'subgroup_tex': 'C_3^3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 93301792
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 108, 'counter': 272, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.34767.16.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '16.d1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.13', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 13, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4:C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '108.34', 'subgroup_hash': 34, 'subgroup_order': 108, 'subgroup_tex': 'C_3^3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 93301793
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 54, 'counter': 273, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.16.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.42', 'subgroup_hash': 42, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 93301794
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 54, 'counter': 274, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.16.e1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.e1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.42', 'subgroup_hash': 42, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 93301795
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 54, 'counter': 275, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.16.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.32', 'subgroup_hash': 32, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 93301796
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 54, 'counter': 276, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.16.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.32', 'subgroup_hash': 32, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 93301797
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 54, 'counter': 277, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.16.g1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.g1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.32', 'subgroup_hash': 32, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 93301798
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 54, 'counter': 278, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.16.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.32', 'subgroup_hash': 32, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 93301799
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 54, 'counter': 279, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.16.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.33', 'subgroup_hash': 33, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 93301801
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 54, 'counter': 280, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.16.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.33', 'subgroup_hash': 33, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 93301802
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 54, 'counter': 281, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.16.j1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.j1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.33', 'subgroup_hash': 33, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 93301803
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 54, 'counter': 282, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.16.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.42', 'subgroup_hash': 42, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 93301804
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 54, 'counter': 283, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.16.k1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.k1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.42', 'subgroup_hash': 42, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 93301805
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 216, 'characteristic': False, 'core_order': 54, 'counter': 284, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.16.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.l1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.35', 'subgroup_hash': 35, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 93301806
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 54, 'counter': 285, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.16.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.m1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.33', 'subgroup_hash': 33, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 93301807
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 54, 'counter': 286, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.16.m1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.m1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.33', 'subgroup_hash': 33, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 93301808
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 54, 'counter': 287, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.16.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.n1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.34', 'subgroup_hash': 34, 'subgroup_order': 108, 'subgroup_tex': 'C_3^3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 93301809
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 24, 'counter': 288, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.18.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '18.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '96.169', 'subgroup_hash': 169, 'subgroup_order': 96, 'subgroup_tex': 'C_{12}.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 93301810
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 24, 'counter': 289, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.18.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '18.a1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '96.169', 'subgroup_hash': 169, 'subgroup_order': 96, 'subgroup_tex': 'C_{12}.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 93301812
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 290, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.18.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '96.85', 'subgroup_hash': 85, 'subgroup_order': 96, 'subgroup_tex': 'C_2^3.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 93301813
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 291, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.18.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '96.85', 'subgroup_hash': 85, 'subgroup_order': 96, 'subgroup_tex': 'C_2^3.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 93301814
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 24, 'counter': 292, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.18.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.130', 'subgroup_hash': 130, 'subgroup_order': 96, 'subgroup_tex': 'C_2^3.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 93301815
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 24, 'counter': 293, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.18.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.c1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '96.130', 'subgroup_hash': 130, 'subgroup_order': 96, 'subgroup_tex': 'C_2^3.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 93301816
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 294, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.18.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.85', 'subgroup_hash': 85, 'subgroup_order': 96, 'subgroup_tex': 'C_2^3.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 93301817
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 295, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.18.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.d1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '96.85', 'subgroup_hash': 85, 'subgroup_order': 96, 'subgroup_tex': 'C_2^3.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 93301818
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 48, 'counter': 296, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.18.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.85', 'subgroup_hash': 85, 'subgroup_order': 96, 'subgroup_tex': 'C_2^3.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 93301819
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 48, 'counter': 297, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.18.e1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.e1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '96.85', 'subgroup_hash': 85, 'subgroup_order': 96, 'subgroup_tex': 'C_2^3.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 93301820
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 298, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.18.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.85', 'subgroup_hash': 85, 'subgroup_order': 96, 'subgroup_tex': 'C_2^3.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 93301821
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 299, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.18.f1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.f1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '96.85', 'subgroup_hash': 85, 'subgroup_order': 96, 'subgroup_tex': 'C_2^3.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 93301824
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 24, 'counter': 300, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.18.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.130', 'subgroup_hash': 130, 'subgroup_order': 96, 'subgroup_tex': 'C_2^3.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 93301825
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 24, 'counter': 301, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.18.g1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.g1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '96.130', 'subgroup_hash': 130, 'subgroup_order': 96, 'subgroup_tex': 'C_2^3.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 93301826
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 302, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.18.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.131', 'subgroup_hash': 131, 'subgroup_order': 96, 'subgroup_tex': 'C_{12}.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 93301827
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 303, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.18.h1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.h1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '96.131', 'subgroup_hash': 131, 'subgroup_order': 96, 'subgroup_tex': 'C_{12}.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 93301828
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 304, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.18.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.85', 'subgroup_hash': 85, 'subgroup_order': 96, 'subgroup_tex': 'C_2^3.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 93301829
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 305, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.18.i1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.i1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '96.85', 'subgroup_hash': 85, 'subgroup_order': 96, 'subgroup_tex': 'C_2^3.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 93301830
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 24, 'counter': 306, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.18.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '18.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.165', 'subgroup_hash': 165, 'subgroup_order': 96, 'subgroup_tex': 'D_4\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 93301831
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 307, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.18.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.141', 'subgroup_hash': 141, 'subgroup_order': 96, 'subgroup_tex': 'C_2^3.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 93301832
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 308, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.18.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.l1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.141', 'subgroup_hash': 141, 'subgroup_order': 96, 'subgroup_tex': 'C_2^3.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 93301833
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 48, 'counter': 309, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.18.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.m1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.103', 'subgroup_hash': 103, 'subgroup_order': 96, 'subgroup_tex': 'D_6:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 93301835
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 48, 'counter': 310, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.18.m1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.m1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '96.103', 'subgroup_hash': 103, 'subgroup_order': 96, 'subgroup_tex': 'D_6:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 93301836
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 48, 'counter': 311, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.18.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.n1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.103', 'subgroup_hash': 103, 'subgroup_order': 96, 'subgroup_tex': 'D_6:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 93301837
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 48, 'counter': 312, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.18.n1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.n1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '96.103', 'subgroup_hash': 103, 'subgroup_order': 96, 'subgroup_tex': 'D_6:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 93301838
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 313, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.18.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.o1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.98', 'subgroup_hash': 98, 'subgroup_order': 96, 'subgroup_tex': 'D_6.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 93301839
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 314, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.18.o1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.o1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '96.98', 'subgroup_hash': 98, 'subgroup_order': 96, 'subgroup_tex': 'D_6.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 93301840
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 315, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.18.p1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.p1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.153', 'subgroup_hash': 153, 'subgroup_order': 96, 'subgroup_tex': 'D_6:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 93301841
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 316, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.18.p1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.p1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '96.153', 'subgroup_hash': 153, 'subgroup_order': 96, 'subgroup_tex': 'D_6:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 93301842
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 48, 'counter': 317, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.18.q1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.q1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.88', 'subgroup_hash': 88, 'subgroup_order': 96, 'subgroup_tex': 'C_2^3.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 93301843
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 48, 'counter': 318, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.18.q1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.q1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '96.88', 'subgroup_hash': 88, 'subgroup_order': 96, 'subgroup_tex': 'C_2^3.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 93301844
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 24, 'counter': 319, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.18.r1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.r1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.135', 'subgroup_hash': 135, 'subgroup_order': 96, 'subgroup_tex': 'C_{12}:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 93301846
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 24, 'counter': 320, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.18.r1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.r1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '96.135', 'subgroup_hash': 135, 'subgroup_order': 96, 'subgroup_tex': 'C_{12}:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 93301847
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 321, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.18.s1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.s1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.88', 'subgroup_hash': 88, 'subgroup_order': 96, 'subgroup_tex': 'C_2^3.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 93301848
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 322, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.18.s1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.s1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '96.88', 'subgroup_hash': 88, 'subgroup_order': 96, 'subgroup_tex': 'C_2^3.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 93301849
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 323, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.18.t1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.t1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.94', 'subgroup_hash': 94, 'subgroup_order': 96, 'subgroup_tex': 'C_3:(C_4\\times Q_8)', 'supersolvable': True, 'sylow': 0}
  • id: 93301850
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 324, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.18.t1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.t1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '96.94', 'subgroup_hash': 94, 'subgroup_order': 96, 'subgroup_tex': 'C_3:(C_4\\times Q_8)', 'supersolvable': True, 'sylow': 0}
  • id: 93301851
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 325, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.18.u1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.u1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.96', 'subgroup_hash': 96, 'subgroup_order': 96, 'subgroup_tex': '(C_2\\times C_4).D_6', 'supersolvable': True, 'sylow': 0}
  • id: 93301852
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 326, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.18.u1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.u1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '96.96', 'subgroup_hash': 96, 'subgroup_order': 96, 'subgroup_tex': '(C_2\\times C_4).D_6', 'supersolvable': True, 'sylow': 0}
  • id: 93301853
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 327, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.18.v1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.v1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.96', 'subgroup_hash': 96, 'subgroup_order': 96, 'subgroup_tex': '(C_2\\times C_4).D_6', 'supersolvable': True, 'sylow': 0}
  • id: 93301854
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 328, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.18.v1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.v1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '96.96', 'subgroup_hash': 96, 'subgroup_order': 96, 'subgroup_tex': '(C_2\\times C_4).D_6', 'supersolvable': True, 'sylow': 0}
  • id: 93301855
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 329, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.18.w1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.w1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.151', 'subgroup_hash': 151, 'subgroup_order': 96, 'subgroup_tex': 'C_{12}.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 93301857
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 330, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.18.w1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.w1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '96.151', 'subgroup_hash': 151, 'subgroup_order': 96, 'subgroup_tex': 'C_{12}.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 93301858
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 48, 'counter': 331, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.18.x1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.x1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.75', 'subgroup_hash': 75, 'subgroup_order': 96, 'subgroup_tex': 'C_{12}:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 93301859
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 332, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.18.y1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.y1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.77', 'subgroup_hash': 77, 'subgroup_order': 96, 'subgroup_tex': 'C_{12}.Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 93301860
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 333, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.18.z1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.z1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.97', 'subgroup_hash': 97, 'subgroup_order': 96, 'subgroup_tex': 'C_{12}.Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 93301861
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 334, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.18.ba1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.ba1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.95', 'subgroup_hash': 95, 'subgroup_order': 96, 'subgroup_tex': 'C_{12}:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 93301862
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 335, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.18.bb1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.bb1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.94', 'subgroup_hash': 94, 'subgroup_order': 96, 'subgroup_tex': 'C_3:(C_4\\times Q_8)', 'supersolvable': True, 'sylow': 0}
  • id: 93301863
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 72, 'counter': 336, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.34767.24.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '24.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '24.14', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 14, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '72.48', 'subgroup_hash': 48, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 93301864
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 72, 'counter': 337, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.34767.24.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '24.a1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '24.14', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 14, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '72.48', 'subgroup_hash': 48, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 93301865
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 72, 'counter': 338, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.34767.24.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '24.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '24.14', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 14, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '72.48', 'subgroup_hash': 48, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 93301866
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 72, 'counter': 339, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.34767.24.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '24.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '24.14', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 14, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '72.48', 'subgroup_hash': 48, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 93301868
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 216, 'characteristic': False, 'core_order': 72, 'counter': 340, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.34767.24.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '24.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '24.14', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 14, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '72.36', 'subgroup_hash': 36, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 93301869
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 216, 'characteristic': False, 'core_order': 72, 'counter': 341, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.34767.24.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '24.c1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '24.14', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 14, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '72.36', 'subgroup_hash': 36, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 93301870
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 72, 'counter': 342, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.34767.24.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '24.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '24.14', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 14, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '72.29', 'subgroup_hash': 29, 'subgroup_order': 72, 'subgroup_tex': 'C_6:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 93301871
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 72, 'counter': 343, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.34767.24.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '24.d1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '24.14', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 14, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '72.29', 'subgroup_hash': 29, 'subgroup_order': 72, 'subgroup_tex': 'C_6:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 93301872
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 72, 'counter': 344, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.34767.24.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '24.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '24.14', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 14, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '72.29', 'subgroup_hash': 29, 'subgroup_order': 72, 'subgroup_tex': 'C_6:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 93301873
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 72, 'counter': 345, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.34767.24.e1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '24.e1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '24.14', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 14, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '72.29', 'subgroup_hash': 29, 'subgroup_order': 72, 'subgroup_tex': 'C_6:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 93301874
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 72, 'counter': 346, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.34767.24.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '24.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '24.14', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 14, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '72.29', 'subgroup_hash': 29, 'subgroup_order': 72, 'subgroup_tex': 'C_6:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 93301875
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 72, 'counter': 347, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.34767.24.f1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '24.f1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '24.14', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 14, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '72.29', 'subgroup_hash': 29, 'subgroup_order': 72, 'subgroup_tex': 'C_6:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 93301876
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 72, 'counter': 348, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.34767.24.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '24.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '24.14', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 14, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '72.34', 'subgroup_hash': 34, 'subgroup_order': 72, 'subgroup_tex': 'C_6.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 93301877
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 72, 'counter': 349, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.34767.24.g1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '24.g1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '24.14', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 14, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '72.34', 'subgroup_hash': 34, 'subgroup_order': 72, 'subgroup_tex': 'C_6.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 93301879
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 72, 'counter': 350, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.34767.24.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '24.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '24.14', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 14, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '72.34', 'subgroup_hash': 34, 'subgroup_order': 72, 'subgroup_tex': 'C_6.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 93301880
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 72, 'counter': 351, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.34767.24.h1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '24.h1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '24.14', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 14, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '72.34', 'subgroup_hash': 34, 'subgroup_order': 72, 'subgroup_tex': 'C_6.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 93301881
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 216, 'characteristic': True, 'core_order': 72, 'counter': 352, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.34767.24.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '24.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '24.14', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 14, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '72.36', 'subgroup_hash': 36, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 93301882
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 72, 'counter': 353, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.34767.24.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '24.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '24.14', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 14, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '72.29', 'subgroup_hash': 29, 'subgroup_order': 72, 'subgroup_tex': 'C_6:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 93301883
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 72, 'counter': 354, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.34767.24.j1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '24.j1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '24.14', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 14, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '72.29', 'subgroup_hash': 29, 'subgroup_order': 72, 'subgroup_tex': 'C_6:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 93301884
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': True, 'core_order': 72, 'counter': 355, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.34767.24.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '24.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '24.14', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 14, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '72.34', 'subgroup_hash': 34, 'subgroup_order': 72, 'subgroup_tex': 'C_6.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 93301885
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': True, 'core_order': 72, 'counter': 356, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.34767.24.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '24.l1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '24.14', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 14, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '72.34', 'subgroup_hash': 34, 'subgroup_order': 72, 'subgroup_tex': 'C_6.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 93301886
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 72, 'counter': 357, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.34767.24.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '24.m1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '24.4', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3:Q_8', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '72.22', 'subgroup_hash': 22, 'subgroup_order': 72, 'subgroup_tex': 'D_6:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 93301887
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 72, 'counter': 358, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.34767.24.m1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '24.m1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '24.4', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3:Q_8', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '72.22', 'subgroup_hash': 22, 'subgroup_order': 72, 'subgroup_tex': 'D_6:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 93301888
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 72, 'counter': 359, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.34767.24.m1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '24.m1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '24.4', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3:Q_8', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '72.22', 'subgroup_hash': 22, 'subgroup_order': 72, 'subgroup_tex': 'D_6:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 93301890
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 72, 'counter': 360, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.34767.24.m1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '24.m1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '24.4', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3:Q_8', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '72.22', 'subgroup_hash': 22, 'subgroup_order': 72, 'subgroup_tex': 'D_6:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 93301891
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 36, 'counter': 361, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.24.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.n1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.50', 'subgroup_hash': 50, 'subgroup_order': 72, 'subgroup_tex': 'C_2\\times C_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 93301892
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 36, 'counter': 362, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.24.n1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.n1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.50', 'subgroup_hash': 50, 'subgroup_order': 72, 'subgroup_tex': 'C_2\\times C_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 93301893
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 24, 'counter': 363, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.24.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.o1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.48', 'subgroup_hash': 48, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 93301894
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 24, 'counter': 364, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.24.o1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.o1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.48', 'subgroup_hash': 48, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 93301895
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 36, 'counter': 365, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.24.p1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.p1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.36', 'subgroup_hash': 36, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 93301896
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 36, 'counter': 366, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.24.p1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.p1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.36', 'subgroup_hash': 36, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 93301897
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 36, 'counter': 367, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.24.q1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.q1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.29', 'subgroup_hash': 29, 'subgroup_order': 72, 'subgroup_tex': 'C_6:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 93301898
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 36, 'counter': 368, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.24.q1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.q1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '72.29', 'subgroup_hash': 29, 'subgroup_order': 72, 'subgroup_tex': 'C_6:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 93301899
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 36, 'counter': 369, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.24.r1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.r1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.29', 'subgroup_hash': 29, 'subgroup_order': 72, 'subgroup_tex': 'C_6:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 93301901
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 36, 'counter': 370, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.24.r1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.r1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '72.29', 'subgroup_hash': 29, 'subgroup_order': 72, 'subgroup_tex': 'C_6:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 93301902
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 36, 'counter': 371, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.24.s1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.s1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.29', 'subgroup_hash': 29, 'subgroup_order': 72, 'subgroup_tex': 'C_6:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 93301903
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 36, 'counter': 372, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.24.s1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.s1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.29', 'subgroup_hash': 29, 'subgroup_order': 72, 'subgroup_tex': 'C_6:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 93301904
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 36, 'counter': 373, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.24.t1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.t1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.29', 'subgroup_hash': 29, 'subgroup_order': 72, 'subgroup_tex': 'C_6:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 93301905
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 36, 'counter': 374, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.24.t1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.t1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.29', 'subgroup_hash': 29, 'subgroup_order': 72, 'subgroup_tex': 'C_6:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 93301906
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 36, 'counter': 375, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.24.u1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.u1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.34', 'subgroup_hash': 34, 'subgroup_order': 72, 'subgroup_tex': 'C_6.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 93301907
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 36, 'counter': 376, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.24.u1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.u1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.34', 'subgroup_hash': 34, 'subgroup_order': 72, 'subgroup_tex': 'C_6.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 93301908
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 36, 'counter': 377, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.24.v1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.v1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.34', 'subgroup_hash': 34, 'subgroup_order': 72, 'subgroup_tex': 'C_6.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 93301909
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 36, 'counter': 378, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.24.v1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.v1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.34', 'subgroup_hash': 34, 'subgroup_order': 72, 'subgroup_tex': 'C_6.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 93301910
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 216, 'characteristic': False, 'core_order': 24, 'counter': 379, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.24.w1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.w1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.36', 'subgroup_hash': 36, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 93301912
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 216, 'characteristic': False, 'core_order': 24, 'counter': 380, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.24.w1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.w1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.36', 'subgroup_hash': 36, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 93301913
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 24, 'counter': 381, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.24.x1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.x1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.29', 'subgroup_hash': 29, 'subgroup_order': 72, 'subgroup_tex': 'C_6:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 93301914
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 24, 'counter': 382, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.24.x1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.x1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.29', 'subgroup_hash': 29, 'subgroup_order': 72, 'subgroup_tex': 'C_6:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 93301915
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 12, 'counter': 383, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.24.y1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.y1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.29', 'subgroup_hash': 29, 'subgroup_order': 72, 'subgroup_tex': 'C_6:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 93301916
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 12, 'counter': 384, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.24.y1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.y1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.29', 'subgroup_hash': 29, 'subgroup_order': 72, 'subgroup_tex': 'C_6:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 93301917
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 12, 'counter': 385, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.24.z1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.z1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.29', 'subgroup_hash': 29, 'subgroup_order': 72, 'subgroup_tex': 'C_6:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 93301918
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 12, 'counter': 386, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.24.z1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.z1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.29', 'subgroup_hash': 29, 'subgroup_order': 72, 'subgroup_tex': 'C_6:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 93301919
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 12, 'counter': 387, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.24.ba1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.ba1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.34', 'subgroup_hash': 34, 'subgroup_order': 72, 'subgroup_tex': 'C_6.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 93301920
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 12, 'counter': 388, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.24.ba1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.ba1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '72.34', 'subgroup_hash': 34, 'subgroup_order': 72, 'subgroup_tex': 'C_6.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 93301921
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 12, 'counter': 389, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.24.bb1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.bb1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.34', 'subgroup_hash': 34, 'subgroup_order': 72, 'subgroup_tex': 'C_6.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 93301923
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 12, 'counter': 390, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.24.bb1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.bb1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.34', 'subgroup_hash': 34, 'subgroup_order': 72, 'subgroup_tex': 'C_6.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 93301924
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 36, 'counter': 391, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.24.bc1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.bc1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.36', 'subgroup_hash': 36, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 93301925
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 36, 'counter': 392, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.24.bd1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.bd1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.36', 'subgroup_hash': 36, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 93301926
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 36, 'counter': 393, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.24.be1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.be1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.29', 'subgroup_hash': 29, 'subgroup_order': 72, 'subgroup_tex': 'C_6:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 93301927
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 36, 'counter': 394, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.24.be1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.be1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.29', 'subgroup_hash': 29, 'subgroup_order': 72, 'subgroup_tex': 'C_6:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 93301928
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 36, 'counter': 395, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.24.bf1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.bf1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.29', 'subgroup_hash': 29, 'subgroup_order': 72, 'subgroup_tex': 'C_6:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 93301929
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 36, 'counter': 396, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.24.bf1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.bf1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.29', 'subgroup_hash': 29, 'subgroup_order': 72, 'subgroup_tex': 'C_6:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 93301930
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 36, 'counter': 397, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.24.bg1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.bg1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.34', 'subgroup_hash': 34, 'subgroup_order': 72, 'subgroup_tex': 'C_6.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 93301931
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 36, 'counter': 398, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.24.bh1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.bh1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.34', 'subgroup_hash': 34, 'subgroup_order': 72, 'subgroup_tex': 'C_6.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 93301932
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 216, 'characteristic': False, 'core_order': 24, 'counter': 399, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.24.bi1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.bi1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.36', 'subgroup_hash': 36, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 93301935
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 24, 'counter': 400, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.24.bj1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.bj1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.29', 'subgroup_hash': 29, 'subgroup_order': 72, 'subgroup_tex': 'C_6:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 93301936
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 24, 'counter': 401, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.24.bk1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.bk1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.29', 'subgroup_hash': 29, 'subgroup_order': 72, 'subgroup_tex': 'C_6:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 93301937
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 12, 'counter': 402, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.24.bl1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.bl1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.29', 'subgroup_hash': 29, 'subgroup_order': 72, 'subgroup_tex': 'C_6:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 93301938
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 12, 'counter': 403, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.24.bm1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.bm1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.29', 'subgroup_hash': 29, 'subgroup_order': 72, 'subgroup_tex': 'C_6:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 93301939
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 12, 'counter': 404, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.24.bn1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.bn1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.34', 'subgroup_hash': 34, 'subgroup_order': 72, 'subgroup_tex': 'C_6.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 93301940
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 12, 'counter': 405, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.24.bo1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.bo1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.34', 'subgroup_hash': 34, 'subgroup_order': 72, 'subgroup_tex': 'C_6.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 93301941
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 216, 'characteristic': False, 'core_order': 8, 'counter': 406, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.24.bp1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.bp1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.36', 'subgroup_hash': 36, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 93301942
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 407, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.24.bq1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.bq1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.34', 'subgroup_hash': 34, 'subgroup_order': 72, 'subgroup_tex': 'C_6.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 93301943
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 408, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.24.br1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.br1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.34', 'subgroup_hash': 34, 'subgroup_order': 72, 'subgroup_tex': 'C_6.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 93301944
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 36, 'counter': 409, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.24.bs1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.bs1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.30', 'subgroup_hash': 30, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 93301946
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 36, 'counter': 410, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.24.bs1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.bs1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '72.30', 'subgroup_hash': 30, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 93301947
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 36, 'counter': 411, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.24.bs1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.bs1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '72.30', 'subgroup_hash': 30, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 93301948
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 36, 'counter': 412, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.24.bs1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.bs1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '72.30', 'subgroup_hash': 30, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 93301949
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 36, 'counter': 413, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.24.bs1.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.bs1.e1', 'outer_equivalence': False, 'perfect': False, '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': '72.30', 'subgroup_hash': 30, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 93301950
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 36, 'counter': 414, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.24.bs1.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.bs1.f1', 'outer_equivalence': False, 'perfect': False, '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': '72.30', 'subgroup_hash': 30, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 93301951
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 36, 'counter': 415, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.24.bs1.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.bs1.g1', 'outer_equivalence': False, 'perfect': False, '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': '72.30', 'subgroup_hash': 30, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 93301952
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 36, 'counter': 416, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.24.bs1.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.bs1.h1', 'outer_equivalence': False, 'perfect': False, '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': '72.30', 'subgroup_hash': 30, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 93301953
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 18, 'counter': 417, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.24.bt1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.bt1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.29', 'subgroup_hash': 29, 'subgroup_order': 72, 'subgroup_tex': 'C_6:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 93301954
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 18, 'counter': 418, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.24.bt1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.bt1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '72.29', 'subgroup_hash': 29, 'subgroup_order': 72, 'subgroup_tex': 'C_6:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 93301955
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 18, 'counter': 419, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.24.bu1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.bu1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.29', 'subgroup_hash': 29, 'subgroup_order': 72, 'subgroup_tex': 'C_6:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 93301957
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 18, 'counter': 420, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.24.bu1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.bu1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '72.29', 'subgroup_hash': 29, 'subgroup_order': 72, 'subgroup_tex': 'C_6:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 93301958
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 18, 'counter': 421, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.24.bv1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.bv1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.20', 'subgroup_hash': 20, 'subgroup_order': 72, 'subgroup_tex': 'C_6.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 93301959
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 18, 'counter': 422, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.24.bv1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.bv1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '72.20', 'subgroup_hash': 20, 'subgroup_order': 72, 'subgroup_tex': 'C_6.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 93301960
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 18, 'counter': 423, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.24.bw1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.bw1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.27', 'subgroup_hash': 27, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 93301961
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 18, 'counter': 424, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.24.bw1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.bw1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '72.27', 'subgroup_hash': 27, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 93301962
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 18, 'counter': 425, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.24.bx1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.bx1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.27', 'subgroup_hash': 27, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 93301963
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 18, 'counter': 426, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.24.bx1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.bx1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '72.27', 'subgroup_hash': 27, 'subgroup_order': 72, 'subgroup_tex': 'S_3\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 93301964
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 18, 'counter': 427, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.24.by1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.by1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.20', 'subgroup_hash': 20, 'subgroup_order': 72, 'subgroup_tex': 'C_6.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 93301965
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 18, 'counter': 428, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.24.by1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.by1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '72.20', 'subgroup_hash': 20, 'subgroup_order': 72, 'subgroup_tex': 'C_6.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 93301966
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 18, 'counter': 429, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.24.bz1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.bz1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '72.26', 'subgroup_hash': 26, 'subgroup_order': 72, 'subgroup_tex': 'C_3^2:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 93301968
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 18, 'counter': 430, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.24.bz1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.bz1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '72.26', 'subgroup_hash': 26, 'subgroup_order': 72, 'subgroup_tex': 'C_3^2:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 93301969
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 18, 'counter': 431, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.24.ca1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.ca1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '72.24', 'subgroup_hash': 24, 'subgroup_order': 72, 'subgroup_tex': 'C_3^2:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 93301970
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 18, 'counter': 432, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.24.ca1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.ca1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '72.24', 'subgroup_hash': 24, 'subgroup_order': 72, 'subgroup_tex': 'C_3^2:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 93301971
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 18, 'counter': 433, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.24.cb1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.cb1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '72.26', 'subgroup_hash': 26, 'subgroup_order': 72, 'subgroup_tex': 'C_3^2:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 93301972
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 18, 'counter': 434, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.24.cb1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.cb1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '72.26', 'subgroup_hash': 26, 'subgroup_order': 72, 'subgroup_tex': 'C_3^2:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 93301973
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 18, 'counter': 435, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.24.cc1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.cc1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '72.34', 'subgroup_hash': 34, 'subgroup_order': 72, 'subgroup_tex': 'C_6.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 93301974
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 18, 'counter': 436, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.24.cc1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.cc1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '72.34', 'subgroup_hash': 34, 'subgroup_order': 72, 'subgroup_tex': 'C_6.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 93301975
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 18, 'counter': 437, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.24.cc1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.cc1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '72.34', 'subgroup_hash': 34, 'subgroup_order': 72, 'subgroup_tex': 'C_6.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 93301976
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 18, 'counter': 438, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.24.cc1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.cc1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '72.34', 'subgroup_hash': 34, 'subgroup_order': 72, 'subgroup_tex': 'C_6.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 93301977
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 18, 'counter': 439, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.24.cd1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.cd1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '72.20', 'subgroup_hash': 20, 'subgroup_order': 72, 'subgroup_tex': 'C_6.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 93301979
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 18, 'counter': 440, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.24.cd1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.cd1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '72.20', 'subgroup_hash': 20, 'subgroup_order': 72, 'subgroup_tex': 'C_6.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 93301980
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 18, 'counter': 441, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.24.cd1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.cd1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '72.20', 'subgroup_hash': 20, 'subgroup_order': 72, 'subgroup_tex': 'C_6.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 93301981
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 18, 'counter': 442, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.24.cd1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.cd1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '72.20', 'subgroup_hash': 20, 'subgroup_order': 72, 'subgroup_tex': 'C_6.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 93301982
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 443, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.24.ce1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.ce1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '72.20', 'subgroup_hash': 20, 'subgroup_order': 72, 'subgroup_tex': 'C_6.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 93301983
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 444, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.24.ce1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.ce1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '72.20', 'subgroup_hash': 20, 'subgroup_order': 72, 'subgroup_tex': 'C_6.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 93301984
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 445, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.24.ce1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.ce1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '72.20', 'subgroup_hash': 20, 'subgroup_order': 72, 'subgroup_tex': 'C_6.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 93301985
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 446, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.24.ce1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.ce1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '72.20', 'subgroup_hash': 20, 'subgroup_order': 72, 'subgroup_tex': 'C_6.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 93301986
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 18, 'counter': 447, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.24.cf1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.cf1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '72.20', 'subgroup_hash': 20, 'subgroup_order': 72, 'subgroup_tex': 'C_6.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 93301987
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 18, 'counter': 448, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.24.cf1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.cf1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '72.20', 'subgroup_hash': 20, 'subgroup_order': 72, 'subgroup_tex': 'C_6.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 93301988
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 18, 'counter': 449, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.24.cf1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.cf1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '72.20', 'subgroup_hash': 20, 'subgroup_order': 72, 'subgroup_tex': 'C_6.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 93301990
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 18, 'counter': 450, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.24.cf1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.cf1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '72.20', 'subgroup_hash': 20, 'subgroup_order': 72, 'subgroup_tex': 'C_6.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 93301991
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 18, 'counter': 451, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.24.cg1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.cg1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '72.31', 'subgroup_hash': 31, 'subgroup_order': 72, 'subgroup_tex': 'C_3^2:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 93301992
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 18, 'counter': 452, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.24.cg1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.cg1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '72.31', 'subgroup_hash': 31, 'subgroup_order': 72, 'subgroup_tex': 'C_3^2:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 93301993
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 18, 'counter': 453, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.24.cg1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.cg1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '72.31', 'subgroup_hash': 31, 'subgroup_order': 72, 'subgroup_tex': 'C_3^2:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 93301994
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 18, 'counter': 454, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.24.cg1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.cg1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '72.31', 'subgroup_hash': 31, 'subgroup_order': 72, 'subgroup_tex': 'C_3^2:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 93301995
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 455, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.24.ch1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.ch1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '72.31', 'subgroup_hash': 31, 'subgroup_order': 72, 'subgroup_tex': 'C_3^2:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 93301996
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 456, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.24.ch1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.ch1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '72.31', 'subgroup_hash': 31, 'subgroup_order': 72, 'subgroup_tex': 'C_3^2:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 93301997
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 457, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.24.ch1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.ch1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '72.31', 'subgroup_hash': 31, 'subgroup_order': 72, 'subgroup_tex': 'C_3^2:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 93301998
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 458, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.24.ch1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.ch1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '72.31', 'subgroup_hash': 31, 'subgroup_order': 72, 'subgroup_tex': 'C_3^2:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 93301999
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 18, 'counter': 459, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.24.ci1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.ci1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '72.31', 'subgroup_hash': 31, 'subgroup_order': 72, 'subgroup_tex': 'C_3^2:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 93302001
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 18, 'counter': 460, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.24.ci1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.ci1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '72.31', 'subgroup_hash': 31, 'subgroup_order': 72, 'subgroup_tex': 'C_3^2:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 93302002
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 461, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.24.cj1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.cj1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '72.31', 'subgroup_hash': 31, 'subgroup_order': 72, 'subgroup_tex': 'C_3^2:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 93302003
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 462, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.24.cj1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.cj1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.31', 'subgroup_hash': 31, 'subgroup_order': 72, 'subgroup_tex': 'C_3^2:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 93302004
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 463, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.24.cj1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.cj1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '72.31', 'subgroup_hash': 31, 'subgroup_order': 72, 'subgroup_tex': 'C_3^2:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 93302005
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 464, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.24.cj1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.cj1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '72.31', 'subgroup_hash': 31, 'subgroup_order': 72, 'subgroup_tex': 'C_3^2:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 93302006
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 465, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.24.ck1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.ck1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '72.31', 'subgroup_hash': 31, 'subgroup_order': 72, 'subgroup_tex': 'C_3^2:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 93302007
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 466, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.24.ck1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.ck1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.31', 'subgroup_hash': 31, 'subgroup_order': 72, 'subgroup_tex': 'C_3^2:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 93302008
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 467, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.24.ck1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.ck1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '72.31', 'subgroup_hash': 31, 'subgroup_order': 72, 'subgroup_tex': 'C_3^2:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 93302009
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 468, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.24.ck1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.ck1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '72.31', 'subgroup_hash': 31, 'subgroup_order': 72, 'subgroup_tex': 'C_3^2:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 93302010
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 469, 'cyclic': False, 'direct': None, 'hall': 2, 'label': '1728.34767.27.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '27.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 27, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.235', 'subgroup_hash': 235, 'subgroup_order': 64, 'subgroup_tex': 'D_4:Q_8', 'supersolvable': True, 'sylow': 2}
  • id: 93302012
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 216, 'characteristic': True, 'core_order': 54, 'counter': 470, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.34767.32.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '32.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '32.47', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 47, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 32, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2\\times Q_8', 'simple': False, 'solvable': True, 'special_labels': ['C5'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '54.15', 'subgroup_hash': 15, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 93302013
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 216, 'characteristic': True, 'core_order': 54, 'counter': 471, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.34767.32.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '32.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '32.49', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 49, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 32, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4:C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '54.15', 'subgroup_hash': 15, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 93302014
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 216, 'characteristic': True, 'core_order': 54, 'counter': 472, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.34767.32.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '32.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '32.48', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 48, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 32, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4:C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '54.15', 'subgroup_hash': 15, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 93302015
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 27, 'counter': 473, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.32.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '32.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': 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: 93302016
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 27, 'counter': 474, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.32.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '32.d1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': 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: 93302017
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 27, 'counter': 475, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.32.d1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '32.d1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': 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: 93302018
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 27, 'counter': 476, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.32.d1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '32.d1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': 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: 93302019
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 48, 'counter': 477, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.34767.36.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '36.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '36.10', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 10, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 36, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '48.14', 'subgroup_hash': 14, 'subgroup_order': 48, 'subgroup_tex': 'D_6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 93302020
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 48, 'counter': 478, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.34767.36.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '36.a1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '36.10', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 10, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 36, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '48.14', 'subgroup_hash': 14, 'subgroup_order': 48, 'subgroup_tex': 'D_6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 93302021
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': True, 'core_order': 48, 'counter': 479, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.34767.36.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '36.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '36.10', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 10, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 36, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '48.13', 'subgroup_hash': 13, 'subgroup_order': 48, 'subgroup_tex': 'C_{12}:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 93302023
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 24, 'counter': 480, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.36.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '48.21', 'subgroup_hash': 21, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 93302024
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 24, 'counter': 481, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.36.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.c1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.21', 'subgroup_hash': 21, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 93302025
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 12, 'counter': 482, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.36.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.44', 'subgroup_hash': 44, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 93302026
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 12, 'counter': 483, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.36.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.d1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.44', 'subgroup_hash': 44, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 93302027
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 24, 'counter': 484, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.36.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.42', 'subgroup_hash': 42, 'subgroup_order': 48, 'subgroup_tex': 'C_6.C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 93302028
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 24, 'counter': 485, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.36.e1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.e1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.42', 'subgroup_hash': 42, 'subgroup_order': 48, 'subgroup_tex': 'C_6.C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 93302029
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 12, 'counter': 486, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.36.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.21', 'subgroup_hash': 21, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 93302030
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 12, 'counter': 487, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.36.f1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.f1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.21', 'subgroup_hash': 21, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 93302031
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 12, 'counter': 488, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.36.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.19', 'subgroup_hash': 19, 'subgroup_order': 48, 'subgroup_tex': 'C_6.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 93302032
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 12, 'counter': 489, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.36.g1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.g1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.19', 'subgroup_hash': 19, 'subgroup_order': 48, 'subgroup_tex': 'C_6.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 93302034
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 12, 'counter': 490, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.36.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.42', 'subgroup_hash': 42, 'subgroup_order': 48, 'subgroup_tex': 'C_6.C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 93302035
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 12, 'counter': 491, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.36.h1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.h1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '48.42', 'subgroup_hash': 42, 'subgroup_order': 48, 'subgroup_tex': 'C_6.C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 93302036
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 24, 'counter': 492, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.36.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.21', 'subgroup_hash': 21, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 93302037
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 24, 'counter': 493, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.36.i1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.i1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '48.21', 'subgroup_hash': 21, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 93302038
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 24, 'counter': 494, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.36.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.42', 'subgroup_hash': 42, 'subgroup_order': 48, 'subgroup_tex': 'C_6.C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 93302039
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 24, 'counter': 495, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.36.j1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.j1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.42', 'subgroup_hash': 42, 'subgroup_order': 48, 'subgroup_tex': 'C_6.C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 93302040
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 12, 'counter': 496, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.36.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.44', 'subgroup_hash': 44, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 93302041
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 12, 'counter': 497, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.36.k1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.k1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.44', 'subgroup_hash': 44, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 93302042
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 24, 'counter': 498, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.36.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.l1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.19', 'subgroup_hash': 19, 'subgroup_order': 48, 'subgroup_tex': 'C_6.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 93302043
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 24, 'counter': 499, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.36.l1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.l1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.19', 'subgroup_hash': 19, 'subgroup_order': 48, 'subgroup_tex': 'C_6.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 93302046
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 12, 'counter': 500, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.36.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.m1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.19', 'subgroup_hash': 19, 'subgroup_order': 48, 'subgroup_tex': 'C_6.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 93302047
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 12, 'counter': 501, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.36.m1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.m1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.19', 'subgroup_hash': 19, 'subgroup_order': 48, 'subgroup_tex': 'C_6.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 93302048
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 12, 'counter': 502, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.36.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.n1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.42', 'subgroup_hash': 42, 'subgroup_order': 48, 'subgroup_tex': 'C_6.C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 93302049
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 12, 'counter': 503, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.36.n1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.n1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.42', 'subgroup_hash': 42, 'subgroup_order': 48, 'subgroup_tex': 'C_6.C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 93302050
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 8, 'counter': 504, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.36.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.o1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.21', 'subgroup_hash': 21, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 93302051
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 8, 'counter': 505, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.36.o1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.o1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.21', 'subgroup_hash': 21, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 93302052
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 506, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.36.p1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.p1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.19', 'subgroup_hash': 19, 'subgroup_order': 48, 'subgroup_tex': 'C_6.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 93302053
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 507, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.36.p1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.p1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.19', 'subgroup_hash': 19, 'subgroup_order': 48, 'subgroup_tex': 'C_6.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 93302054
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 508, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.36.q1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.q1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.42', 'subgroup_hash': 42, 'subgroup_order': 48, 'subgroup_tex': 'C_6.C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 93302055
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 509, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.36.q1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.q1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '48.42', 'subgroup_hash': 42, 'subgroup_order': 48, 'subgroup_tex': 'C_6.C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 93302057
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 12, 'counter': 510, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.36.r1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.r1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.45', 'subgroup_hash': 45, 'subgroup_order': 48, 'subgroup_tex': 'C_6\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 93302058
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 24, 'counter': 511, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.36.s1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.s1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.35', 'subgroup_hash': 35, 'subgroup_order': 48, 'subgroup_tex': 'C_4\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 93302059
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 24, 'counter': 512, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.36.s1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.s1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '48.35', 'subgroup_hash': 35, 'subgroup_order': 48, 'subgroup_tex': 'C_4\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 93302060
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 24, 'counter': 513, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.36.t1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.t1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.35', 'subgroup_hash': 35, 'subgroup_order': 48, 'subgroup_tex': 'C_4\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 93302061
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 24, 'counter': 514, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.36.t1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.t1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '48.35', 'subgroup_hash': 35, 'subgroup_order': 48, 'subgroup_tex': 'C_4\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 93302062
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 24, 'counter': 515, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.36.u1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.u1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.14', 'subgroup_hash': 14, 'subgroup_order': 48, 'subgroup_tex': 'D_6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 93302063
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 24, 'counter': 516, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.36.u1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.u1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '48.14', 'subgroup_hash': 14, 'subgroup_order': 48, 'subgroup_tex': 'D_6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 93302064
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 24, 'counter': 517, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.36.v1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.v1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.14', 'subgroup_hash': 14, 'subgroup_order': 48, 'subgroup_tex': 'D_6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 93302065
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 24, 'counter': 518, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.36.v1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.v1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '48.14', 'subgroup_hash': 14, 'subgroup_order': 48, 'subgroup_tex': 'D_6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 93302066
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 24, 'counter': 519, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.36.w1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.w1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.35', 'subgroup_hash': 35, 'subgroup_order': 48, 'subgroup_tex': 'C_4\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 93302068
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 24, 'counter': 520, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.36.w1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.w1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '48.35', 'subgroup_hash': 35, 'subgroup_order': 48, 'subgroup_tex': 'C_4\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 93302069
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 24, 'counter': 521, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.36.x1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.x1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.43', 'subgroup_hash': 43, 'subgroup_order': 48, 'subgroup_tex': 'C_6:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 93302070
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 24, 'counter': 522, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.36.x1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.x1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.43', 'subgroup_hash': 43, 'subgroup_order': 48, 'subgroup_tex': 'C_6:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 93302071
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 24, 'counter': 523, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.36.y1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.y1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.22', 'subgroup_hash': 22, 'subgroup_order': 48, 'subgroup_tex': 'C_4:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 93302072
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 24, 'counter': 524, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.36.y1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.y1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.22', 'subgroup_hash': 22, 'subgroup_order': 48, 'subgroup_tex': 'C_4:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 93302073
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 24, 'counter': 525, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.36.z1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.z1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.11', 'subgroup_hash': 11, 'subgroup_order': 48, 'subgroup_tex': 'C_{12}:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 93302074
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 24, 'counter': 526, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.36.z1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.z1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.11', 'subgroup_hash': 11, 'subgroup_order': 48, 'subgroup_tex': 'C_{12}:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 93302075
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 24, 'counter': 527, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.36.ba1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.ba1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.22', 'subgroup_hash': 22, 'subgroup_order': 48, 'subgroup_tex': 'C_4:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 93302076
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 24, 'counter': 528, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.36.ba1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.ba1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '48.22', 'subgroup_hash': 22, 'subgroup_order': 48, 'subgroup_tex': 'C_4:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 93302077
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 24, 'counter': 529, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.36.bb1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.bb1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.12', 'subgroup_hash': 12, 'subgroup_order': 48, 'subgroup_tex': 'C_6.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 93302079
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 24, 'counter': 530, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.36.bb1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.bb1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.12', 'subgroup_hash': 12, 'subgroup_order': 48, 'subgroup_tex': 'C_6.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 93302080
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 531, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.36.bc1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.bc1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.34', 'subgroup_hash': 34, 'subgroup_order': 48, 'subgroup_tex': 'C_6:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 93302081
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 532, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.36.bc1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.bc1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.34', 'subgroup_hash': 34, 'subgroup_order': 48, 'subgroup_tex': 'C_6:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 93302082
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 12, 'counter': 533, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.36.bd1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.bd1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.22', 'subgroup_hash': 22, 'subgroup_order': 48, 'subgroup_tex': 'C_4:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 93302083
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 12, 'counter': 534, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.36.bd1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.bd1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '48.22', 'subgroup_hash': 22, 'subgroup_order': 48, 'subgroup_tex': 'C_4:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 93302084
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 24, 'counter': 535, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.36.be1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.be1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.12', 'subgroup_hash': 12, 'subgroup_order': 48, 'subgroup_tex': 'C_6.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 93302085
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 24, 'counter': 536, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.36.be1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.be1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '48.12', 'subgroup_hash': 12, 'subgroup_order': 48, 'subgroup_tex': 'C_6.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 93302086
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 12, 'counter': 537, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.36.bf1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.bf1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.11', 'subgroup_hash': 11, 'subgroup_order': 48, 'subgroup_tex': 'C_{12}:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 93302087
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 12, 'counter': 538, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.36.bf1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.bf1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.11', 'subgroup_hash': 11, 'subgroup_order': 48, 'subgroup_tex': 'C_{12}:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 93302088
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 12, 'counter': 539, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.36.bg1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.bg1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.12', 'subgroup_hash': 12, 'subgroup_order': 48, 'subgroup_tex': 'C_6.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 93302090
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 12, 'counter': 540, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.36.bg1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.bg1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.12', 'subgroup_hash': 12, 'subgroup_order': 48, 'subgroup_tex': 'C_6.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 93302091
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 12, 'counter': 541, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.36.bh1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.bh1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.46', 'subgroup_hash': 46, 'subgroup_order': 48, 'subgroup_tex': 'C_6\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 93302092
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 12, 'counter': 542, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.36.bh1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.bh1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '48.46', 'subgroup_hash': 46, 'subgroup_order': 48, 'subgroup_tex': 'C_6\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 93302093
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 12, 'counter': 543, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.36.bi1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.bi1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.12', 'subgroup_hash': 12, 'subgroup_order': 48, 'subgroup_tex': 'C_6.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 93302094
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 12, 'counter': 544, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.36.bi1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.bi1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.12', 'subgroup_hash': 12, 'subgroup_order': 48, 'subgroup_tex': 'C_6.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 93302095
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 12, 'counter': 545, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.36.bj1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.bj1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.13', 'subgroup_hash': 13, 'subgroup_order': 48, 'subgroup_tex': 'C_{12}:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 93302096
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 12, 'counter': 546, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.36.bj1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.bj1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.13', 'subgroup_hash': 13, 'subgroup_order': 48, 'subgroup_tex': 'C_{12}:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 93302097
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 24, 'counter': 547, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.36.bk1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.bk1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.34', 'subgroup_hash': 34, 'subgroup_order': 48, 'subgroup_tex': 'C_6:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 93302098
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 24, 'counter': 548, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.36.bk1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.bk1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '48.34', 'subgroup_hash': 34, 'subgroup_order': 48, 'subgroup_tex': 'C_6:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 93302099
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 24, 'counter': 549, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.36.bl1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.bl1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.12', 'subgroup_hash': 12, 'subgroup_order': 48, 'subgroup_tex': 'C_6.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 93302101
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 24, 'counter': 550, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.36.bl1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.bl1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.12', 'subgroup_hash': 12, 'subgroup_order': 48, 'subgroup_tex': 'C_6.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 93302102
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 551, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.36.bm1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.bm1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.12', 'subgroup_hash': 12, 'subgroup_order': 48, 'subgroup_tex': 'C_6.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 93302103
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 552, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.36.bm1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.bm1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.12', 'subgroup_hash': 12, 'subgroup_order': 48, 'subgroup_tex': 'C_6.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 93302104
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 24, 'counter': 553, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.36.bn1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.bn1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.12', 'subgroup_hash': 12, 'subgroup_order': 48, 'subgroup_tex': 'C_6.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 93302105
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 24, 'counter': 554, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.36.bn1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.bn1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '48.12', 'subgroup_hash': 12, 'subgroup_order': 48, 'subgroup_tex': 'C_6.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 93302106
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 12, 'counter': 555, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.36.bo1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.bo1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.11', 'subgroup_hash': 11, 'subgroup_order': 48, 'subgroup_tex': 'C_{12}:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 93302107
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 12, 'counter': 556, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.36.bo1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.bo1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '48.11', 'subgroup_hash': 11, 'subgroup_order': 48, 'subgroup_tex': 'C_{12}:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 93302108
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 12, 'counter': 557, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.36.bp1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.bp1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.12', 'subgroup_hash': 12, 'subgroup_order': 48, 'subgroup_tex': 'C_6.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 93302109
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 12, 'counter': 558, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.36.bp1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.bp1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '48.12', 'subgroup_hash': 12, 'subgroup_order': 48, 'subgroup_tex': 'C_6.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 93302110
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 12, 'counter': 559, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.36.bq1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.bq1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.12', 'subgroup_hash': 12, 'subgroup_order': 48, 'subgroup_tex': 'C_6.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 93302112
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 12, 'counter': 560, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.36.bq1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.bq1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '48.12', 'subgroup_hash': 12, 'subgroup_order': 48, 'subgroup_tex': 'C_6.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 93302113
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 12, 'counter': 561, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.36.br1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.br1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.12', 'subgroup_hash': 12, 'subgroup_order': 48, 'subgroup_tex': 'C_6.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 93302114
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 12, 'counter': 562, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.36.br1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.br1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '48.12', 'subgroup_hash': 12, 'subgroup_order': 48, 'subgroup_tex': 'C_6.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 93302115
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 12, 'counter': 563, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.36.bs1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.bs1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.12', 'subgroup_hash': 12, 'subgroup_order': 48, 'subgroup_tex': 'C_6.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 93302116
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 12, 'counter': 564, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.36.bs1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.bs1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '48.12', 'subgroup_hash': 12, 'subgroup_order': 48, 'subgroup_tex': 'C_6.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 93302117
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 12, 'counter': 565, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.36.bt1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.bt1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.13', 'subgroup_hash': 13, 'subgroup_order': 48, 'subgroup_tex': 'C_{12}:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 93302118
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 12, 'counter': 566, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.36.bt1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.bt1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '48.13', 'subgroup_hash': 13, 'subgroup_order': 48, 'subgroup_tex': 'C_{12}:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 93302119
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 24, 'counter': 567, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.36.bu1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.bu1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.20', 'subgroup_hash': 20, 'subgroup_order': 48, 'subgroup_tex': 'C_4\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 93302120
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 24, 'counter': 568, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.36.bv1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.bv1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.12', 'subgroup_hash': 12, 'subgroup_order': 48, 'subgroup_tex': 'C_6.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 93302121
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 24, 'counter': 569, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.36.bv1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.bv1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '48.12', 'subgroup_hash': 12, 'subgroup_order': 48, 'subgroup_tex': 'C_6.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 93302123
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 24, 'counter': 570, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.36.bw1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.bw1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.34', 'subgroup_hash': 34, 'subgroup_order': 48, 'subgroup_tex': 'C_6:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 93302124
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 24, 'counter': 571, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.36.bx1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.bx1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.12', 'subgroup_hash': 12, 'subgroup_order': 48, 'subgroup_tex': 'C_6.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 93302125
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 24, 'counter': 572, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.36.bx1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.bx1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '48.12', 'subgroup_hash': 12, 'subgroup_order': 48, 'subgroup_tex': 'C_6.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 93302126
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 24, 'counter': 573, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.36.by1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.by1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.11', 'subgroup_hash': 11, 'subgroup_order': 48, 'subgroup_tex': 'C_{12}:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 93302127
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 24, 'counter': 574, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.36.bz1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.bz1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.12', 'subgroup_hash': 12, 'subgroup_order': 48, 'subgroup_tex': 'C_6.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 93302128
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 24, 'counter': 575, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.36.ca1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.ca1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.34', 'subgroup_hash': 34, 'subgroup_order': 48, 'subgroup_tex': 'C_6:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 93302129
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 24, 'counter': 576, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.36.ca1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.ca1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '48.34', 'subgroup_hash': 34, 'subgroup_order': 48, 'subgroup_tex': 'C_6:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 93302130
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 12, 'counter': 577, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.36.cb1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.cb1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.12', 'subgroup_hash': 12, 'subgroup_order': 48, 'subgroup_tex': 'C_6.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 93302131
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 12, 'counter': 578, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.36.cb1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.cb1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '48.12', 'subgroup_hash': 12, 'subgroup_order': 48, 'subgroup_tex': 'C_6.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 93302132
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 12, 'counter': 579, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.36.cc1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.cc1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.13', 'subgroup_hash': 13, 'subgroup_order': 48, 'subgroup_tex': 'C_{12}:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 93302134
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 12, 'counter': 580, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.36.cc1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.cc1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '48.13', 'subgroup_hash': 13, 'subgroup_order': 48, 'subgroup_tex': 'C_{12}:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 93302135
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 12, 'counter': 581, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.36.cd1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.cd1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.22', 'subgroup_hash': 22, 'subgroup_order': 48, 'subgroup_tex': 'C_4:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 93302136
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 24, 'counter': 582, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.36.ce1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.ce1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.11', 'subgroup_hash': 11, 'subgroup_order': 48, 'subgroup_tex': 'C_{12}:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 93302137
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 24, 'counter': 583, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.36.cf1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.cf1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.12', 'subgroup_hash': 12, 'subgroup_order': 48, 'subgroup_tex': 'C_6.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 93302138
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 12, 'counter': 584, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.36.cg1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.cg1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.13', 'subgroup_hash': 13, 'subgroup_order': 48, 'subgroup_tex': 'C_{12}:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 93302139
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 12, 'counter': 585, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.36.ch1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.ch1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.13', 'subgroup_hash': 13, 'subgroup_order': 48, 'subgroup_tex': 'C_{12}:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 93302140
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 12, 'counter': 586, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.36.ci1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.ci1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.12', 'subgroup_hash': 12, 'subgroup_order': 48, 'subgroup_tex': 'C_6.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 93302141
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 12, 'counter': 587, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.36.ci1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.ci1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '48.12', 'subgroup_hash': 12, 'subgroup_order': 48, 'subgroup_tex': 'C_6.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 93302142
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 8, 'counter': 588, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.36.cj1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.cj1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.12', 'subgroup_hash': 12, 'subgroup_order': 48, 'subgroup_tex': 'C_6.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 93302143
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 8, 'counter': 589, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.36.cj1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.cj1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.12', 'subgroup_hash': 12, 'subgroup_order': 48, 'subgroup_tex': 'C_6.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 93302145
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 590, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.36.ck1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.ck1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.34', 'subgroup_hash': 34, 'subgroup_order': 48, 'subgroup_tex': 'C_6:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 93302146
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 591, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.36.ck1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.ck1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.34', 'subgroup_hash': 34, 'subgroup_order': 48, 'subgroup_tex': 'C_6:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 93302147
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 592, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.36.cl1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.cl1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.12', 'subgroup_hash': 12, 'subgroup_order': 48, 'subgroup_tex': 'C_6.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 93302148
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 593, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.36.cl1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.cl1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '48.12', 'subgroup_hash': 12, 'subgroup_order': 48, 'subgroup_tex': 'C_6.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 93302149
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 594, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.36.cm1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.cm1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.13', 'subgroup_hash': 13, 'subgroup_order': 48, 'subgroup_tex': 'C_{12}:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 93302150
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 595, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.36.cm1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.cm1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.13', 'subgroup_hash': 13, 'subgroup_order': 48, 'subgroup_tex': 'C_{12}:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 93302151
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 8, 'counter': 596, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.36.cn1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.cn1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.22', 'subgroup_hash': 22, 'subgroup_order': 48, 'subgroup_tex': 'C_4:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 93302152
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 8, 'counter': 597, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.36.co1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.co1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.11', 'subgroup_hash': 11, 'subgroup_order': 48, 'subgroup_tex': 'C_{12}:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 93302153
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 598, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.36.cp1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.cp1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.34', 'subgroup_hash': 34, 'subgroup_order': 48, 'subgroup_tex': 'C_6:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 93302154
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 599, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.36.cq1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.cq1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.11', 'subgroup_hash': 11, 'subgroup_order': 48, 'subgroup_tex': 'C_{12}:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 93302157
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 600, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.36.cr1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.cr1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.12', 'subgroup_hash': 12, 'subgroup_order': 48, 'subgroup_tex': 'C_6.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 93302158
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 601, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.36.cs1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.cs1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.11', 'subgroup_hash': 11, 'subgroup_order': 48, 'subgroup_tex': 'C_{12}:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 93302159
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 602, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.36.ct1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.ct1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.12', 'subgroup_hash': 12, 'subgroup_order': 48, 'subgroup_tex': 'C_6.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 93302160
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 603, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.36.cu1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.cu1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.34', 'subgroup_hash': 34, 'subgroup_order': 48, 'subgroup_tex': 'C_6:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 93302161
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 432, 'characteristic': False, 'core_order': 36, 'counter': 604, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.34767.48.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '48.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '48.51', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 51, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 48, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2\\times D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '36.14', 'subgroup_hash': 14, 'subgroup_order': 36, 'subgroup_tex': 'C_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 93302162
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 432, 'characteristic': False, 'core_order': 36, 'counter': 605, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.34767.48.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '48.a1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '48.51', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 51, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 48, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2\\times D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '36.14', 'subgroup_hash': 14, 'subgroup_order': 36, 'subgroup_tex': 'C_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 93302163
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 432, 'characteristic': True, 'core_order': 36, 'counter': 606, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.34767.48.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '48.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '48.51', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 51, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 48, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2\\times D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '36.14', 'subgroup_hash': 14, 'subgroup_order': 36, 'subgroup_tex': 'C_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 93302164
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 36, 'counter': 607, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.34767.48.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '48.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '48.40', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 40, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 48, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3\\times Q_8', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 93302165
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 36, 'counter': 608, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.34767.48.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '48.c1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '48.40', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 40, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 48, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3\\times Q_8', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 93302166
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 36, 'counter': 609, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.34767.48.c1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '48.c1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '48.40', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 40, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 48, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3\\times Q_8', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 93302168
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 36, 'counter': 610, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.34767.48.c1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '48.c1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '48.40', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 40, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 48, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3\\times Q_8', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 93302169
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 36, 'counter': 611, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.34767.48.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '48.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '48.34', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 34, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 48, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6:Q_8', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 93302170
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 36, 'counter': 612, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.34767.48.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '48.d1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '48.34', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 34, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 48, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6:Q_8', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 93302171
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 36, 'counter': 613, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.34767.48.d1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '48.d1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '48.34', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 34, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 48, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6:Q_8', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 93302172
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 36, 'counter': 614, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.34767.48.d1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '48.d1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '48.34', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 34, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 48, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6:Q_8', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 93302173
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 36, 'counter': 615, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.34767.48.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '48.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '48.34', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 34, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 48, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6:Q_8', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, '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: 93302174
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 36, 'counter': 616, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.34767.48.e1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '48.e1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '48.34', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 34, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 48, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6:Q_8', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, '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: 93302175
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 216, 'characteristic': False, 'core_order': 12, 'counter': 617, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.48.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.14', 'subgroup_hash': 14, 'subgroup_order': 36, 'subgroup_tex': 'C_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 93302176
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 216, 'characteristic': False, 'core_order': 12, 'counter': 618, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.48.f1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.f1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.14', 'subgroup_hash': 14, 'subgroup_order': 36, 'subgroup_tex': 'C_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 93302177
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 216, 'characteristic': False, 'core_order': 12, 'counter': 619, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.48.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.14', 'subgroup_hash': 14, 'subgroup_order': 36, 'subgroup_tex': 'C_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 93302179
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 216, 'characteristic': False, 'core_order': 4, 'counter': 620, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.48.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.14', 'subgroup_hash': 14, 'subgroup_order': 36, 'subgroup_tex': 'C_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 93302180
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 18, 'counter': 621, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.48.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.14', 'subgroup_hash': 14, 'subgroup_order': 36, 'subgroup_tex': 'C_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 93302181
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 18, 'counter': 622, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.48.i1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.i1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.14', 'subgroup_hash': 14, 'subgroup_order': 36, 'subgroup_tex': 'C_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 93302182
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 18, 'counter': 623, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.48.i1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.i1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.14', 'subgroup_hash': 14, 'subgroup_order': 36, 'subgroup_tex': 'C_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 93302183
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 18, 'counter': 624, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.48.i1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.i1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.14', 'subgroup_hash': 14, 'subgroup_order': 36, 'subgroup_tex': 'C_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 93302184
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 12, 'counter': 625, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.48.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 93302185
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 12, 'counter': 626, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.48.j1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.j1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 93302186
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 12, 'counter': 627, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.48.j1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.j1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 93302187
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 12, 'counter': 628, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.48.j1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.j1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 93302188
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 18, 'counter': 629, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.48.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.6', 'subgroup_hash': 6, 'subgroup_order': 36, 'subgroup_tex': 'C_3:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 93302190
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 18, 'counter': 630, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.48.k1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.k1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.6', 'subgroup_hash': 6, 'subgroup_order': 36, 'subgroup_tex': 'C_3:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 93302191
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 18, 'counter': 631, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.48.k1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.k1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.6', 'subgroup_hash': 6, 'subgroup_order': 36, 'subgroup_tex': 'C_3:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 93302192
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 18, 'counter': 632, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.48.k1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.k1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.6', 'subgroup_hash': 6, 'subgroup_order': 36, 'subgroup_tex': 'C_3:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 93302193
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 6, 'counter': 633, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.48.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.l1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.6', 'subgroup_hash': 6, 'subgroup_order': 36, 'subgroup_tex': 'C_3:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 93302194
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 6, 'counter': 634, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.48.l1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.l1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.6', 'subgroup_hash': 6, 'subgroup_order': 36, 'subgroup_tex': 'C_3:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 93302195
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 18, 'counter': 635, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.48.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.m1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.14', 'subgroup_hash': 14, 'subgroup_order': 36, 'subgroup_tex': 'C_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 93302196
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 18, 'counter': 636, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.48.m1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.m1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.14', 'subgroup_hash': 14, 'subgroup_order': 36, 'subgroup_tex': 'C_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 93302197
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 18, 'counter': 637, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.48.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.n1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 93302198
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 18, 'counter': 638, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.48.n1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.n1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 93302199
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 6, 'counter': 639, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.48.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.o1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 93302201
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 6, 'counter': 640, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.48.o1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.o1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 93302202
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 18, 'counter': 641, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.48.p1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.p1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 93302203
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 18, 'counter': 642, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.48.p1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.p1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 93302204
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 18, 'counter': 643, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.48.q1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.q1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.6', 'subgroup_hash': 6, 'subgroup_order': 36, 'subgroup_tex': 'C_3:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 93302205
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 18, 'counter': 644, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.48.q1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.q1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.6', 'subgroup_hash': 6, 'subgroup_order': 36, 'subgroup_tex': 'C_3:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 93302206
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 18, 'counter': 645, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.48.r1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.r1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.8', 'subgroup_hash': 8, 'subgroup_order': 36, 'subgroup_tex': 'C_3\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 93302207
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 18, 'counter': 646, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.48.r1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.r1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.8', 'subgroup_hash': 8, 'subgroup_order': 36, 'subgroup_tex': 'C_3\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 93302208
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 18, 'counter': 647, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.48.s1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.s1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.6', 'subgroup_hash': 6, 'subgroup_order': 36, 'subgroup_tex': 'C_3:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 93302209
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 18, 'counter': 648, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.48.s1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.s1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.6', 'subgroup_hash': 6, 'subgroup_order': 36, 'subgroup_tex': 'C_3:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 93302210
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 18, 'counter': 649, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.48.t1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.t1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.6', 'subgroup_hash': 6, 'subgroup_order': 36, 'subgroup_tex': 'C_3:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 93302212
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 18, 'counter': 650, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.48.t1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.t1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.6', 'subgroup_hash': 6, 'subgroup_order': 36, 'subgroup_tex': 'C_3:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 93302213
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 18, 'counter': 651, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.48.u1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.u1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.6', 'subgroup_hash': 6, 'subgroup_order': 36, 'subgroup_tex': 'C_3:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 93302214
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 18, 'counter': 652, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.48.u1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.u1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.6', 'subgroup_hash': 6, 'subgroup_order': 36, 'subgroup_tex': 'C_3:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 93302215
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 18, 'counter': 653, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.48.v1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.v1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.6', 'subgroup_hash': 6, 'subgroup_order': 36, 'subgroup_tex': 'C_3:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 93302216
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 18, 'counter': 654, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.48.v1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.v1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.6', 'subgroup_hash': 6, 'subgroup_order': 36, 'subgroup_tex': 'C_3:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 93302217
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 18, 'counter': 655, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.48.w1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.w1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.7', 'subgroup_hash': 7, 'subgroup_order': 36, 'subgroup_tex': 'C_3^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 93302218
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 18, 'counter': 656, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.48.w1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.w1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.7', 'subgroup_hash': 7, 'subgroup_order': 36, 'subgroup_tex': 'C_3^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 93302219
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 6, 'counter': 657, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.48.x1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.x1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.6', 'subgroup_hash': 6, 'subgroup_order': 36, 'subgroup_tex': 'C_3:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 93302220
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 6, 'counter': 658, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.48.x1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.x1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.6', 'subgroup_hash': 6, 'subgroup_order': 36, 'subgroup_tex': 'C_3:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 93302221
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 6, 'counter': 659, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.48.y1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.y1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.6', 'subgroup_hash': 6, 'subgroup_order': 36, 'subgroup_tex': 'C_3:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 93302223
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 6, 'counter': 660, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.48.y1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.y1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.6', 'subgroup_hash': 6, 'subgroup_order': 36, 'subgroup_tex': 'C_3:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 93302224
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 18, 'counter': 661, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.48.z1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.z1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.8', 'subgroup_hash': 8, 'subgroup_order': 36, 'subgroup_tex': 'C_3\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 93302225
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 18, 'counter': 662, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.48.ba1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.ba1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.6', 'subgroup_hash': 6, 'subgroup_order': 36, 'subgroup_tex': 'C_3:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 93302226
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 18, 'counter': 663, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.48.ba1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.ba1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.6', 'subgroup_hash': 6, 'subgroup_order': 36, 'subgroup_tex': 'C_3:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 93302227
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 18, 'counter': 664, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.48.bb1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.bb1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.8', 'subgroup_hash': 8, 'subgroup_order': 36, 'subgroup_tex': 'C_3\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 93302228
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 18, 'counter': 665, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.48.bc1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.bc1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.7', 'subgroup_hash': 7, 'subgroup_order': 36, 'subgroup_tex': 'C_3^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 93302229
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 18, 'counter': 666, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.48.bd1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.bd1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.6', 'subgroup_hash': 6, 'subgroup_order': 36, 'subgroup_tex': 'C_3:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 93302230
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 18, 'counter': 667, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.48.bd1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.bd1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.6', 'subgroup_hash': 6, 'subgroup_order': 36, 'subgroup_tex': 'C_3:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 93302231
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 6, 'counter': 668, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.48.be1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.be1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.6', 'subgroup_hash': 6, 'subgroup_order': 36, 'subgroup_tex': 'C_3:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 93302232
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 6, 'counter': 669, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.48.bf1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.bf1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.6', 'subgroup_hash': 6, 'subgroup_order': 36, 'subgroup_tex': 'C_3:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 93302234
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 6, 'counter': 670, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.48.bg1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.bg1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.6', 'subgroup_hash': 6, 'subgroup_order': 36, 'subgroup_tex': 'C_3:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 93302235
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 18, 'counter': 671, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.48.bh1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.bh1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.14', 'subgroup_hash': 14, 'subgroup_order': 36, 'subgroup_tex': 'C_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 93302236
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 18, 'counter': 672, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.48.bh1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.bh1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.14', 'subgroup_hash': 14, 'subgroup_order': 36, 'subgroup_tex': 'C_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 93302237
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 18, 'counter': 673, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.48.bi1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.bi1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 93302238
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 18, 'counter': 674, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.48.bi1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.bi1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 93302239
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 6, 'counter': 675, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.48.bj1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.bj1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 93302240
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 6, 'counter': 676, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.48.bj1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.bj1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 93302241
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 18, 'counter': 677, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.48.bk1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.bk1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 93302242
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 18, 'counter': 678, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.48.bk1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.bk1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 93302243
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 216, 'characteristic': False, 'core_order': 18, 'counter': 679, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.48.bl1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.bl1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.8', 'subgroup_hash': 8, 'subgroup_order': 36, 'subgroup_tex': 'C_3\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 93302245
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 216, 'characteristic': False, 'core_order': 18, 'counter': 680, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.48.bl1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.bl1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.8', 'subgroup_hash': 8, 'subgroup_order': 36, 'subgroup_tex': 'C_3\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 93302246
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 18, 'counter': 681, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.48.bm1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.bm1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.6', 'subgroup_hash': 6, 'subgroup_order': 36, 'subgroup_tex': 'C_3:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 93302247
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 18, 'counter': 682, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.48.bm1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.bm1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.6', 'subgroup_hash': 6, 'subgroup_order': 36, 'subgroup_tex': 'C_3:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 93302248
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 18, 'counter': 683, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.48.bn1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.bn1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.7', 'subgroup_hash': 7, 'subgroup_order': 36, 'subgroup_tex': 'C_3^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 93302249
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 18, 'counter': 684, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.48.bn1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.bn1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.7', 'subgroup_hash': 7, 'subgroup_order': 36, 'subgroup_tex': 'C_3^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 93302250
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 18, 'counter': 685, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.48.bo1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.bo1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.7', 'subgroup_hash': 7, 'subgroup_order': 36, 'subgroup_tex': 'C_3^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 93302251
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 18, 'counter': 686, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.48.bo1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.bo1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.7', 'subgroup_hash': 7, 'subgroup_order': 36, 'subgroup_tex': 'C_3^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 93302252
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 18, 'counter': 687, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.48.bo1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.bo1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.7', 'subgroup_hash': 7, 'subgroup_order': 36, 'subgroup_tex': 'C_3^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 93302253
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 18, 'counter': 688, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.48.bo1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.bo1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.7', 'subgroup_hash': 7, 'subgroup_order': 36, 'subgroup_tex': 'C_3^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 93302254
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 18, 'counter': 689, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.48.bp1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.bp1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.7', 'subgroup_hash': 7, 'subgroup_order': 36, 'subgroup_tex': 'C_3^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 93302256
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 18, 'counter': 690, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.48.bp1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.bp1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.7', 'subgroup_hash': 7, 'subgroup_order': 36, 'subgroup_tex': 'C_3^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 93302257
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 216, 'characteristic': False, 'core_order': 6, 'counter': 691, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.48.bq1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.bq1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.8', 'subgroup_hash': 8, 'subgroup_order': 36, 'subgroup_tex': 'C_3\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 93302258
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 216, 'characteristic': False, 'core_order': 6, 'counter': 692, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.48.bq1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.bq1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.8', 'subgroup_hash': 8, 'subgroup_order': 36, 'subgroup_tex': 'C_3\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 93302259
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 6, 'counter': 693, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.48.br1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.br1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.6', 'subgroup_hash': 6, 'subgroup_order': 36, 'subgroup_tex': 'C_3:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 93302260
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 6, 'counter': 694, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.48.br1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.br1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.6', 'subgroup_hash': 6, 'subgroup_order': 36, 'subgroup_tex': 'C_3:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 93302261
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 695, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.48.bs1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.bs1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.7', 'subgroup_hash': 7, 'subgroup_order': 36, 'subgroup_tex': 'C_3^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 93302262
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 696, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.48.bs1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.bs1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.7', 'subgroup_hash': 7, 'subgroup_order': 36, 'subgroup_tex': 'C_3^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 93302263
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 697, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.48.bs1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.bs1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.7', 'subgroup_hash': 7, 'subgroup_order': 36, 'subgroup_tex': 'C_3^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 93302264
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 698, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.48.bs1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.bs1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.7', 'subgroup_hash': 7, 'subgroup_order': 36, 'subgroup_tex': 'C_3^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 93302265
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 699, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.48.bt1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.bt1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.7', 'subgroup_hash': 7, 'subgroup_order': 36, 'subgroup_tex': 'C_3^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 93302268
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 700, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.48.bt1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.bt1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.7', 'subgroup_hash': 7, 'subgroup_order': 36, 'subgroup_tex': 'C_3^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 93302269
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 216, 'characteristic': False, 'core_order': 18, 'counter': 701, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.48.bu1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.bu1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.8', 'subgroup_hash': 8, 'subgroup_order': 36, 'subgroup_tex': 'C_3\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 93302270
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 18, 'counter': 702, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.48.bv1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.bv1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.6', 'subgroup_hash': 6, 'subgroup_order': 36, 'subgroup_tex': 'C_3:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 93302271
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 18, 'counter': 703, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.48.bv1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.bv1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.6', 'subgroup_hash': 6, 'subgroup_order': 36, 'subgroup_tex': 'C_3:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 93302272
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 18, 'counter': 704, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.48.bw1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.bw1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.7', 'subgroup_hash': 7, 'subgroup_order': 36, 'subgroup_tex': 'C_3^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 93302273
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 18, 'counter': 705, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.48.bw1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.bw1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.7', 'subgroup_hash': 7, 'subgroup_order': 36, 'subgroup_tex': 'C_3^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 93302274
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 18, 'counter': 706, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.48.bx1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.bx1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.7', 'subgroup_hash': 7, 'subgroup_order': 36, 'subgroup_tex': 'C_3^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 93302275
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 216, 'characteristic': False, 'core_order': 6, 'counter': 707, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.48.by1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.by1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.8', 'subgroup_hash': 8, 'subgroup_order': 36, 'subgroup_tex': 'C_3\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 93302276
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 216, 'characteristic': False, 'core_order': 6, 'counter': 708, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.48.by1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.by1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.8', 'subgroup_hash': 8, 'subgroup_order': 36, 'subgroup_tex': 'C_3\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 93302277
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 709, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.48.bz1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.bz1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.7', 'subgroup_hash': 7, 'subgroup_order': 36, 'subgroup_tex': 'C_3^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 93302279
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 710, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.48.bz1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.bz1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.7', 'subgroup_hash': 7, 'subgroup_order': 36, 'subgroup_tex': 'C_3^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 93302280
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 711, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.48.ca1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.ca1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.7', 'subgroup_hash': 7, 'subgroup_order': 36, 'subgroup_tex': 'C_3^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 93302281
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 712, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.48.ca1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.ca1.a2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.7', 'subgroup_hash': 7, 'subgroup_order': 36, 'subgroup_tex': 'C_3^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 93302282
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 216, 'characteristic': False, 'core_order': 2, 'counter': 713, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.48.cb1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.cb1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.8', 'subgroup_hash': 8, 'subgroup_order': 36, 'subgroup_tex': 'C_3\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 93302283
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 216, 'characteristic': False, 'core_order': 2, 'counter': 714, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.48.cb1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.cb1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.8', 'subgroup_hash': 8, 'subgroup_order': 36, 'subgroup_tex': 'C_3\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 93302284
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 715, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.48.cc1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.cc1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.7', 'subgroup_hash': 7, 'subgroup_order': 36, 'subgroup_tex': 'C_3^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 93302285
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 716, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.48.cc1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.cc1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.7', 'subgroup_hash': 7, 'subgroup_order': 36, 'subgroup_tex': 'C_3^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 93302286
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 717, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.48.cd1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.cd1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.7', 'subgroup_hash': 7, 'subgroup_order': 36, 'subgroup_tex': 'C_3^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 93302287
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 718, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.48.cd1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.cd1.a2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.7', 'subgroup_hash': 7, 'subgroup_order': 36, 'subgroup_tex': 'C_3^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 93302288
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 8, 'counter': 719, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.54.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '54.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.29', 'subgroup_hash': 29, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 93302290
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 8, 'counter': 720, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.54.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '54.a1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '32.29', 'subgroup_hash': 29, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 93302291
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 721, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.54.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '54.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.29', 'subgroup_hash': 29, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 93302292
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 722, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.54.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '54.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '32.29', 'subgroup_hash': 29, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 93302293
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 723, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.54.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '54.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.23', 'subgroup_hash': 23, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 93302294
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 724, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.54.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '54.c1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '32.23', 'subgroup_hash': 23, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 93302295
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 725, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.54.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '54.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.29', 'subgroup_hash': 29, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 93302296
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 726, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.54.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '54.d1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '32.29', 'subgroup_hash': 29, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 93302297
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 8, 'counter': 727, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.54.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '54.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.25', 'subgroup_hash': 25, 'subgroup_order': 32, 'subgroup_tex': 'C_4\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 93302298
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 728, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.54.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '54.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.25', 'subgroup_hash': 25, 'subgroup_order': 32, 'subgroup_tex': 'C_4\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 93302299
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 729, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.54.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '54.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.25', 'subgroup_hash': 25, 'subgroup_order': 32, 'subgroup_tex': 'C_4\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 93302301
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 730, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.54.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '54.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.26', 'subgroup_hash': 26, 'subgroup_order': 32, 'subgroup_tex': 'C_4\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 93302302
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 731, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.54.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '54.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.32', 'subgroup_hash': 32, 'subgroup_order': 32, 'subgroup_tex': 'C_4.Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 93302303
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 732, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.54.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '54.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.32', 'subgroup_hash': 32, 'subgroup_order': 32, 'subgroup_tex': 'C_4.Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 93302304
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 733, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.54.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '54.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 54, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.35', 'subgroup_hash': 35, 'subgroup_order': 32, 'subgroup_tex': 'C_4:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 93302305
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 216, 'characteristic': True, 'core_order': 27, 'counter': 734, 'cyclic': False, 'direct': False, 'hall': 3, 'label': '1728.34767.64.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '64.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '64.235', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 235, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 64, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4:Q_8', 'simple': False, 'solvable': True, 'special_labels': ['L2', 'C6'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 3}
  • id: 93302306
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 24, 'counter': 735, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.34767.72.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '72.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '72.46', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 46, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 72, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3\\times D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 93302307
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 24, 'counter': 736, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.34767.72.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '72.a1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '72.46', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 46, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 72, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3\\times D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 93302308
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 216, 'characteristic': False, 'core_order': 24, 'counter': 737, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.34767.72.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '72.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '72.46', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 46, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 72, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3\\times D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '24.9', 'subgroup_hash': 9, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 93302309
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 216, 'characteristic': False, 'core_order': 24, 'counter': 738, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.34767.72.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '72.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '72.46', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 46, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 72, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3\\times D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '24.9', 'subgroup_hash': 9, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 93302310
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 24, 'counter': 739, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.34767.72.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '72.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '72.46', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 46, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 72, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3\\times D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '24.7', 'subgroup_hash': 7, 'subgroup_order': 24, 'subgroup_tex': 'C_6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 93302312
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 24, 'counter': 740, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.34767.72.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '72.c1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '72.46', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 46, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 72, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3\\times D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '24.7', 'subgroup_hash': 7, 'subgroup_order': 24, 'subgroup_tex': 'C_6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 93302313
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 432, 'characteristic': True, 'core_order': 24, 'counter': 741, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.34767.72.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '72.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '72.46', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 46, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 72, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3\\times D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '24.9', 'subgroup_hash': 9, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 93302314
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': True, 'core_order': 24, 'counter': 742, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.34767.72.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '72.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '72.46', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 46, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 72, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3\\times D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '24.7', 'subgroup_hash': 7, 'subgroup_order': 24, 'subgroup_tex': 'C_6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 93302315
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': True, 'core_order': 24, 'counter': 743, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.34767.72.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '72.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '72.46', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 46, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 72, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3\\times D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '24.7', 'subgroup_hash': 7, 'subgroup_order': 24, 'subgroup_tex': 'C_6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 93302316
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 12, 'counter': 744, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.72.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.15', 'subgroup_hash': 15, 'subgroup_order': 24, 'subgroup_tex': 'C_2^2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 93302317
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 12, 'counter': 745, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.72.g1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.g1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.15', 'subgroup_hash': 15, 'subgroup_order': 24, 'subgroup_tex': 'C_2^2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 93302318
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 12, 'counter': 746, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.72.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.15', 'subgroup_hash': 15, 'subgroup_order': 24, 'subgroup_tex': 'C_2^2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 93302319
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 12, 'counter': 747, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.72.h1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.h1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '24.15', 'subgroup_hash': 15, 'subgroup_order': 24, 'subgroup_tex': 'C_2^2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 93302320
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 4, 'counter': 748, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.72.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.15', 'subgroup_hash': 15, 'subgroup_order': 24, 'subgroup_tex': 'C_2^2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 93302321
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 4, 'counter': 749, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.72.i1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.i1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '24.15', 'subgroup_hash': 15, 'subgroup_order': 24, 'subgroup_tex': 'C_2^2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 93302323
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 12, 'counter': 750, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.72.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.9', 'subgroup_hash': 9, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 93302324
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 12, 'counter': 751, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.72.j1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.j1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.9', 'subgroup_hash': 9, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 93302325
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 12, 'counter': 752, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.72.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.9', 'subgroup_hash': 9, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 93302326
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 12, 'counter': 753, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.72.k1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.k1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.9', 'subgroup_hash': 9, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 93302327
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 12, 'counter': 754, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.72.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.l1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.9', 'subgroup_hash': 9, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 93302328
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 12, 'counter': 755, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.72.l1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.l1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.9', 'subgroup_hash': 9, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 93302329
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 12, 'counter': 756, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.72.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.m1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.7', 'subgroup_hash': 7, 'subgroup_order': 24, 'subgroup_tex': 'C_6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 93302330
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 12, 'counter': 757, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.72.m1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.m1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.7', 'subgroup_hash': 7, 'subgroup_order': 24, 'subgroup_tex': 'C_6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 93302331
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 12, 'counter': 758, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.72.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.n1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.7', 'subgroup_hash': 7, 'subgroup_order': 24, 'subgroup_tex': 'C_6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 93302332
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 12, 'counter': 759, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.72.n1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.n1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.7', 'subgroup_hash': 7, 'subgroup_order': 24, 'subgroup_tex': 'C_6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 93302334
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 12, 'counter': 760, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.72.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.o1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.9', 'subgroup_hash': 9, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 93302335
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 12, 'counter': 761, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.72.o1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.o1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.9', 'subgroup_hash': 9, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 93302336
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 12, 'counter': 762, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.72.p1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.p1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.7', 'subgroup_hash': 7, 'subgroup_order': 24, 'subgroup_tex': 'C_6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 93302337
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 12, 'counter': 763, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.72.p1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.p1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.7', 'subgroup_hash': 7, 'subgroup_order': 24, 'subgroup_tex': 'C_6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 93302338
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 12, 'counter': 764, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.72.q1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.q1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.9', 'subgroup_hash': 9, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 93302339
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 12, 'counter': 765, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.72.q1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.q1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '24.9', 'subgroup_hash': 9, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 93302340
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 12, 'counter': 766, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.72.r1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.r1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.7', 'subgroup_hash': 7, 'subgroup_order': 24, 'subgroup_tex': 'C_6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 93302341
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 12, 'counter': 767, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.72.r1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.r1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '24.7', 'subgroup_hash': 7, 'subgroup_order': 24, 'subgroup_tex': 'C_6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 93302342
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 12, 'counter': 768, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.72.s1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.s1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.7', 'subgroup_hash': 7, 'subgroup_order': 24, 'subgroup_tex': 'C_6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 93302343
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 12, 'counter': 769, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.72.s1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.s1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '24.7', 'subgroup_hash': 7, 'subgroup_order': 24, 'subgroup_tex': 'C_6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 93302345
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 12, 'counter': 770, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.72.t1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.t1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.7', 'subgroup_hash': 7, 'subgroup_order': 24, 'subgroup_tex': 'C_6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 93302346
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 12, 'counter': 771, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.72.t1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.t1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '24.7', 'subgroup_hash': 7, 'subgroup_order': 24, 'subgroup_tex': 'C_6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 93302347
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 12, 'counter': 772, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.72.u1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.u1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.9', 'subgroup_hash': 9, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 93302348
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 12, 'counter': 773, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.72.u1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.u1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '24.9', 'subgroup_hash': 9, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 93302349
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 12, 'counter': 774, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.72.v1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.v1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.9', 'subgroup_hash': 9, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 93302350
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 12, 'counter': 775, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.72.w1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.w1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.9', 'subgroup_hash': 9, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 93302351
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 12, 'counter': 776, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.72.x1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.x1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.7', 'subgroup_hash': 7, 'subgroup_order': 24, 'subgroup_tex': 'C_6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 93302352
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 12, 'counter': 777, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.72.x1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.x1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.7', 'subgroup_hash': 7, 'subgroup_order': 24, 'subgroup_tex': 'C_6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 93302353
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 12, 'counter': 778, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.72.y1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.y1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.7', 'subgroup_hash': 7, 'subgroup_order': 24, 'subgroup_tex': 'C_6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 93302354
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 12, 'counter': 779, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.72.y1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.y1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.7', 'subgroup_hash': 7, 'subgroup_order': 24, 'subgroup_tex': 'C_6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 93302356
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 12, 'counter': 780, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.72.z1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.z1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.7', 'subgroup_hash': 7, 'subgroup_order': 24, 'subgroup_tex': 'C_6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 93302357
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 12, 'counter': 781, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.72.ba1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ba1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.7', 'subgroup_hash': 7, 'subgroup_order': 24, 'subgroup_tex': 'C_6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 93302358
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 216, 'characteristic': False, 'core_order': 8, 'counter': 782, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.72.bb1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.bb1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.9', 'subgroup_hash': 9, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 93302359
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 216, 'characteristic': False, 'core_order': 8, 'counter': 783, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.72.bb1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.bb1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.9', 'subgroup_hash': 9, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 93302360
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 4, 'counter': 784, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.72.bc1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.bc1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.9', 'subgroup_hash': 9, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 93302361
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 4, 'counter': 785, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.72.bc1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.bc1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.9', 'subgroup_hash': 9, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 93302362
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 4, 'counter': 786, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.72.bd1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.bd1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.7', 'subgroup_hash': 7, 'subgroup_order': 24, 'subgroup_tex': 'C_6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 93302363
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 4, 'counter': 787, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.72.bd1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.bd1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '24.7', 'subgroup_hash': 7, 'subgroup_order': 24, 'subgroup_tex': 'C_6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 93302364
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 4, 'counter': 788, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.72.be1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.be1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.7', 'subgroup_hash': 7, 'subgroup_order': 24, 'subgroup_tex': 'C_6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 93302365
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 4, 'counter': 789, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.72.be1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.be1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '24.7', 'subgroup_hash': 7, 'subgroup_order': 24, 'subgroup_tex': 'C_6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 93302367
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 790, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.72.bf1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.bf1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.7', 'subgroup_hash': 7, 'subgroup_order': 24, 'subgroup_tex': 'C_6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 93302368
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 791, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.72.bf1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.bf1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.7', 'subgroup_hash': 7, 'subgroup_order': 24, 'subgroup_tex': 'C_6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 93302369
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 792, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.72.bg1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.bg1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.7', 'subgroup_hash': 7, 'subgroup_order': 24, 'subgroup_tex': 'C_6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 93302370
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 793, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.72.bg1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.bg1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.7', 'subgroup_hash': 7, 'subgroup_order': 24, 'subgroup_tex': 'C_6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 93302371
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 216, 'characteristic': False, 'core_order': 8, 'counter': 794, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.72.bh1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.bh1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.9', 'subgroup_hash': 9, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 93302372
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 4, 'counter': 795, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.72.bi1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.bi1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.9', 'subgroup_hash': 9, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 93302373
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 4, 'counter': 796, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.72.bj1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.bj1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.9', 'subgroup_hash': 9, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 93302374
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 4, 'counter': 797, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.72.bk1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.bk1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.7', 'subgroup_hash': 7, 'subgroup_order': 24, 'subgroup_tex': 'C_6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 93302375
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 4, 'counter': 798, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.72.bl1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.bl1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.7', 'subgroup_hash': 7, 'subgroup_order': 24, 'subgroup_tex': 'C_6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 93302376
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 799, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.72.bm1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.bm1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.7', 'subgroup_hash': 7, 'subgroup_order': 24, 'subgroup_tex': 'C_6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 93302379
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 800, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.72.bn1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.bn1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.7', 'subgroup_hash': 7, 'subgroup_order': 24, 'subgroup_tex': 'C_6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 93302380
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 216, 'characteristic': False, 'core_order': 8, 'counter': 801, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.72.bo1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.bo1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.9', 'subgroup_hash': 9, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 93302381
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 802, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.72.bp1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.bp1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.7', 'subgroup_hash': 7, 'subgroup_order': 24, 'subgroup_tex': 'C_6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 93302382
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 803, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.72.bq1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.bq1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.7', 'subgroup_hash': 7, 'subgroup_order': 24, 'subgroup_tex': 'C_6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 93302383
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 6, 'counter': 804, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.72.br1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.br1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.10', 'subgroup_hash': 10, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 93302384
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 6, 'counter': 805, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.72.br1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.br1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.10', 'subgroup_hash': 10, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 93302385
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 6, 'counter': 806, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.72.br1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.br1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '24.10', 'subgroup_hash': 10, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 93302386
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 6, 'counter': 807, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.72.br1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.br1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '24.10', 'subgroup_hash': 10, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 93302387
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 12, 'counter': 808, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.72.bs1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.bs1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.8', 'subgroup_hash': 8, 'subgroup_order': 24, 'subgroup_tex': 'C_3:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 93302388
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 12, 'counter': 809, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.72.bs1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.bs1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.8', 'subgroup_hash': 8, 'subgroup_order': 24, 'subgroup_tex': 'C_3:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 93302390
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 12, 'counter': 810, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.72.bs1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.bs1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '24.8', 'subgroup_hash': 8, 'subgroup_order': 24, 'subgroup_tex': 'C_3:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 93302391
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 12, 'counter': 811, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.72.bs1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.bs1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '24.8', 'subgroup_hash': 8, 'subgroup_order': 24, 'subgroup_tex': 'C_3:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 93302392
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 12, 'counter': 812, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.72.bs1.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.bs1.e1', 'outer_equivalence': False, 'perfect': False, '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': '24.8', 'subgroup_hash': 8, 'subgroup_order': 24, 'subgroup_tex': 'C_3:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 93302393
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 12, 'counter': 813, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.72.bs1.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.bs1.f1', 'outer_equivalence': False, 'perfect': False, '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': '24.8', 'subgroup_hash': 8, 'subgroup_order': 24, 'subgroup_tex': 'C_3:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 93302394
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 12, 'counter': 814, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.72.bs1.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.bs1.g1', 'outer_equivalence': False, 'perfect': False, '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': '24.8', 'subgroup_hash': 8, 'subgroup_order': 24, 'subgroup_tex': 'C_3:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 93302395
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 12, 'counter': 815, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.72.bs1.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.bs1.h1', 'outer_equivalence': False, 'perfect': False, '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': '24.8', 'subgroup_hash': 8, 'subgroup_order': 24, 'subgroup_tex': 'C_3:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 93302396
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 6, 'counter': 816, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.72.bt1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.bt1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.9', 'subgroup_hash': 9, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 93302397
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 6, 'counter': 817, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.72.bt1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.bt1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.9', 'subgroup_hash': 9, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 93302398
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 6, 'counter': 818, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.72.bu1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.bu1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.7', 'subgroup_hash': 7, 'subgroup_order': 24, 'subgroup_tex': 'C_6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 93302399
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 6, 'counter': 819, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.72.bu1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.bu1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.7', 'subgroup_hash': 7, 'subgroup_order': 24, 'subgroup_tex': 'C_6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 93302401
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 6, 'counter': 820, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.72.bv1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.bv1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.7', 'subgroup_hash': 7, 'subgroup_order': 24, 'subgroup_tex': 'C_6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 93302402
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 6, 'counter': 821, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.72.bv1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.bv1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.7', 'subgroup_hash': 7, 'subgroup_order': 24, 'subgroup_tex': 'C_6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 93302403
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 6, 'counter': 822, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.72.bw1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.bw1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.9', 'subgroup_hash': 9, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 93302404
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 6, 'counter': 823, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.72.bw1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.bw1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.9', 'subgroup_hash': 9, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 93302405
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 6, 'counter': 824, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.72.bx1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.bx1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.5', 'subgroup_hash': 5, 'subgroup_order': 24, 'subgroup_tex': 'C_4\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 93302406
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 6, 'counter': 825, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.72.bx1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.bx1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.5', 'subgroup_hash': 5, 'subgroup_order': 24, 'subgroup_tex': 'C_4\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 93302407
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 6, 'counter': 826, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.72.by1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.by1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.5', 'subgroup_hash': 5, 'subgroup_order': 24, 'subgroup_tex': 'C_4\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 93302408
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 6, 'counter': 827, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.72.by1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.by1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '24.5', 'subgroup_hash': 5, 'subgroup_order': 24, 'subgroup_tex': 'C_4\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 93302409
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 6, 'counter': 828, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.72.bz1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.bz1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.11', 'subgroup_hash': 11, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 93302410
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 6, 'counter': 829, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.72.bz1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.bz1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '24.11', 'subgroup_hash': 11, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 93302412
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 6, 'counter': 830, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.72.ca1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ca1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.4', 'subgroup_hash': 4, 'subgroup_order': 24, 'subgroup_tex': 'C_3:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 93302413
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 6, 'counter': 831, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.72.ca1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ca1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '24.4', 'subgroup_hash': 4, 'subgroup_order': 24, 'subgroup_tex': 'C_3:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 93302414
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 6, 'counter': 832, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.72.cb1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.cb1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.4', 'subgroup_hash': 4, 'subgroup_order': 24, 'subgroup_tex': 'C_3:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 93302415
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 6, 'counter': 833, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.72.cb1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.cb1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '24.4', 'subgroup_hash': 4, 'subgroup_order': 24, 'subgroup_tex': 'C_3:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 93302416
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 834, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.72.cc1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.cc1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.7', 'subgroup_hash': 7, 'subgroup_order': 24, 'subgroup_tex': 'C_6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 93302417
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 835, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.72.cc1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.cc1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '24.7', 'subgroup_hash': 7, 'subgroup_order': 24, 'subgroup_tex': 'C_6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 93302418
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 836, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.72.cc1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.cc1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '24.7', 'subgroup_hash': 7, 'subgroup_order': 24, 'subgroup_tex': 'C_6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 93302419
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 837, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.72.cc1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.cc1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '24.7', 'subgroup_hash': 7, 'subgroup_order': 24, 'subgroup_tex': 'C_6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 93302420
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 838, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.72.cd1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.cd1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.7', 'subgroup_hash': 7, 'subgroup_order': 24, 'subgroup_tex': 'C_6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 93302421
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 839, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.72.cd1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.cd1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.7', 'subgroup_hash': 7, 'subgroup_order': 24, 'subgroup_tex': 'C_6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 93302423
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 840, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.72.cd1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.cd1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '24.7', 'subgroup_hash': 7, 'subgroup_order': 24, 'subgroup_tex': 'C_6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 93302424
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 841, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.72.cd1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.cd1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '24.7', 'subgroup_hash': 7, 'subgroup_order': 24, 'subgroup_tex': 'C_6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 93302425
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 842, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.72.ce1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ce1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.7', 'subgroup_hash': 7, 'subgroup_order': 24, 'subgroup_tex': 'C_6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 93302426
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 843, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.72.ce1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ce1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.7', 'subgroup_hash': 7, 'subgroup_order': 24, 'subgroup_tex': 'C_6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 93302427
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 844, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.72.ce1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ce1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '24.7', 'subgroup_hash': 7, 'subgroup_order': 24, 'subgroup_tex': 'C_6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 93302428
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 845, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.72.ce1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ce1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '24.7', 'subgroup_hash': 7, 'subgroup_order': 24, 'subgroup_tex': 'C_6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 93302429
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 846, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.72.cf1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.cf1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.5', 'subgroup_hash': 5, 'subgroup_order': 24, 'subgroup_tex': 'C_4\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 93302430
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 847, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.72.cf1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.cf1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '24.5', 'subgroup_hash': 5, 'subgroup_order': 24, 'subgroup_tex': 'C_4\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 93302431
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 848, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.72.cf1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.cf1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '24.5', 'subgroup_hash': 5, 'subgroup_order': 24, 'subgroup_tex': 'C_4\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 93302432
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 849, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.72.cf1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.cf1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '24.5', 'subgroup_hash': 5, 'subgroup_order': 24, 'subgroup_tex': 'C_4\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 93302434
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 850, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.72.cg1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.cg1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.4', 'subgroup_hash': 4, 'subgroup_order': 24, 'subgroup_tex': 'C_3:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 93302435
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 851, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.72.cg1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.cg1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '24.4', 'subgroup_hash': 4, 'subgroup_order': 24, 'subgroup_tex': 'C_3:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 93302436
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 852, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.72.cg1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.cg1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '24.4', 'subgroup_hash': 4, 'subgroup_order': 24, 'subgroup_tex': 'C_3:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 93302437
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 853, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.72.cg1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.cg1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '24.4', 'subgroup_hash': 4, 'subgroup_order': 24, 'subgroup_tex': 'C_3:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 93302438
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 854, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.72.ch1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ch1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.4', 'subgroup_hash': 4, 'subgroup_order': 24, 'subgroup_tex': 'C_3:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 93302439
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 855, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.72.ch1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ch1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '24.4', 'subgroup_hash': 4, 'subgroup_order': 24, 'subgroup_tex': 'C_3:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 93302440
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 856, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.72.ci1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ci1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.4', 'subgroup_hash': 4, 'subgroup_order': 24, 'subgroup_tex': 'C_3:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 93302441
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 857, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.72.ci1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ci1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.4', 'subgroup_hash': 4, 'subgroup_order': 24, 'subgroup_tex': 'C_3:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 93302442
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 858, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.72.ci1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ci1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '24.4', 'subgroup_hash': 4, 'subgroup_order': 24, 'subgroup_tex': 'C_3:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 93302443
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 859, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.72.ci1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ci1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '24.4', 'subgroup_hash': 4, 'subgroup_order': 24, 'subgroup_tex': 'C_3:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 93302445
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 860, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.72.cj1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.cj1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.4', 'subgroup_hash': 4, 'subgroup_order': 24, 'subgroup_tex': 'C_3:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 93302446
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 861, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.72.cj1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.cj1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.4', 'subgroup_hash': 4, 'subgroup_order': 24, 'subgroup_tex': 'C_3:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 93302447
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 862, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.72.cj1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.cj1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '24.4', 'subgroup_hash': 4, 'subgroup_order': 24, 'subgroup_tex': 'C_3:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 93302448
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 863, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.72.cj1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.cj1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '24.4', 'subgroup_hash': 4, 'subgroup_order': 24, 'subgroup_tex': 'C_3:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 93302449
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 864, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.72.ck1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ck1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.4', 'subgroup_hash': 4, 'subgroup_order': 24, 'subgroup_tex': 'C_3:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 93302450
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 865, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.72.ck1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ck1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.4', 'subgroup_hash': 4, 'subgroup_order': 24, 'subgroup_tex': 'C_3:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 93302451
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 866, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.72.ck1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ck1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '24.4', 'subgroup_hash': 4, 'subgroup_order': 24, 'subgroup_tex': 'C_3:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 93302452
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 867, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.72.ck1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.ck1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '24.4', 'subgroup_hash': 4, 'subgroup_order': 24, 'subgroup_tex': 'C_3:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 93302453
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 432, 'characteristic': False, 'core_order': 18, 'counter': 868, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.34767.96.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '96.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '96.212', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 212, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 96, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'Q_8\\times D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 93302454
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 432, 'characteristic': False, 'core_order': 18, 'counter': 869, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.34767.96.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '96.a1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '96.212', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 212, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 96, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'Q_8\\times D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 93302456
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 432, 'characteristic': True, 'core_order': 18, 'counter': 870, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.34767.96.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '96.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '96.205', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 205, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 96, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6.C_2^4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 93302457
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 432, 'characteristic': False, 'core_order': 18, 'counter': 871, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.34767.96.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '96.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '96.211', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 211, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 96, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4:D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 93302458
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 432, 'characteristic': False, 'core_order': 18, 'counter': 872, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.34767.96.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '96.c1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '96.211', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 211, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 96, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4:D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 93302459
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 432, 'characteristic': True, 'core_order': 18, 'counter': 873, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.34767.96.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '96.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '96.211', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 211, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 96, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4:D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 93302460
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 432, 'characteristic': False, 'core_order': 18, 'counter': 874, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.34767.96.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '96.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '96.215', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 215, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 96, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4:D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 93302461
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 432, 'characteristic': False, 'core_order': 18, 'counter': 875, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.34767.96.e1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '96.e1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '96.215', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 215, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 96, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4:D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 93302462
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 432, 'characteristic': True, 'core_order': 18, 'counter': 876, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.34767.96.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '96.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '96.215', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 215, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 96, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4:D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 93302463
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 216, 'characteristic': False, 'core_order': 6, 'counter': 877, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.96.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': 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: 93302464
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 216, 'characteristic': False, 'core_order': 6, 'counter': 878, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.96.g1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.g1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': 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: 93302465
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 216, 'characteristic': False, 'core_order': 6, 'counter': 879, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.96.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': 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: 93302467
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 216, 'characteristic': False, 'core_order': 2, 'counter': 880, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.96.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': 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: 93302468
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 216, 'characteristic': False, 'core_order': 6, 'counter': 881, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.96.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': 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: 93302469
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 216, 'characteristic': False, 'core_order': 6, 'counter': 882, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.96.j1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.j1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': 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: 93302470
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 216, 'characteristic': False, 'core_order': 6, 'counter': 883, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.96.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': 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: 93302471
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 216, 'characteristic': False, 'core_order': 2, 'counter': 884, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.96.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.l1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': 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: 93302472
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 216, 'characteristic': False, 'core_order': 6, 'counter': 885, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.96.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.m1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': 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: 93302473
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 216, 'characteristic': False, 'core_order': 6, 'counter': 886, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.96.m1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.m1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': 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: 93302474
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 216, 'characteristic': False, 'core_order': 6, 'counter': 887, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.96.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.n1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': 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: 93302475
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 216, 'characteristic': False, 'core_order': 2, 'counter': 888, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.96.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.o1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': 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: 93302476
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 9, 'counter': 889, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.96.p1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.p1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': 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: 93302478
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 9, 'counter': 890, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.96.p1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.p1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': 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: 93302479
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 9, 'counter': 891, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.96.p1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.p1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': 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: 93302480
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 9, 'counter': 892, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.96.p1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.p1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': 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: 93302481
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 9, 'counter': 893, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.96.q1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.q1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': 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: 93302482
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 9, 'counter': 894, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.96.q1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.q1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': 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: 93302483
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 9, 'counter': 895, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.96.q1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.q1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': 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: 93302484
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 9, 'counter': 896, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.96.q1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.q1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': 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: 93302485
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 3, 'counter': 897, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.96.r1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.r1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': 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: 93302486
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 3, 'counter': 898, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.96.r1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.r1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': 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: 93302487
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 3, 'counter': 899, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.96.r1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.r1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': 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: 93302490
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 3, 'counter': 900, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.96.r1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.r1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': 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: 93302491
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 9, 'counter': 901, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.96.s1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.s1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': 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: 93302492
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 9, 'counter': 902, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.96.s1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.s1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': 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: 93302493
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 9, 'counter': 903, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.96.s1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.s1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': 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: 93302494
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 9, 'counter': 904, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.96.s1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '96.s1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': 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: 93302495
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 8, 'counter': 905, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.108.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 93302496
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 8, 'counter': 906, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.108.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.a1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 93302497
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 4, 'counter': 907, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.108.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 93302498
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 4, 'counter': 908, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.108.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 93302499
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 4, 'counter': 909, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.108.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 93302501
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 4, 'counter': 910, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.108.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.c1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 93302502
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 4, 'counter': 911, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.108.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 93302503
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 4, 'counter': 912, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.108.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.d1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 93302504
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 913, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.108.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 93302505
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 914, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.108.e1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.e1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 93302506
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 915, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.108.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 93302507
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 916, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.108.f1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.f1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 93302508
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 4, 'counter': 917, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.108.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 93302509
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 8, 'counter': 918, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.108.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.4', 'subgroup_hash': 4, 'subgroup_order': 16, 'subgroup_tex': 'C_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 93302510
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 8, 'counter': 919, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.108.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.2', 'subgroup_hash': 2, 'subgroup_order': 16, 'subgroup_tex': 'C_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 93302512
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 8, 'counter': 920, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.108.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.4', 'subgroup_hash': 4, 'subgroup_order': 16, 'subgroup_tex': 'C_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 93302513
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 8, 'counter': 921, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.108.j1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.j1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.4', 'subgroup_hash': 4, 'subgroup_order': 16, 'subgroup_tex': 'C_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 93302514
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 922, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.108.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.12', 'subgroup_hash': 12, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 93302515
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 4, 'counter': 923, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.108.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.l1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.4', 'subgroup_hash': 4, 'subgroup_order': 16, 'subgroup_tex': 'C_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 93302516
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 4, 'counter': 924, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.108.l1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.l1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.4', 'subgroup_hash': 4, 'subgroup_order': 16, 'subgroup_tex': 'C_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 93302517
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 925, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.108.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.m1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.2', 'subgroup_hash': 2, 'subgroup_order': 16, 'subgroup_tex': 'C_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 93302518
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 926, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.108.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.n1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.4', 'subgroup_hash': 4, 'subgroup_order': 16, 'subgroup_tex': 'C_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 93302519
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 4, 'counter': 927, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.108.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.o1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.12', 'subgroup_hash': 12, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 93302520
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 4, 'counter': 928, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.108.o1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.o1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.12', 'subgroup_hash': 12, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 93302521
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 929, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.108.p1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.p1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.4', 'subgroup_hash': 4, 'subgroup_order': 16, 'subgroup_tex': 'C_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 93302523
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 930, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.108.p1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.p1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.4', 'subgroup_hash': 4, 'subgroup_order': 16, 'subgroup_tex': 'C_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 93302524
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 931, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.108.q1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.q1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.4', 'subgroup_hash': 4, 'subgroup_order': 16, 'subgroup_tex': 'C_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 93302525
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 932, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.108.q1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.q1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '16.4', 'subgroup_hash': 4, 'subgroup_order': 16, 'subgroup_tex': 'C_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 93302526
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 4, 'counter': 933, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.108.r1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.r1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.4', 'subgroup_hash': 4, 'subgroup_order': 16, 'subgroup_tex': 'C_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 93302527
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 934, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.108.s1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.s1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.2', 'subgroup_hash': 2, 'subgroup_order': 16, 'subgroup_tex': 'C_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 93302528
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 935, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.108.t1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.t1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.4', 'subgroup_hash': 4, 'subgroup_order': 16, 'subgroup_tex': 'C_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 93302529
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 936, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.108.u1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.u1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.4', 'subgroup_hash': 4, 'subgroup_order': 16, 'subgroup_tex': 'C_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 93302530
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 937, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.108.v1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.v1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.4', 'subgroup_hash': 4, 'subgroup_order': 16, 'subgroup_tex': 'C_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 93302531
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 938, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.108.w1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.w1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.4', 'subgroup_hash': 4, 'subgroup_order': 16, 'subgroup_tex': 'C_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 93302532
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 939, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.108.w1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.w1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '16.4', 'subgroup_hash': 4, 'subgroup_order': 16, 'subgroup_tex': 'C_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 93302534
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 864, 'characteristic': False, 'core_order': 12, 'counter': 940, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.34767.144.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '144.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '144.192', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 192, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 144, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_6^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 93302535
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 864, 'characteristic': False, 'core_order': 12, 'counter': 941, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.34767.144.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '144.a1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '144.192', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 192, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 144, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_6^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 93302536
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 864, 'characteristic': True, 'core_order': 12, 'counter': 942, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.34767.144.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '144.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '144.192', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 192, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 144, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_6^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 93302537
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 12, 'counter': 943, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.34767.144.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '144.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '144.137', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 137, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 144, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{12}.D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 93302538
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 12, 'counter': 944, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.34767.144.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '144.c1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '144.137', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 137, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 144, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{12}.D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 93302539
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 12, 'counter': 945, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.34767.144.c1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '144.c1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '144.137', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 137, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 144, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{12}.D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 93302540
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 12, 'counter': 946, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.34767.144.c1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '144.c1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '144.137', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 137, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 144, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{12}.D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 93302541
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 432, 'characteristic': False, 'core_order': 4, 'counter': 947, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.144.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 93302542
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 432, 'characteristic': False, 'core_order': 4, 'counter': 948, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.144.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.d1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 93302543
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 432, 'characteristic': False, 'core_order': 4, 'counter': 949, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.144.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 93302545
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 216, 'characteristic': False, 'core_order': 4, 'counter': 950, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.144.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 93302546
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 6, 'counter': 951, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.144.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 93302547
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 6, 'counter': 952, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.144.g1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.g1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 93302548
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 6, 'counter': 953, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.144.g1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.g1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 93302549
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 6, 'counter': 954, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.144.g1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.g1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 93302550
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 6, 'counter': 955, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.144.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 93302551
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 6, 'counter': 956, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.144.h1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.h1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 93302552
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 6, 'counter': 957, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.144.h1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.h1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 93302553
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 6, 'counter': 958, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.144.h1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.h1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 93302554
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 2, 'counter': 959, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.144.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 93302556
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 2, 'counter': 960, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.144.i1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.i1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 93302557
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 2, 'counter': 961, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.144.i1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.i1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 93302558
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 2, 'counter': 962, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.144.i1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.i1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 93302559
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 6, 'counter': 963, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.144.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.1', 'subgroup_hash': 1, 'subgroup_order': 12, 'subgroup_tex': 'C_3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 93302560
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 6, 'counter': 964, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.144.j1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.j1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.1', 'subgroup_hash': 1, 'subgroup_order': 12, 'subgroup_tex': 'C_3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 93302561
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 6, 'counter': 965, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.144.j1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.j1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.1', 'subgroup_hash': 1, 'subgroup_order': 12, 'subgroup_tex': 'C_3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 93302562
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 6, 'counter': 966, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.144.j1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.j1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.1', 'subgroup_hash': 1, 'subgroup_order': 12, 'subgroup_tex': 'C_3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 93302563
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 6, 'counter': 967, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1728.34767.144.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 93302564
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 6, 'counter': 968, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1728.34767.144.k1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.k1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 93302565
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 2, 'counter': 969, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.144.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.l1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.1', 'subgroup_hash': 1, 'subgroup_order': 12, 'subgroup_tex': 'C_3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 93302567
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 2, 'counter': 970, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.144.l1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.l1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.1', 'subgroup_hash': 1, 'subgroup_order': 12, 'subgroup_tex': 'C_3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 93302568
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 6, 'counter': 971, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.144.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.m1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 93302569
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 6, 'counter': 972, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.144.m1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.m1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 93302570
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 6, 'counter': 973, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.144.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.n1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 93302571
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 6, 'counter': 974, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.144.n1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.n1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 93302572
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 2, 'counter': 975, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.144.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.o1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 93302573
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 2, 'counter': 976, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.144.o1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.o1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 93302574
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 6, 'counter': 977, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.144.p1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.p1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 93302575
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 6, 'counter': 978, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.144.p1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.p1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 93302576
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 6, 'counter': 979, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1728.34767.144.q1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.q1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 93302578
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 6, 'counter': 980, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1728.34767.144.q1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.q1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 93302579
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 6, 'counter': 981, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1728.34767.144.r1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.r1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 93302580
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 6, 'counter': 982, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1728.34767.144.r1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.r1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 93302581
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 6, 'counter': 983, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.144.s1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.s1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.1', 'subgroup_hash': 1, 'subgroup_order': 12, 'subgroup_tex': 'C_3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 93302582
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 6, 'counter': 984, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.144.s1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.s1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.1', 'subgroup_hash': 1, 'subgroup_order': 12, 'subgroup_tex': 'C_3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 93302583
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 6, 'counter': 985, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1728.34767.144.t1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.t1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 93302584
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 6, 'counter': 986, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1728.34767.144.t1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.t1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 93302585
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 6, 'counter': 987, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.144.u1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.u1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.1', 'subgroup_hash': 1, 'subgroup_order': 12, 'subgroup_tex': 'C_3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 93302586
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 6, 'counter': 988, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.144.u1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.u1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.1', 'subgroup_hash': 1, 'subgroup_order': 12, 'subgroup_tex': 'C_3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 93302587
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 6, 'counter': 989, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1728.34767.144.v1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.v1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 93302589
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 6, 'counter': 990, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1728.34767.144.v1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.v1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 93302590
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 6, 'counter': 991, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.144.w1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.w1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.1', 'subgroup_hash': 1, 'subgroup_order': 12, 'subgroup_tex': 'C_3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 93302591
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 6, 'counter': 992, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.144.w1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.w1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.1', 'subgroup_hash': 1, 'subgroup_order': 12, 'subgroup_tex': 'C_3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 93302592
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 6, 'counter': 993, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.144.x1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.x1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.1', 'subgroup_hash': 1, 'subgroup_order': 12, 'subgroup_tex': 'C_3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 93302593
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 6, 'counter': 994, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1728.34767.144.y1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.y1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 93302594
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 6, 'counter': 995, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1728.34767.144.y1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.y1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 93302595
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 6, 'counter': 996, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.144.z1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.z1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.1', 'subgroup_hash': 1, 'subgroup_order': 12, 'subgroup_tex': 'C_3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 93302596
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 6, 'counter': 997, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1728.34767.144.ba1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.ba1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 93302597
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 6, 'counter': 998, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.144.bb1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.bb1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.1', 'subgroup_hash': 1, 'subgroup_order': 12, 'subgroup_tex': 'C_3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 93302598
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 6, 'counter': 999, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.144.bb1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.bb1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.1', 'subgroup_hash': 1, 'subgroup_order': 12, 'subgroup_tex': 'C_3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 93301434
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 2, 'counter': 1000, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1728.34767.144.bc1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.bc1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 93301435
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 2, 'counter': 1001, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1728.34767.144.bc1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.bc1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 93301436
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 2, 'counter': 1002, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.144.bd1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.bd1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.1', 'subgroup_hash': 1, 'subgroup_order': 12, 'subgroup_tex': 'C_3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 93301437
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 2, 'counter': 1003, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.144.bd1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.bd1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.1', 'subgroup_hash': 1, 'subgroup_order': 12, 'subgroup_tex': 'C_3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 93301438
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 2, 'counter': 1004, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1728.34767.144.be1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.be1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 93301439
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 2, 'counter': 1005, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1728.34767.144.bf1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.bf1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 93301440
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 2, 'counter': 1006, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.144.bg1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.bg1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.1', 'subgroup_hash': 1, 'subgroup_order': 12, 'subgroup_tex': 'C_3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 93301441
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 6, 'counter': 1007, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.144.bh1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.bh1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 93301442
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 6, 'counter': 1008, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.144.bh1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.bh1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 93301443
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 6, 'counter': 1009, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.144.bi1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.bi1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 93301445
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 6, 'counter': 1010, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.144.bi1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.bi1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 93301446
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 2, 'counter': 1011, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.144.bj1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.bj1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 93301447
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 2, 'counter': 1012, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.144.bj1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.bj1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 93301448
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 6, 'counter': 1013, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.144.bk1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.bk1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 93301449
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 6, 'counter': 1014, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.144.bk1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.bk1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 93301450
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 216, 'characteristic': False, 'core_order': 6, 'counter': 1015, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1728.34767.144.bl1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.bl1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 93301451
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 216, 'characteristic': False, 'core_order': 6, 'counter': 1016, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1728.34767.144.bl1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.bl1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 93301452
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 6, 'counter': 1017, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1728.34767.144.bm1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.bm1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 93301453
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 6, 'counter': 1018, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1728.34767.144.bm1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.bm1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 93301454
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 6, 'counter': 1019, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.144.bn1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.bn1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.1', 'subgroup_hash': 1, 'subgroup_order': 12, 'subgroup_tex': 'C_3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 93301456
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 6, 'counter': 1020, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.144.bn1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.bn1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.1', 'subgroup_hash': 1, 'subgroup_order': 12, 'subgroup_tex': 'C_3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 93301457
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 6, 'counter': 1021, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.144.bo1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.bo1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.1', 'subgroup_hash': 1, 'subgroup_order': 12, 'subgroup_tex': 'C_3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 93301458
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 6, 'counter': 1022, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.144.bo1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.bo1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.1', 'subgroup_hash': 1, 'subgroup_order': 12, 'subgroup_tex': 'C_3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 93301459
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 6, 'counter': 1023, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.144.bo1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.bo1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.1', 'subgroup_hash': 1, 'subgroup_order': 12, 'subgroup_tex': 'C_3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 93301460
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 6, 'counter': 1024, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.144.bo1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.bo1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.1', 'subgroup_hash': 1, 'subgroup_order': 12, 'subgroup_tex': 'C_3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 93301461
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 1025, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.144.bp1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.bp1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.1', 'subgroup_hash': 1, 'subgroup_order': 12, 'subgroup_tex': 'C_3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 93301462
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 1026, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.144.bp1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.bp1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.1', 'subgroup_hash': 1, 'subgroup_order': 12, 'subgroup_tex': 'C_3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 93301463
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 432, 'characteristic': False, 'core_order': 6, 'counter': 1027, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1728.34767.144.bq1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.bq1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 93301464
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 6, 'counter': 1028, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.144.br1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.br1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.1', 'subgroup_hash': 1, 'subgroup_order': 12, 'subgroup_tex': 'C_3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 93301465
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 6, 'counter': 1029, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.144.br1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.br1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.1', 'subgroup_hash': 1, 'subgroup_order': 12, 'subgroup_tex': 'C_3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 93301467
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 6, 'counter': 1030, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.144.bs1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.bs1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.1', 'subgroup_hash': 1, 'subgroup_order': 12, 'subgroup_tex': 'C_3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 93301468
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 6, 'counter': 1031, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.144.bs1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.bs1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.1', 'subgroup_hash': 1, 'subgroup_order': 12, 'subgroup_tex': 'C_3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 93301469
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 1032, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.144.bt1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.bt1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.1', 'subgroup_hash': 1, 'subgroup_order': 12, 'subgroup_tex': 'C_3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 93301470
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 216, 'characteristic': False, 'core_order': 2, 'counter': 1033, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1728.34767.144.bu1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.bu1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 93301471
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 216, 'characteristic': False, 'core_order': 2, 'counter': 1034, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1728.34767.144.bu1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.bu1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 93301472
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 2, 'counter': 1035, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.144.bv1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.bv1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.1', 'subgroup_hash': 1, 'subgroup_order': 12, 'subgroup_tex': 'C_3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 93301473
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 2, 'counter': 1036, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.144.bv1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.bv1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.1', 'subgroup_hash': 1, 'subgroup_order': 12, 'subgroup_tex': 'C_3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 93301474
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 1037, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.144.bw1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.bw1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.1', 'subgroup_hash': 1, 'subgroup_order': 12, 'subgroup_tex': 'C_3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 93301475
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 1038, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.144.bw1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.bw1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.1', 'subgroup_hash': 1, 'subgroup_order': 12, 'subgroup_tex': 'C_3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 93301476
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 1039, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.144.bw1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.bw1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.1', 'subgroup_hash': 1, 'subgroup_order': 12, 'subgroup_tex': 'C_3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 93301478
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 1040, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.144.bw1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.bw1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.1', 'subgroup_hash': 1, 'subgroup_order': 12, 'subgroup_tex': 'C_3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 93301479
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 1041, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.144.bx1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.bx1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.1', 'subgroup_hash': 1, 'subgroup_order': 12, 'subgroup_tex': 'C_3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 93301480
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 1042, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.144.bx1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.bx1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.1', 'subgroup_hash': 1, 'subgroup_order': 12, 'subgroup_tex': 'C_3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 93301481
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 216, 'characteristic': False, 'core_order': 2, 'counter': 1043, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1728.34767.144.by1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.by1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 93301482
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 216, 'characteristic': False, 'core_order': 2, 'counter': 1044, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1728.34767.144.by1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.by1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 93301483
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 1045, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.144.bz1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.bz1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.1', 'subgroup_hash': 1, 'subgroup_order': 12, 'subgroup_tex': 'C_3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 93301484
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 1046, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.144.bz1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.bz1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.1', 'subgroup_hash': 1, 'subgroup_order': 12, 'subgroup_tex': 'C_3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 93301485
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 1047, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.144.ca1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.ca1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.1', 'subgroup_hash': 1, 'subgroup_order': 12, 'subgroup_tex': 'C_3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 93301486
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 1048, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.144.ca1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.ca1.a2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.1', 'subgroup_hash': 1, 'subgroup_order': 12, 'subgroup_tex': 'C_3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 93301487
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 216, 'characteristic': False, 'core_order': 2, 'counter': 1049, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1728.34767.144.cb1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.cb1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 93301489
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 216, 'characteristic': False, 'core_order': 2, 'counter': 1050, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1728.34767.144.cb1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.cb1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 93301490
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 1051, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.144.cc1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.cc1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.1', 'subgroup_hash': 1, 'subgroup_order': 12, 'subgroup_tex': 'C_3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 93301491
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 1052, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.144.cc1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.cc1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.1', 'subgroup_hash': 1, 'subgroup_order': 12, 'subgroup_tex': 'C_3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 93301492
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 1053, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.144.cd1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.cd1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.1', 'subgroup_hash': 1, 'subgroup_order': 12, 'subgroup_tex': 'C_3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 93301493
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 1054, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.144.cd1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '144.cd1.a2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.1', 'subgroup_hash': 1, 'subgroup_order': 12, 'subgroup_tex': 'C_3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 93301494
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 432, 'characteristic': False, 'core_order': 9, 'counter': 1055, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.34767.192.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '192.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '192.1195', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1195, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 192, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2.(Q_8\\times D_6)', 'simple': False, 'solvable': True, 'special_labels': ['C7'], '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: 93301495
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 432, 'characteristic': False, 'core_order': 9, 'counter': 1056, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.34767.192.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '192.a1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '192.1195', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1195, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 192, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2.(Q_8\\times D_6)', 'simple': False, 'solvable': True, 'special_labels': ['C7'], '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: 93301496
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 432, 'characteristic': True, 'core_order': 9, 'counter': 1057, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.34767.192.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '192.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '192.1098', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1098, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 192, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4^2.D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 93301497
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 216, 'characteristic': False, 'core_order': 3, 'counter': 1058, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.192.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': 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: 93301498
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 216, 'characteristic': False, 'core_order': 3, 'counter': 1059, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.192.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.c1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': 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: 93301500
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 216, 'characteristic': False, 'core_order': 3, 'counter': 1060, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.192.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': 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: 93301501
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 216, 'characteristic': False, 'core_order': 1, 'counter': 1061, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.192.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': 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: 93301502
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 432, 'characteristic': True, 'core_order': 8, 'counter': 1062, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.34767.216.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '216.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '216.162', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 162, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 216, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3^3', 'simple': False, 'solvable': True, 'special_labels': ['U0'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 93301503
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 288, 'characteristic': False, 'core_order': 4, 'counter': 1063, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.216.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 93301504
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 288, 'characteristic': False, 'core_order': 4, 'counter': 1064, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.216.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 93301505
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 288, 'characteristic': False, 'core_order': 4, 'counter': 1065, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.216.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 93301506
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 4, 'counter': 1066, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.216.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 93301507
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 4, 'counter': 1067, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.216.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.d1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 93301508
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 4, 'counter': 1068, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.216.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 93301509
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 4, 'counter': 1069, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.216.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 93301511
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 4, 'counter': 1070, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.216.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 93301512
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 4, 'counter': 1071, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.216.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 93301513
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 4, 'counter': 1072, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.216.h1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.h1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 93301514
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 4, 'counter': 1073, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.216.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 93301515
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 4, 'counter': 1074, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.216.i1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.i1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 93301516
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 1075, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.216.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 93301517
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 1076, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.216.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 93301518
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 2, 'counter': 1077, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.216.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.l1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 93301519
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 2, 'counter': 1078, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.216.l1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.l1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 93301520
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 2, 'counter': 1079, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.216.l1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.l1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 93301522
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 2, 'counter': 1080, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.216.l1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.l1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 93301523
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 2, 'counter': 1081, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.216.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.m1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 93301524
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 2, 'counter': 1082, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.216.m1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.m1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 93301525
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 2, 'counter': 1083, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.216.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.n1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 93301526
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 2, 'counter': 1084, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.216.n1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.n1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 93301527
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 2, 'counter': 1085, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.216.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.o1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.4', 'subgroup_hash': 4, 'subgroup_order': 8, 'subgroup_tex': 'Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 93301528
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 2, 'counter': 1086, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.216.o1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.o1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.4', 'subgroup_hash': 4, 'subgroup_order': 8, 'subgroup_tex': 'Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 93301529
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 1087, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.216.p1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.p1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 93301530
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 1088, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.216.p1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.p1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 93301531
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 1089, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.216.p1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.p1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 93301533
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 1090, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.216.p1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.p1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 93301534
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 1091, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.216.q1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.q1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.4', 'subgroup_hash': 4, 'subgroup_order': 8, 'subgroup_tex': 'Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 93301535
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 1092, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.216.q1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.q1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.4', 'subgroup_hash': 4, 'subgroup_order': 8, 'subgroup_tex': 'Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 93301536
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 864, 'characteristic': False, 'core_order': 6, 'counter': 1093, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '1728.34767.288.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '288.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '288.942', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 942, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 288, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2.D_6^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 93301537
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 864, 'characteristic': False, 'core_order': 6, 'counter': 1094, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '1728.34767.288.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '288.a1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '288.942', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 942, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 288, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2.D_6^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 93301538
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 864, 'characteristic': True, 'core_order': 6, 'counter': 1095, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '1728.34767.288.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '288.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '288.965', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 965, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 288, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'Q_8\\times S_3^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 93301539
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 864, 'characteristic': False, 'core_order': 6, 'counter': 1096, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '1728.34767.288.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '288.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '288.961', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 961, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 288, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_{12}:D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 93301540
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 864, 'characteristic': False, 'core_order': 6, 'counter': 1097, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '1728.34767.288.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '288.c1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '288.961', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 961, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 288, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_{12}:D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 93301541
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 864, 'characteristic': True, 'core_order': 6, 'counter': 1098, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '1728.34767.288.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '288.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '288.961', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 961, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 288, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_{12}:D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 93301542
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 864, 'characteristic': False, 'core_order': 6, 'counter': 1099, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '1728.34767.288.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '288.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '288.960', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 960, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 288, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4:S_3^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 93301545
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 864, 'characteristic': False, 'core_order': 6, 'counter': 1100, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '1728.34767.288.e1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '288.e1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '288.960', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 960, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 288, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4:S_3^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 93301546
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 864, 'characteristic': True, 'core_order': 6, 'counter': 1101, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '1728.34767.288.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '288.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '288.954', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 954, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 288, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_{12}:D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 93301547
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 432, 'characteristic': False, 'core_order': 2, 'counter': 1102, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1728.34767.288.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '288.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': 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: 93301548
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 432, 'characteristic': False, 'core_order': 2, 'counter': 1103, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1728.34767.288.g1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '288.g1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': 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: 93301549
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 432, 'characteristic': False, 'core_order': 2, 'counter': 1104, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1728.34767.288.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '288.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': 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: 93301550
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 216, 'characteristic': False, 'core_order': 2, 'counter': 1105, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1728.34767.288.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '288.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': 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: 93301551
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 432, 'characteristic': False, 'core_order': 2, 'counter': 1106, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1728.34767.288.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '288.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': 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: 93301552
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 432, 'characteristic': False, 'core_order': 2, 'counter': 1107, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1728.34767.288.j1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '288.j1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': 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: 93301553
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 432, 'characteristic': False, 'core_order': 2, 'counter': 1108, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1728.34767.288.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '288.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': 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: 93301554
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 216, 'characteristic': False, 'core_order': 2, 'counter': 1109, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1728.34767.288.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '288.l1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': 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: 93301556
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 432, 'characteristic': False, 'core_order': 2, 'counter': 1110, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1728.34767.288.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '288.m1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': 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: 93301557
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 432, 'characteristic': False, 'core_order': 2, 'counter': 1111, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1728.34767.288.m1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '288.m1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': 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: 93301558
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 432, 'characteristic': False, 'core_order': 2, 'counter': 1112, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1728.34767.288.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '288.n1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': 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: 93301559
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 216, 'characteristic': False, 'core_order': 2, 'counter': 1113, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1728.34767.288.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '288.o1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': 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: 93301560
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 3, 'counter': 1114, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1728.34767.288.p1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '288.p1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': 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: 93301561
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 3, 'counter': 1115, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1728.34767.288.p1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '288.p1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': 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: 93301562
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 3, 'counter': 1116, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1728.34767.288.p1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '288.p1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': 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: 93301563
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 3, 'counter': 1117, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1728.34767.288.p1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '288.p1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': 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: 93301564
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 3, 'counter': 1118, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1728.34767.288.q1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '288.q1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': 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: 93301565
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 3, 'counter': 1119, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1728.34767.288.q1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '288.q1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': 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: 93301567
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 3, 'counter': 1120, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1728.34767.288.q1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '288.q1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': 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: 93301568
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 3, 'counter': 1121, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1728.34767.288.q1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '288.q1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': 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: 93301569
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 1, 'counter': 1122, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1728.34767.288.r1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '288.r1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': 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: 93301570
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 1, 'counter': 1123, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1728.34767.288.r1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '288.r1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': 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: 93301571
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 1, 'counter': 1124, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1728.34767.288.r1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '288.r1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': 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: 93301572
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 1, 'counter': 1125, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1728.34767.288.r1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '288.r1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': 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: 93301573
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 3, 'counter': 1126, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.288.s1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.s1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': 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: 93301574
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 3, 'counter': 1127, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.288.s1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.s1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': 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: 93301575
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 3, 'counter': 1128, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.288.s1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.s1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': 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: 93301576
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 3, 'counter': 1129, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.288.s1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '288.s1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 288, 'quotient_simple': 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: 93301578
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': True, 'central_factor': False, 'centralizer_order': 1728, 'characteristic': True, 'core_order': 4, 'counter': 1130, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.34767.432.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '432.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '432.759', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 759, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 432, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times S_3^3', 'simple': False, 'solvable': True, 'special_labels': ['Z', 'Phi', 'U1'], 'split': False, 'standard_generators': False, 'stem': True, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 93301579
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 288, 'characteristic': False, 'core_order': 2, 'counter': 1131, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.432.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': 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: 93301580
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 288, 'characteristic': False, 'core_order': 2, 'counter': 1132, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.432.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': 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: 93301581
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 288, 'characteristic': False, 'core_order': 2, 'counter': 1133, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.432.b1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.b1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': 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: 93301582
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 288, 'characteristic': False, 'core_order': 2, 'counter': 1134, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.432.b1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.b1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': 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: 93301583
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 2, 'counter': 1135, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1728.34767.432.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 93301584
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 2, 'counter': 1136, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1728.34767.432.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.c1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': 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: 93301585
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 288, 'characteristic': False, 'core_order': 2, 'counter': 1137, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.432.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 93301586
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 288, 'characteristic': False, 'core_order': 2, 'counter': 1138, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.432.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.d1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': 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: 93301587
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 288, 'characteristic': False, 'core_order': 2, 'counter': 1139, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1728.34767.432.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 93301589
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 2, 'counter': 1140, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1728.34767.432.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 93301590
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 2, 'counter': 1141, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1728.34767.432.f1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.f1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': 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: 93301591
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 2, 'counter': 1142, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1728.34767.432.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 93301592
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 2, 'counter': 1143, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1728.34767.432.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 93301593
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 2, 'counter': 1144, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1728.34767.432.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 93301594
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 2, 'counter': 1145, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1728.34767.432.i1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.i1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': 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: 93301595
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 288, 'characteristic': False, 'core_order': 2, 'counter': 1146, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.432.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 93301596
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 288, 'characteristic': False, 'core_order': 2, 'counter': 1147, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1728.34767.432.j1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.j1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': 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: 93301597
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 432, 'characteristic': False, 'core_order': 2, 'counter': 1148, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1728.34767.432.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 93301598
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 2, 'counter': 1149, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1728.34767.432.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.l1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 93301600
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 2, 'counter': 1150, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1728.34767.432.l1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.l1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': 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: 93301601
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 1151, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1728.34767.432.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.m1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 93301602
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 1152, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1728.34767.432.m1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.m1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': 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: 93301603
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 1153, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1728.34767.432.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.n1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': 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: 93301604
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 864, 'characteristic': False, 'core_order': 3, 'counter': 1154, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '1728.34767.576.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '576.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '576.6038', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 6038, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 576, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2.D_6^2', 'simple': True, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '3.1', 'subgroup_hash': 1, 'subgroup_order': 3, 'subgroup_tex': 'C_3', 'supersolvable': True, 'sylow': 0}
  • id: 93301605
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 864, 'characteristic': False, 'core_order': 3, 'counter': 1155, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '1728.34767.576.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '576.a1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '576.6038', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 6038, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 576, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2.D_6^2', 'simple': True, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '3.1', 'subgroup_hash': 1, 'subgroup_order': 3, 'subgroup_tex': 'C_3', 'supersolvable': True, 'sylow': 0}
  • id: 93301606
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 864, 'characteristic': True, 'core_order': 3, 'counter': 1156, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '1728.34767.576.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '576.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '576.6416', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 6416, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 576, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2.D_6^2', 'simple': True, 'solvable': True, 'special_labels': ['C8'], '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: 93301607
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 432, 'characteristic': False, 'core_order': 1, 'counter': 1157, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1728.34767.576.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '576.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, '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: 93301608
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 432, 'characteristic': False, 'core_order': 1, 'counter': 1158, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1728.34767.576.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '576.c1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, '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: 93301609
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 432, 'characteristic': False, 'core_order': 1, 'counter': 1159, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1728.34767.576.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '576.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, '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: 93301611
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 216, 'characteristic': False, 'core_order': 1, 'counter': 1160, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1728.34767.576.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '576.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 576, '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: 93301612
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': True, 'central_factor': False, 'centralizer_order': 1728, 'characteristic': True, 'core_order': 2, 'counter': 1161, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '1728.34767.864.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '864.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '864.4337', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4337, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 864, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4.S_3^3', 'simple': True, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': True, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
  • id: 93301613
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': True, 'central_factor': False, 'centralizer_order': 1728, 'characteristic': True, 'core_order': 2, 'counter': 1162, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '1728.34767.864.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '864.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '864.4349', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4349, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 864, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_{12}:S_3^2', 'simple': True, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': True, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
  • id: 93301614
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': True, 'central_factor': False, 'centralizer_order': 1728, 'characteristic': True, 'core_order': 2, 'counter': 1163, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '1728.34767.864.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '864.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '864.4378', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4378, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 864, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6.D_6^2', 'simple': True, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': True, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
  • id: 93301615
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 288, 'characteristic': False, 'core_order': 1, 'counter': 1164, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1728.34767.864.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, '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: 93301616
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 288, 'characteristic': False, 'core_order': 1, 'counter': 1165, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1728.34767.864.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.d1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, '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: 93301617
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 288, 'characteristic': False, 'core_order': 1, 'counter': 1166, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1728.34767.864.d1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.d1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, '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: 93301618
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 288, 'characteristic': False, 'core_order': 1, 'counter': 1167, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1728.34767.864.d1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '864.d1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 864, '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: 93301619
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1728.34767', 'ambient_counter': 34767, 'ambient_order': 1728, 'ambient_tex': '(C_2\\times C_4).S_3^3', 'central': True, 'central_factor': False, 'centralizer_order': 1728, 'characteristic': True, 'core_order': 1, 'counter': 1168, 'cyclic': True, 'direct': True, 'hall': 1, 'label': '1728.34767.1728.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '1728.a1.a1', 'outer_equivalence': False, 'perfect': True, 'proper': False, 'quotient': '1728.34767', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 34767, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 1728, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': '(C_2\\times C_4).S_3^3', 'simple': False, 'solvable': True, 'special_labels': ['PC', 'U2', 'D2', 'C9'], '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: 93301431
    {'ambient': '1728.34767', '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': '432.a1.a1', 'complements': ['1728.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': [], 'contains': ['2.a1.a1', '2.a1.b1', '2.b1.a1', '2.b1.b1', '2.c1.a1', '2.c1.b1', '2.d1.a1', '2.d1.b1', '2.e1.a1', '2.f1.a1', '2.g1.a1', '2.h1.a1', '2.i1.a1', '2.j1.a1', '2.k1.a1', '3.a1.a1', '3.a1.b1', '3.b1.a1'], 'core': '1.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [1, 576, 936, 864, 6, 432, 48, 4, 36], 'label': '1728.34767.1.a1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1.a1', 'normal_contained_in': [], 'normal_contains': ['2.a1.b1', '2.a1.a1', '2.b1.b1', '2.b1.a1', '2.c1.b1', '2.c1.a1', '2.d1.b1', '2.d1.a1', '2.e1.a1', '2.f1.a1', '2.g1.a1', '2.h1.a1', '2.i1.a1', '2.j1.a1', '2.k1.a1'], 'normalizer': '1.a1.a1', 'old_label': '1.a1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1.a1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301432
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '2.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1', '4.a1.b1', '4.c1.a1', '4.c1.b1', '4.g1.a1', '4.i1.a1', '4.r1.a1', '6.b1.a1', '6.o1.a1', '6.o1.b1'], 'core': '2.e1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [1, 936, 864, 6, 576, 48, 4, 432], 'label': '1728.34767.2.e1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.a1.b1', '4.a1.a1', '4.c1.b1', '4.c1.a1', '4.g1.a1', '4.i1.a1', '4.r1.a1', '6.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.e1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2.e1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301433
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '6.z1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.j1.a1', '3.b1.a1'], 'contains': ['12.l1.a1', '12.cc1.a1', '12.cc1.b1', '12.cd1.a1', '12.ch1.a1', '12.ch1.b1', '12.cl1.a1', '18.v1.a1', '18.v1.b1'], 'core': '12.l1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [433, 4, 864, 438, 48, 36, 72], 'label': '1728.34767.6.z1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.j1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '6.z1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.z1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301434
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '144.bc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.p1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.r1.a1', '48.x1.b1', '72.bc1.a1'], 'contains': ['288.j1.a1', '432.f1.a1'], 'core': '864.b1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [433, 1200, 72], 'label': '1728.34767.144.bc1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bl1.a1', 'old_label': '144.bc1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.bc1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301435
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '144.bc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.p1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.r1.b1', '48.x1.a1', '72.bc1.b1'], 'contains': ['288.j1.b1', '432.f1.b1'], 'core': '864.b1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [438, 1156, 72], 'label': '1728.34767.144.bc1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.d1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bl1.b1', 'old_label': '144.bc1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.bc1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301436
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '144.bd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.w1.a1', '48.y1.b1', '72.bd1.a1'], 'contains': ['288.j1.a1', '432.i1.a1'], 'core': '864.b1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [42, 72, 1200], 'label': '1728.34767.144.bd1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bv1.b1', 'old_label': '144.bd1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.bd1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301437
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '144.bd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.w1.b1', '48.y1.a1', '72.bd1.b1'], 'contains': ['288.j1.b1', '432.i1.b1'], 'core': '864.b1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [37, 72, 1156], 'label': '1728.34767.144.bd1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.g1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bv1.a1', 'old_label': '144.bd1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.bd1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301438
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '144.be1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.bc1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.z1.a1', '48.be1.a1', '72.bi1.a1'], 'contains': ['288.k1.a1', '432.e1.a1'], 'core': '864.b1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [36, 100, 72], 'label': '1728.34767.144.be1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.cd1.a1', 'old_label': '144.be1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.be1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301439
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '144.bf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.bd1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.bb1.a1', '48.bf1.a1', '72.bj1.a1'], 'contains': ['288.k1.a1', '432.g1.a1'], 'core': '864.b1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [468, 100, 72], 'label': '1728.34767.144.bf1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.ci1.a1', 'old_label': '144.bf1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.bf1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301440
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '144.bg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.bc1.a1', '48.bg1.a1', '72.bl1.a1'], 'contains': ['288.k1.a1', '432.h1.a1'], 'core': '864.b1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [439, 72, 100], 'label': '1728.34767.144.bg1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.l1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.co1.a1', 'old_label': '144.bg1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.bg1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301441
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '144.bh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12.n1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.bh1.a1', '48.bk1.a1', '72.g1.a1', '72.cc1.a1', '72.cc1.b1'], 'contains': ['288.e1.b1', '288.p1.a1', '288.p1.b1', '432.j1.a1'], 'core': '288.e1.b1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [6, 864, 4], 'label': '1728.34767.144.bh1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.e1.a1', 'old_label': '144.bh1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.bh1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301442
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '144.bh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12.n1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.bh1.b1', '48.bk1.b1', '72.g1.b1', '72.cc1.c1', '72.cc1.d1'], 'contains': ['288.e1.a1', '288.p1.c1', '288.p1.d1', '432.j1.b1'], 'core': '288.e1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [1, 864, 48], 'label': '1728.34767.144.bh1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.e1.b1', 'old_label': '144.bh1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.bh1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301443
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '144.bi1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12.o1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.bh1.a1', '48.bi1.a1', '72.h1.a1', '72.cd1.a1', '72.cd1.b1'], 'contains': ['288.f1.a1', '288.q1.a1', '288.q1.b1', '432.j1.a1'], 'core': '288.f1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [6, 864, 576], 'label': '1728.34767.144.bi1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.e1.a1', 'old_label': '144.bi1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.bi1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301444
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '6.ba1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.k1.a1', '3.b1.a1'], 'contains': ['12.l1.a1', '12.cf1.a1', '12.cf1.b1', '12.cg1.a1', '12.cg1.b1', '12.ci1.a1', '12.ck1.a1', '18.w1.a1', '18.w1.b1'], 'core': '12.l1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [433, 4, 864, 438, 48, 468, 72], 'label': '1728.34767.6.ba1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.k1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '6.ba1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.ba1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301445
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '144.bi1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12.o1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.bh1.b1', '48.bi1.b1', '72.h1.b1', '72.cd1.c1', '72.cd1.d1'], 'contains': ['288.f1.a1', '288.q1.c1', '288.q1.d1', '432.j1.b1'], 'core': '288.f1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [1, 864, 576], 'label': '1728.34767.144.bi1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.e1.b1', 'old_label': '144.bi1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.bi1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301446
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '144.bj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.n1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.bh1.a1', '48.bj1.a1', '72.i1.a1', '72.ce1.a1', '72.ce1.b1'], 'contains': ['288.m1.b1', '288.r1.a1', '288.r1.b1', '432.j1.a1'], 'core': '864.c1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [6, 864, 1156], 'label': '1728.34767.144.bj1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.r1.a1', 'old_label': '144.bj1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.bj1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301447
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '144.bj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.n1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.bh1.b1', '48.bj1.b1', '72.i1.b1', '72.ce1.c1', '72.ce1.d1'], 'contains': ['288.m1.a1', '288.r1.c1', '288.r1.d1', '432.j1.b1'], 'core': '864.c1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [1, 864, 1200], 'label': '1728.34767.144.bj1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.r1.b1', 'old_label': '144.bj1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.bj1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301448
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '144.bk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12.i1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.bi1.a1', '48.bj1.a1', '48.bk1.a1', '72.a1.a1', '72.cf1.a1', '72.cf1.b1'], 'contains': ['288.e1.a1', '288.s1.a1', '288.s1.b1', '432.j1.a1'], 'core': '288.e1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [6, 864, 48], 'label': '1728.34767.144.bk1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '72.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '144.bk1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.bk1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301449
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '144.bk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.bi1.b1', '48.bj1.b1', '48.bk1.b1', '72.a1.b1', '72.cf1.c1', '72.cf1.d1'], 'contains': ['288.e1.b1', '288.s1.c1', '288.s1.d1', '432.j1.b1'], 'core': '288.e1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [1, 864, 4], 'label': '1728.34767.144.bk1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '72.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.b1', 'old_label': '144.bk1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.bk1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301450
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '144.bl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.bl1.a1', '48.bq1.a1', '48.bu1.a1', '72.b1.a1', '72.cg1.a1', '72.cg1.b1'], 'contains': ['288.e1.a1', '432.k1.a1'], 'core': '288.e1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [432, 48, 864], 'label': '1728.34767.144.bl1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '72.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.h1.a1', 'old_label': '144.bl1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.bl1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301451
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '144.bl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.bl1.b1', '48.bq1.b1', '48.bu1.a1', '72.b1.b1', '72.cg1.c1', '72.cg1.d1'], 'contains': ['288.e1.b1', '432.k1.a1'], 'core': '288.e1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [432, 4, 864], 'label': '1728.34767.144.bl1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '72.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.h1.a1', 'old_label': '144.bl1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.bl1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301452
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '144.bm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.q1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.bm1.a1', '48.br1.a1', '48.bv1.a1', '72.q1.a1', '72.cf1.a1', '72.cf1.b1'], 'contains': ['288.e1.a1', '432.l1.a1'], 'core': '288.e1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [469, 48, 864], 'label': '1728.34767.144.bm1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.i1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.o1.a1', 'old_label': '144.bm1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.bm1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301453
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '144.bm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.q1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.bm1.b1', '48.br1.b1', '48.bv1.b1', '72.q1.b1', '72.cf1.c1', '72.cf1.d1'], 'contains': ['288.e1.b1', '432.l1.b1'], 'core': '288.e1.b1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [474, 4, 864], 'label': '1728.34767.144.bm1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.i1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.o1.b1', 'old_label': '144.bm1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.bm1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301454
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '144.bn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.bn1.a1', '48.bv1.b1', '72.r1.a1', '72.cc1.c1', '72.cc1.d1'], 'contains': ['288.e1.a1', '432.l1.b1'], 'core': '288.e1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [474, 864, 48], 'label': '1728.34767.144.bn1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.h1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.m1.b1', 'old_label': '144.bn1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.bn1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301455
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '6.bb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.h1.a1'], 'contains': ['12.cn1.a1', '12.co1.a1', '12.cp1.a1', '12.cq1.a1', '12.cr1.a1', '12.cs1.a1', '12.ct1.a1', '18.x1.a1', '18.bb1.a1'], 'core': '36.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [7, 100, 864, 36, 576, 432, 936], 'label': '1728.34767.6.bb1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.h1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.bb1.a1', 'old_label': '6.bb1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.bb1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301456
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '144.bn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.bn1.b1', '48.bv1.a1', '72.r1.b1', '72.cc1.a1', '72.cc1.b1'], 'contains': ['288.e1.b1', '432.l1.a1'], 'core': '288.e1.b1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [469, 864, 4], 'label': '1728.34767.144.bn1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.h1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.m1.a1', 'old_label': '144.bn1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.bn1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301457
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '144.bo1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '108.d1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.bo1.a1', '48.bs1.a1', '48.bw1.a1', '72.s1.a1', '72.cc1.c1', '72.cf1.a1', '72.cg1.a1'], 'contains': ['288.e1.a1', '432.m1.a1'], 'core': '288.e1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [1411, 864, 48], 'label': '1728.34767.144.bo1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '16.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1.b1', 'old_label': '144.bo1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.bo1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301458
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '144.bo1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '108.d1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.bo1.b1', '48.bs1.b1', '48.bw1.b1', '72.s1.a1', '72.cc1.d1', '72.cf1.b1', '72.cg1.b1'], 'contains': ['288.e1.a1', '432.m1.b1'], 'core': '288.e1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [475, 864, 48], 'label': '1728.34767.144.bo1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '16.d1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1.b1', 'old_label': '144.bo1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.bo1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301459
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '144.bo1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '108.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.bo1.c1', '48.bs1.c1', '48.bw1.a1', '72.s1.b1', '72.cc1.a1', '72.cf1.c1', '72.cg1.c1'], 'contains': ['288.e1.b1', '432.m1.a1'], 'core': '288.e1.b1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [1411, 864, 4], 'label': '1728.34767.144.bo1.c1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '16.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1.a1', 'old_label': '144.bo1.c1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.bo1.c1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301460
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '144.bo1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '108.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.bo1.d1', '48.bs1.d1', '48.bw1.b1', '72.s1.b1', '72.cc1.b1', '72.cf1.d1', '72.cg1.d1'], 'contains': ['288.e1.b1', '432.m1.b1'], 'core': '288.e1.b1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [475, 864, 4], 'label': '1728.34767.144.bo1.d1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '16.d1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1.a1', 'old_label': '144.bo1.d1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.bo1.d1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301461
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '144.bp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.bp1.a1', '48.bt1.a1', '48.bx1.a1', '72.t1.a1', '72.cg1.a1', '72.cg1.b1'], 'contains': ['288.e1.a1', '432.n1.a1'], 'core': '288.e1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [43, 864, 48], 'label': '1728.34767.144.bp1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.k1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.t1.a1', 'old_label': '144.bp1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.bp1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301462
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '144.bp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.bp1.b1', '48.bt1.b1', '48.bx1.a1', '72.t1.b1', '72.cg1.c1', '72.cg1.d1'], 'contains': ['288.e1.b1', '432.n1.a1'], 'core': '288.e1.b1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [43, 864, 4], 'label': '1728.34767.144.bp1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.k1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.t1.b1', 'old_label': '144.bp1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.bp1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301463
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '144.bq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.bl1.a1', '48.bl1.b1', '48.by1.a1', '48.by1.b1', '72.d1.a1', '72.ch1.a1', '72.ch1.b1'], 'contains': ['288.f1.a1', '432.k1.a1'], 'core': '288.f1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [432, 576, 864], 'label': '1728.34767.144.bq1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '72.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.h1.a1', 'old_label': '144.bq1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.bq1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301464
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '144.br1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.bm1.a1', '48.bn1.b1', '72.y1.a1', '72.cd1.a1', '72.cd1.b1'], 'contains': ['288.f1.a1', '432.l1.a1'], 'core': '288.f1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [469, 864, 576], 'label': '1728.34767.144.br1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.h1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.h1.a1', 'old_label': '144.br1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.br1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301465
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '144.br1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.bm1.b1', '48.bn1.a1', '72.y1.b1', '72.cd1.c1', '72.cd1.d1'], 'contains': ['288.f1.a1', '432.l1.b1'], 'core': '288.f1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [474, 864, 576], 'label': '1728.34767.144.br1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.h1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.h1.b1', 'old_label': '144.br1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.br1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301466
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '8.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.a1.b1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '4.b1.a1', '4.c1.a1', '4.d1.a1', '4.e1.a1', '4.f1.a1', '4.g1.a1'], 'contains': ['16.a1.a1', '16.b1.a1', '16.b1.b1', '16.e1.a1', '16.k1.a1', '24.a1.a1', '24.b1.a1', '24.n1.a1', '24.o1.a1'], 'core': '8.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [6, 48, 576, 936, 864, 4], 'label': '1728.34767.8.a1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1.a1', 'normal_contained_in': ['4.a1.a1', '4.b1.a1', '4.c1.a1', '4.d1.a1', '4.f1.a1', '4.e1.a1', '4.g1.a1'], 'normal_contains': ['16.a1.a1', '16.b1.a1', '16.b1.b1', '24.a1.a1', '24.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.a1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.a1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301467
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '144.bs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '108.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.bo1.a1', '48.bo1.c1', '48.bz1.a1', '72.z1.a1', '72.cd1.a1', '72.cd1.c1', '72.ch1.a1'], 'contains': ['288.f1.a1', '432.m1.a1'], 'core': '288.f1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [1411, 864, 576], 'label': '1728.34767.144.bs1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '16.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '144.bs1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.bs1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301468
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '144.bs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '108.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.bo1.b1', '48.bo1.d1', '48.bz1.b1', '72.z1.a1', '72.cd1.b1', '72.cd1.d1', '72.ch1.b1'], 'contains': ['288.f1.a1', '432.m1.b1'], 'core': '288.f1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [475, 864, 576], 'label': '1728.34767.144.bs1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '16.d1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '144.bs1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.bs1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301469
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '144.bt1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.bp1.a1', '48.bp1.b1', '48.ca1.a1', '48.ca1.a2', '72.ba1.a1', '72.ch1.a1', '72.ch1.b1'], 'contains': ['288.f1.a1', '432.n1.a1'], 'core': '288.f1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [43, 864, 576], 'label': '1728.34767.144.bt1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.k1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.x1.a1', 'old_label': '144.bt1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.bt1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301470
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '144.bu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.bl1.a1', '48.bq1.b1', '48.cb1.a1', '48.cb1.b1', '72.bb1.a1', '72.ci1.a1', '72.ci1.b1'], 'contains': ['288.m1.a1', '432.k1.a1'], 'core': '864.c1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [432, 1200, 864], 'label': '1728.34767.144.bu1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.k1.a1', 'old_label': '144.bu1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.bu1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301471
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '144.bu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.bl1.b1', '48.bq1.a1', '48.cb1.a1', '48.cb1.b1', '72.bb1.b1', '72.ci1.c1', '72.ci1.d1'], 'contains': ['288.m1.b1', '432.k1.a1'], 'core': '864.c1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [432, 1156, 864], 'label': '1728.34767.144.bu1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.c1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.k1.a1', 'old_label': '144.bu1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.bu1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301472
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '144.bv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.bn1.a1', '48.br1.b1', '72.be1.a1', '72.ce1.c1', '72.ce1.d1'], 'contains': ['288.m1.a1', '432.l1.b1'], 'core': '864.c1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [474, 864, 1200], 'label': '1728.34767.144.bv1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.h1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.x1.b1', 'old_label': '144.bv1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.bv1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301473
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '144.bv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.bn1.b1', '48.br1.a1', '72.be1.b1', '72.ce1.a1', '72.ce1.b1'], 'contains': ['288.m1.b1', '432.l1.a1'], 'core': '864.c1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [469, 864, 1156], 'label': '1728.34767.144.bv1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.h1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.x1.a1', 'old_label': '144.bv1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.bv1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301474
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '144.bw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.bo1.a1', '48.bs1.c1', '48.cc1.a1', '72.bf1.a1', '72.ce1.c1', '72.ci1.a1'], 'contains': ['288.m1.a1', '432.m1.a1'], 'core': '864.c1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [1411, 864, 1200], 'label': '1728.34767.144.bw1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '16.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.i1.b1', 'old_label': '144.bw1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.bw1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301475
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '144.bw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.bo1.b1', '48.bs1.d1', '48.cc1.b1', '72.bf1.a1', '72.ce1.d1', '72.ci1.b1'], 'contains': ['288.m1.a1', '432.m1.b1'], 'core': '864.c1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [475, 864, 1200], 'label': '1728.34767.144.bw1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '16.d1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.i1.b1', 'old_label': '144.bw1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.bw1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301476
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '144.bw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.bo1.c1', '48.bs1.a1', '48.cc1.a1', '72.bf1.b1', '72.ce1.a1', '72.ci1.c1'], 'contains': ['288.m1.b1', '432.m1.a1'], 'core': '864.c1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [1411, 864, 1156], 'label': '1728.34767.144.bw1.c1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '16.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.i1.a1', 'old_label': '144.bw1.c1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.bw1.c1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301477
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '8.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.b1', '4.b1.b1', '4.c1.b1', '4.d1.b1', '4.e1.b1', '4.f1.b1', '4.g1.a1'], 'contains': ['16.a1.a1', '16.b1.c1', '16.b1.d1', '16.e1.b1', '16.k1.b1', '24.a1.b1', '24.b1.b1', '24.n1.b1', '24.o1.b1'], 'core': '8.a1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [1, 4, 576, 936, 864, 48], 'label': '1728.34767.8.a1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1.b1', 'normal_contained_in': ['4.a1.b1', '4.b1.b1', '4.c1.b1', '4.d1.b1', '4.f1.b1', '4.e1.b1', '4.g1.a1'], 'normal_contains': ['16.a1.a1', '16.b1.c1', '16.b1.d1', '24.a1.b1', '24.b1.b1'], 'normalizer': '1.a1.a1', 'old_label': '8.a1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.a1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301478
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '144.bw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.bo1.d1', '48.bs1.b1', '48.cc1.b1', '72.bf1.b1', '72.ce1.b1', '72.ci1.d1'], 'contains': ['288.m1.b1', '432.m1.b1'], 'core': '864.c1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [475, 864, 1156], 'label': '1728.34767.144.bw1.d1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '16.d1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.i1.a1', 'old_label': '144.bw1.d1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.bw1.d1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301479
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '144.bx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.bp1.a1', '48.bt1.b1', '48.cd1.a1', '48.cd1.a2', '72.bg1.a1', '72.ci1.a1', '72.ci1.b1'], 'contains': ['288.m1.a1', '432.n1.a1'], 'core': '864.c1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [43, 864, 1200], 'label': '1728.34767.144.bx1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.k1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.ck1.a1', 'old_label': '144.bx1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.bx1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301480
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '144.bx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.bp1.b1', '48.bt1.a1', '48.cd1.a1', '48.cd1.a2', '72.bg1.b1', '72.ci1.c1', '72.ci1.d1'], 'contains': ['288.m1.b1', '432.n1.a1'], 'core': '864.c1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [43, 864, 1156], 'label': '1728.34767.144.bx1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.k1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.ck1.b1', 'old_label': '144.bx1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.bx1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301481
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '144.by1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.bu1.a1', '48.by1.a1', '48.cb1.a1', '72.bh1.a1', '72.cj1.a1', '72.cj1.c1'], 'contains': ['288.n1.a1', '432.k1.a1'], 'core': '864.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [432, 52, 864], 'label': '1728.34767.144.by1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.i1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.h1.a1', 'old_label': '144.by1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.by1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301482
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '144.by1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.bu1.a1', '48.by1.b1', '48.cb1.b1', '72.bh1.a1', '72.cj1.b1', '72.cj1.d1'], 'contains': ['288.n1.a1', '432.k1.a1'], 'core': '864.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [432, 100, 864], 'label': '1728.34767.144.by1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.i1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.h1.a1', 'old_label': '144.by1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.by1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301483
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '144.bz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.bw1.a1', '48.bz1.a1', '48.cc1.a1', '72.bm1.a1', '72.cj1.a1', '72.cj1.b1'], 'contains': ['288.n1.a1', '432.m1.a1'], 'core': '864.c1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [1411, 864, 100], 'label': '1728.34767.144.bz1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '16.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bb1.a1', 'old_label': '144.bz1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.bz1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301484
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '144.bz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.bw1.b1', '48.bz1.b1', '48.cc1.b1', '72.bm1.a1', '72.cj1.c1', '72.cj1.d1'], 'contains': ['288.n1.a1', '432.m1.b1'], 'core': '864.c1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [475, 864, 100], 'label': '1728.34767.144.bz1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '16.d1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bb1.a1', 'old_label': '144.bz1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.bz1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301485
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '144.ca1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.bx1.a1', '48.ca1.a1', '48.cd1.a1', '72.bn1.a1', '72.cj1.a1', '72.cj1.d1'], 'contains': ['288.n1.a1', '432.n1.a1'], 'core': '864.c1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [43, 864, 100], 'label': '1728.34767.144.ca1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.k1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bb1.a1', 'old_label': '144.ca1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.ca1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301486
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '144.ca1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.bx1.a1', '48.ca1.a2', '48.cd1.a2', '72.bn1.a1', '72.cj1.b1', '72.cj1.c1'], 'contains': ['288.n1.a1', '432.n1.a1'], 'core': '864.c1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [43, 864, 52], 'label': '1728.34767.144.ca1.a2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.k1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bb1.a1', 'old_label': '144.ca1.a2', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.ca1.a2', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301487
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '144.cb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.bq1.a1', '48.bq1.b1', '48.by1.a1', '48.cb1.b1', '72.bo1.a1', '72.ck1.a1', '72.ck1.c1'], 'contains': ['288.o1.a1', '432.k1.a1'], 'core': '864.c1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [432, 1204, 864], 'label': '1728.34767.144.cb1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.k1.a1', 'old_label': '144.cb1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.cb1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301488
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '8.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '4.a1.b1', '4.h1.a1', '4.i1.a1', '4.j1.a1', '4.j1.b1', '4.k1.a1'], 'contains': ['16.a1.a1', '16.l1.a1', '24.c1.a1', '24.c1.b1', '24.i1.a1', '24.w1.a1', '24.w1.b1', '24.bi1.a1', '24.bp1.a1'], 'core': '8.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [432, 864, 576, 936, 4, 48], 'label': '1728.34767.8.b1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.b1.a1', 'normal_contained_in': ['4.a1.b1', '4.a1.a1', '4.h1.a1', '4.i1.a1', '4.j1.a1', '4.j1.b1', '4.k1.a1'], 'normal_contains': ['16.a1.a1', '24.c1.b1', '24.c1.a1', '24.i1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.b1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.b1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301489
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '144.cb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.bq1.a1', '48.bq1.b1', '48.by1.b1', '48.cb1.a1', '72.bo1.a1', '72.ck1.b1', '72.ck1.d1'], 'contains': ['288.o1.a1', '432.k1.a1'], 'core': '864.c1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [432, 676, 864], 'label': '1728.34767.144.cb1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.k1.a1', 'old_label': '144.cb1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.cb1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301490
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '144.cc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.bs1.a1', '48.bs1.c1', '48.bz1.a1', '48.cc1.a1', '72.bp1.a1', '72.ck1.a1', '72.ck1.b1'], 'contains': ['288.o1.a1', '432.m1.a1'], 'core': '864.c1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [1411, 864, 1204], 'label': '1728.34767.144.cc1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '16.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.cu1.a1', 'old_label': '144.cc1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.cc1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301491
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '144.cc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.bs1.b1', '48.bs1.d1', '48.bz1.b1', '48.cc1.b1', '72.bp1.a1', '72.ck1.c1', '72.ck1.d1'], 'contains': ['288.o1.a1', '432.m1.b1'], 'core': '864.c1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [475, 864, 1204], 'label': '1728.34767.144.cc1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '16.d1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.cu1.a1', 'old_label': '144.cc1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.cc1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301492
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '144.cd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.bt1.a1', '48.bt1.b1', '48.ca1.a1', '48.cd1.a2', '72.bq1.a1', '72.ck1.a1', '72.ck1.d1'], 'contains': ['288.o1.a1', '432.n1.a1'], 'core': '864.c1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [43, 864, 676], 'label': '1728.34767.144.cd1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.k1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.cu1.a1', 'old_label': '144.cd1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.cd1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301493
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '144.cd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.bt1.a1', '48.bt1.b1', '48.ca1.a2', '48.cd1.a1', '72.bq1.a1', '72.ck1.b1', '72.ck1.c1'], 'contains': ['288.o1.a1', '432.n1.a1'], 'core': '864.c1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [43, 864, 1204], 'label': '1728.34767.144.cd1.a2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.k1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.cu1.a1', 'old_label': '144.cd1.a2', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.cd1.a2', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301494
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '192.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.a1.b1', 'complements': ['9.b1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['64.a1.a1', '96.a1.a1', '96.c1.a1', '96.e1.a1', '96.p1.c1', '96.p1.d1', '96.q1.a1', '96.q1.b1'], 'contains': ['576.a1.a1', '576.b1.a1', '576.c1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [48, 576], 'label': '1728.34767.192.a1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '192.a1.a1', 'normal_contained_in': ['64.a1.a1', '96.a1.a1', '96.c1.a1', '96.e1.a1'], 'normal_contains': ['576.a1.a1', '576.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '192.a1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.a1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301495
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '192.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.a1.a1', 'complements': ['9.b1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['64.a1.a1', '96.a1.b1', '96.c1.b1', '96.e1.b1', '96.p1.a1', '96.p1.b1', '96.q1.c1', '96.q1.d1'], 'contains': ['576.a1.b1', '576.b1.a1', '576.c1.b1'], 'core': '192.a1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [4, 576], 'label': '1728.34767.192.a1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '192.a1.b1', 'normal_contained_in': ['64.a1.a1', '96.a1.b1', '96.c1.b1', '96.e1.b1'], 'normal_contains': ['576.a1.b1', '576.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '192.a1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.a1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301496
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '192.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.h1.a1', 'complements': ['9.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['64.a1.a1', '96.b1.a1', '96.d1.a1', '96.f1.a1', '96.s1.a1', '96.s1.b1', '96.s1.c1', '96.s1.d1'], 'contains': ['576.a1.a1', '576.a1.b1', '576.d1.a1'], 'core': '192.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [4, 48], 'label': '1728.34767.192.b1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '192.b1.a1', 'normal_contained_in': ['64.a1.a1', '96.b1.a1', '96.d1.a1', '96.f1.a1'], 'normal_contains': ['576.a1.b1', '576.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '192.b1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.b1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301497
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '192.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['64.a1.a1', '96.g1.a1', '96.j1.a1', '96.m1.a1', '96.r1.a1', '96.r1.b1'], 'contains': ['576.a1.a1', '576.c1.b1', '576.e1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [1156, 48], 'label': '1728.34767.192.c1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '64.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '192.c1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.c1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301498
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '192.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['64.a1.a1', '96.g1.b1', '96.j1.b1', '96.m1.b1', '96.r1.c1', '96.r1.d1'], 'contains': ['576.a1.b1', '576.c1.a1', '576.e1.a1'], 'core': '576.a1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [4, 1200], 'label': '1728.34767.192.c1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '64.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.b1', 'old_label': '192.c1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.c1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301499
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '8.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '4.b1.b1', '4.h1.a1', '4.l1.a1', '4.l1.b1', '4.m1.a1', '4.n1.a1'], 'contains': ['16.a1.a1', '16.f1.a1', '24.d1.a1', '24.d1.b1', '24.bc1.a1', '24.bj1.a1'], 'core': '8.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [36, 576, 72, 864, 4, 48], 'label': '1728.34767.8.c1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.c1.a1', 'normal_contained_in': ['4.b1.b1', '4.b1.a1', '4.h1.a1', '4.l1.b1', '4.l1.a1', '4.m1.a1', '4.n1.a1'], 'normal_contains': ['16.a1.a1', '24.d1.b1', '24.d1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.c1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.c1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301500
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '192.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['64.a1.a1', '96.h1.a1', '96.k1.a1', '96.n1.a1'], 'contains': ['576.b1.a1', '576.d1.a1', '576.e1.a1'], 'core': '576.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [100, 576], 'label': '1728.34767.192.d1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '64.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.h1.a1', 'old_label': '192.d1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.d1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301501
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '192.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['64.a1.a1', '96.i1.a1', '96.l1.a1', '96.o1.a1'], 'contains': ['576.c1.a1', '576.c1.b1', '576.d1.a1', '576.e1.a1'], 'core': '1728.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [1156, 1200], 'label': '1728.34767.192.e1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '64.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.k1.a1', 'old_label': '192.e1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.e1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301502
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '216.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.i1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['72.b1.a1', '72.b1.b1', '72.d1.a1', '72.bb1.a1', '72.bb1.b1', '72.bh1.a1', '72.bo1.a1', '108.a1.a1', '108.a1.b1', '108.h1.a1', '108.i1.a1', '108.j1.a1', '108.j1.b1', '108.k1.a1'], 'contains': ['432.a1.a1', '432.k1.a1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [432, 936], 'label': '1728.34767.216.a1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '216.a1.a1', 'normal_contained_in': ['72.b1.b1', '72.b1.a1', '72.d1.a1'], 'normal_contains': ['432.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '216.a1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.a1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301503
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '216.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.a1.a1', '72.g1.a1', '72.h1.a1', '72.i1.a1', '108.a1.a1', '108.b1.a1', '108.c1.a1', '108.d1.a1', '108.e1.a1', '108.f1.a1', '108.g1.a1'], 'contains': ['432.a1.a1', '432.b1.a1', '432.b1.b1', '432.d1.a1', '432.j1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [6, 936, 864], 'label': '1728.34767.216.b1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '72.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '216.b1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.b1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301504
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '216.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6.e1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.a1.b1', '72.g1.b1', '72.h1.b1', '72.i1.b1', '108.a1.b1', '108.b1.b1', '108.c1.b1', '108.d1.b1', '108.e1.b1', '108.f1.b1', '108.g1.a1'], 'contains': ['432.a1.a1', '432.b1.c1', '432.b1.d1', '432.d1.b1', '432.j1.b1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [1, 936, 864], 'label': '1728.34767.216.b1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '72.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.b1', 'old_label': '216.b1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.b1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301505
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '216.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6.r1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.e1.a1', '72.j1.a1', '72.j1.b1', '72.bi1.a1', '108.b1.a1', '108.b1.b1', '108.h1.a1', '108.l1.a1', '108.l1.b1', '108.m1.a1', '108.n1.a1'], 'contains': ['432.a1.a1', '432.e1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [36, 864], 'label': '1728.34767.216.c1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '72.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '216.c1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.c1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301506
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '216.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12.s1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.c1.b1', '72.k1.a1', '72.u1.a1', '72.bc1.a1', '108.a1.b1', '108.c1.a1', '108.l1.a1', '108.o1.a1', '108.p1.a1', '108.q1.a1', '108.r1.a1'], 'contains': ['432.a1.a1', '432.f1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [433, 864], 'label': '1728.34767.216.d1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '72.c1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.b1', 'old_label': '216.d1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.d1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301507
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '216.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12.s1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.c1.a1', '72.k1.b1', '72.u1.b1', '72.bc1.b1', '108.a1.a1', '108.c1.b1', '108.l1.b1', '108.o1.b1', '108.p1.b1', '108.q1.b1', '108.r1.a1'], 'contains': ['432.a1.a1', '432.f1.b1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [438, 864], 'label': '1728.34767.216.d1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '72.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '216.d1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.d1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301508
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '216.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12.ci1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.f1.a1', '72.l1.a1', '72.l1.b1', '72.bj1.a1', '108.d1.a1', '108.d1.b1', '108.h1.a1', '108.o1.a1', '108.o1.b1', '108.s1.a1', '108.t1.a1'], 'contains': ['432.a1.a1', '432.g1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [468, 864], 'label': '1728.34767.216.e1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '72.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '216.e1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.e1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301509
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '216.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '18.x1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.m1.a1', '72.m1.b1', '72.v1.a1', '72.bk1.a1', '108.g1.a1', '108.i1.a1', '108.m1.a1', '108.r1.a1', '108.s1.a1', '108.u1.a1', '108.v1.a1'], 'contains': ['432.a1.a1', '432.c1.a1', '432.c1.b1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [7, 864], 'label': '1728.34767.216.f1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.k1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '216.f1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.f1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301510
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '8.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.b1', '4.c1.a1', '4.l1.a1', '4.o1.a1', '4.p1.a1', '4.q1.a1', '4.r1.a1'], 'contains': ['16.a1.a1', '16.g1.a1', '24.e1.b1', '24.j1.a1', '24.p1.a1', '24.x1.b1'], 'core': '8.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [433, 4, 72, 864, 48, 576], 'label': '1728.34767.8.d1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.d1.a1', 'normal_contained_in': ['4.a1.b1', '4.c1.a1', '4.l1.a1', '4.o1.a1', '4.q1.a1', '4.p1.a1', '4.r1.a1'], 'normal_contains': ['16.a1.a1', '24.e1.b1', '24.j1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.d1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.d1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301511
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '216.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '18.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.n1.a1', '72.n1.b1', '72.w1.a1', '72.bl1.a1', '108.c1.a1', '108.c1.b1', '108.i1.a1', '108.n1.a1', '108.t1.a1', '108.w1.a1', '108.w1.b1'], 'contains': ['432.a1.a1', '432.h1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [439, 864], 'label': '1728.34767.216.g1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.l1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '216.g1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.g1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301512
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '216.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '36.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.o1.b1', '72.p1.a1', '72.x1.a1', '72.bd1.a1', '108.b1.a1', '108.e1.b1', '108.j1.a1', '108.o1.b1', '108.p1.a1', '108.u1.a1', '108.w1.a1'], 'contains': ['432.a1.a1', '432.i1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [42, 864], 'label': '1728.34767.216.h1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1.a1', 'old_label': '216.h1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.h1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301513
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '216.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '36.d1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.o1.a1', '72.p1.b1', '72.x1.b1', '72.bd1.b1', '108.b1.b1', '108.e1.a1', '108.j1.b1', '108.o1.a1', '108.p1.b1', '108.u1.a1', '108.w1.b1'], 'contains': ['432.a1.a1', '432.i1.b1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [37, 864], 'label': '1728.34767.216.h1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.g1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1.b1', 'old_label': '216.h1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.h1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301514
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '216.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '36.w1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.q1.a1', '72.r1.b1', '72.y1.a1', '72.be1.b1', '108.d1.b1', '108.f1.a1', '108.j1.b1', '108.l1.a1', '108.q1.b1', '108.v1.a1', '108.w1.a1'], 'contains': ['432.a1.a1', '432.l1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [469, 936], 'label': '1728.34767.216.i1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.h1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1.b1', 'old_label': '216.i1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.i1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301515
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '216.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '36.w1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.q1.b1', '72.r1.a1', '72.y1.b1', '72.be1.a1', '108.d1.a1', '108.f1.b1', '108.j1.a1', '108.l1.b1', '108.q1.a1', '108.v1.a1', '108.w1.b1'], 'contains': ['432.a1.a1', '432.l1.b1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [474, 936], 'label': '1728.34767.216.i1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.h1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1.a1', 'old_label': '216.i1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.i1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301516
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '216.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '54.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.s1.a1', '72.s1.b1', '72.z1.a1', '72.bf1.a1', '72.bf1.b1', '72.bm1.a1', '72.bp1.a1', '108.f1.a1', '108.f1.b1', '108.k1.a1', '108.n1.a1', '108.p1.a1', '108.p1.b1', '108.s1.a1'], 'contains': ['432.a1.a1', '432.m1.a1', '432.m1.b1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [475, 936], 'label': '1728.34767.216.j1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.j1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1.a1', 'old_label': '216.j1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.j1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301517
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '216.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '108.m1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.t1.a1', '72.t1.b1', '72.ba1.a1', '72.bg1.a1', '72.bg1.b1', '72.bn1.a1', '72.bq1.a1', '108.e1.a1', '108.e1.b1', '108.k1.a1', '108.m1.a1', '108.q1.a1', '108.q1.b1', '108.t1.a1'], 'contains': ['432.a1.a1', '432.n1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [43, 936], 'label': '1728.34767.216.k1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.k1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1.a1', 'old_label': '216.k1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.k1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301518
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '216.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '36.bz1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.br1.a1', '72.bs1.a1', '72.bs1.c1', '108.g1.a1'], 'contains': ['432.b1.a1', '432.b1.c1', '432.c1.a1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [1, 6], 'label': '1728.34767.216.l1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.m1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '216.l1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.l1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301519
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '216.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '36.bz1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.br1.b1', '72.bs1.b1', '72.bs1.d1', '108.g1.a1'], 'contains': ['432.b1.a1', '432.b1.d1', '432.c1.b1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [865, 6], 'label': '1728.34767.216.l1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.m1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '216.l1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.l1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301520
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '216.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '36.bz1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.br1.c1', '72.bs1.e1', '72.bs1.g1', '108.g1.a1'], 'contains': ['432.b1.b1', '432.b1.c1', '432.c1.b1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [1, 870], 'label': '1728.34767.216.l1.c1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.m1.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '216.l1.c1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.l1.c1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301521
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '8.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.a1.b1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '4.c1.b1', '4.l1.b1', '4.o1.b1', '4.p1.b1', '4.q1.b1', '4.r1.a1'], 'contains': ['16.a1.a1', '16.g1.b1', '24.e1.a1', '24.j1.b1', '24.p1.b1', '24.x1.a1'], 'core': '8.d1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [438, 48, 72, 864, 4, 576], 'label': '1728.34767.8.d1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.d1.b1', 'normal_contained_in': ['4.a1.a1', '4.c1.b1', '4.l1.b1', '4.o1.b1', '4.q1.b1', '4.p1.b1', '4.r1.a1'], 'normal_contains': ['16.a1.a1', '24.e1.a1', '24.j1.b1'], 'normalizer': '1.a1.a1', 'old_label': '8.d1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.d1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301522
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '216.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '36.bz1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.br1.d1', '72.bs1.f1', '72.bs1.h1', '108.g1.a1'], 'contains': ['432.b1.b1', '432.b1.d1', '432.c1.a1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [865, 870], 'label': '1728.34767.216.l1.d1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.m1.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '216.l1.d1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.l1.d1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301523
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '216.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '36.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.bt1.a1', '72.bv1.a1', '72.bx1.a1', '108.b1.a1'], 'contains': ['432.d1.a1', '432.e1.a1', '432.i1.a1'], 'core': '864.b1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [6, 36], 'label': '1728.34767.216.m1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.d1.a1', 'old_label': '216.m1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.m1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301524
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '216.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '36.d1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.bt1.b1', '72.bv1.b1', '72.bx1.b1', '108.b1.b1'], 'contains': ['432.d1.b1', '432.e1.a1', '432.i1.b1'], 'core': '864.b1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [1, 36], 'label': '1728.34767.216.m1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.d1.b1', 'old_label': '216.m1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.m1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301525
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '216.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '36.k1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.bu1.a1', '72.bw1.a1', '72.by1.a1', '108.c1.a1'], 'contains': ['432.d1.a1', '432.f1.a1', '432.h1.a1'], 'core': '864.b1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [433, 6], 'label': '1728.34767.216.n1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.k1.a1', 'old_label': '216.n1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.n1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301526
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '216.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '36.k1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.bu1.b1', '72.bw1.b1', '72.by1.b1', '108.c1.b1'], 'contains': ['432.d1.b1', '432.f1.b1', '432.h1.a1'], 'core': '864.b1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [1, 438], 'label': '1728.34767.216.n1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.e1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.k1.b1', 'old_label': '216.n1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.n1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301527
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '216.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.bz1.a1', '72.ca1.b1', '72.cb1.a1', '108.o1.a1'], 'contains': ['432.f1.a1', '432.g1.a1', '432.i1.b1'], 'core': '864.b1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [433, 468], 'label': '1728.34767.216.o1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.j1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.bh1.a1', 'old_label': '216.o1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.o1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301528
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '216.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.bz1.b1', '72.ca1.a1', '72.cb1.b1', '108.o1.b1'], 'contains': ['432.f1.b1', '432.g1.a1', '432.i1.a1'], 'core': '864.b1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [438, 468], 'label': '1728.34767.216.o1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.j1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.bh1.b1', 'old_label': '216.o1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.o1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301529
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '216.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '108.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.cc1.a1', '72.cd1.a1', '72.ce1.a1', '72.cf1.a1', '108.f1.a1'], 'contains': ['432.j1.a1', '432.l1.a1', '432.m1.a1'], 'core': '864.c1.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [469, 6], 'label': '1728.34767.216.p1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.c1.a1', 'old_label': '216.p1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.p1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301530
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '216.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '108.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.cc1.b1', '72.cd1.b1', '72.ce1.b1', '72.cf1.b1', '108.f1.a1'], 'contains': ['432.j1.a1', '432.l1.a1', '432.m1.b1'], 'core': '864.c1.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [1405, 6], 'label': '1728.34767.216.p1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.c1.a1', 'old_label': '216.p1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.p1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301531
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '216.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '108.f1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.cc1.c1', '72.cd1.c1', '72.ce1.c1', '72.cf1.c1', '108.f1.b1'], 'contains': ['432.j1.b1', '432.l1.b1', '432.m1.a1'], 'core': '864.c1.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [937, 474], 'label': '1728.34767.216.p1.c1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.f1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.c1.b1', 'old_label': '216.p1.c1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.p1.c1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301532
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '8.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.d1.a1', '4.d1.b1', '4.h1.a1', '4.o1.a1', '4.o1.b1', '4.s1.a1', '4.t1.a1'], 'contains': ['16.a1.a1', '16.h1.a1', '24.f1.a1', '24.f1.b1', '24.bd1.a1', '24.bk1.a1'], 'core': '8.e1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [468, 576, 72, 864, 4, 48], 'label': '1728.34767.8.e1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.e1.a1', 'normal_contained_in': ['4.d1.b1', '4.d1.a1', '4.h1.a1', '4.o1.b1', '4.o1.a1', '4.s1.a1', '4.t1.a1'], 'normal_contains': ['16.a1.a1', '24.f1.b1', '24.f1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.e1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.e1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301533
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '216.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '108.f1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.cc1.d1', '72.cd1.d1', '72.ce1.d1', '72.cf1.d1', '108.f1.b1'], 'contains': ['432.j1.b1', '432.l1.b1', '432.m1.b1'], 'core': '864.c1.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [1, 474], 'label': '1728.34767.216.p1.d1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.f1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.c1.b1', 'old_label': '216.p1.d1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.p1.d1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301534
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '216.q1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.cg1.a1', '72.cg1.c1', '72.ch1.a1', '72.ci1.a1', '72.ci1.c1', '72.cj1.a1', '72.cj1.b1', '72.ck1.a1', '72.ck1.b1', '108.k1.a1'], 'contains': ['432.k1.a1', '432.m1.a1', '432.n1.a1'], 'core': '864.c1.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [979, 432], 'label': '1728.34767.216.q1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.k1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.h1.a1', 'old_label': '216.q1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.q1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301535
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '216.q1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.cg1.b1', '72.cg1.d1', '72.ch1.b1', '72.ci1.b1', '72.ci1.d1', '72.cj1.c1', '72.cj1.d1', '72.ck1.c1', '72.ck1.d1', '108.k1.a1'], 'contains': ['432.k1.a1', '432.m1.b1', '432.n1.a1'], 'core': '864.c1.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [43, 432], 'label': '1728.34767.216.q1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.k1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.h1.a1', 'old_label': '216.q1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.q1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301536
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '288.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2.a1.b1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['96.a1.a1', '96.b1.a1', '96.g1.a1', '144.a1.a1', '144.c1.a1', '144.c1.b1', '144.g1.c1', '144.g1.d1', '144.j1.a1', '144.j1.b1'], 'contains': ['576.a1.a1', '864.a1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [936, 48], 'label': '1728.34767.288.a1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '288.a1.a1', 'normal_contained_in': ['96.a1.a1', '96.b1.a1', '144.a1.a1', '144.c1.a1', '144.c1.b1'], 'normal_contains': ['576.a1.a1', '864.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '288.a1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.a1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301537
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '288.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['96.a1.b1', '96.b1.a1', '96.g1.b1', '144.a1.b1', '144.c1.c1', '144.c1.d1', '144.g1.a1', '144.g1.b1', '144.j1.c1', '144.j1.d1'], 'contains': ['576.a1.b1', '864.a1.a1'], 'core': '288.a1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [936, 4], 'label': '1728.34767.288.a1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '288.a1.b1', 'normal_contained_in': ['96.a1.b1', '96.b1.a1', '144.a1.b1', '144.c1.c1', '144.c1.d1'], 'normal_contains': ['576.a1.b1', '864.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '288.a1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.a1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301538
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '288.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2.e1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['96.a1.a1', '96.a1.b1', '96.h1.a1', '144.b1.a1', '144.h1.a1', '144.h1.b1', '144.h1.c1', '144.h1.d1', '144.k1.a1', '144.k1.b1'], 'contains': ['576.b1.a1', '864.a1.a1'], 'core': '288.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [936, 576], 'label': '1728.34767.288.b1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '288.b1.a1', 'normal_contained_in': ['96.a1.b1', '96.a1.a1', '144.b1.a1'], 'normal_contains': ['576.b1.a1', '864.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '288.b1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.b1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301539
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '288.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2.a1.b1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['96.c1.a1', '96.d1.a1', '96.j1.a1', '144.a1.a1', '144.m1.b1', '144.p1.a1', '144.q1.a1', '144.r1.a1', '144.s1.a1', '144.t1.a1', '144.u1.a1', '144.v1.a1', '144.w1.a1'], 'contains': ['576.a1.a1', '864.b1.a1'], 'core': '288.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [72, 48], 'label': '1728.34767.288.c1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '288.c1.a1', 'normal_contained_in': ['96.c1.a1', '96.d1.a1', '144.a1.a1'], 'normal_contains': ['576.a1.a1', '864.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '288.c1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.c1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301557
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '288.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.e1.b1', '96.m1.a1', '96.o1.a1', '144.d1.b1', '144.bj1.a1', '144.bu1.b1', '144.bv1.b1', '144.bw1.c1', '144.bw1.d1', '144.bx1.b1'], 'contains': ['576.c1.b1', '864.c1.a1'], 'core': '864.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [864, 1156], 'label': '1728.34767.288.m1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '96.e1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '288.m1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.m1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301540
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '288.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['96.c1.b1', '96.d1.a1', '96.j1.b1', '144.a1.b1', '144.m1.a1', '144.p1.b1', '144.q1.b1', '144.r1.b1', '144.s1.b1', '144.t1.b1', '144.u1.b1', '144.v1.b1', '144.w1.b1'], 'contains': ['576.a1.b1', '864.b1.a1'], 'core': '288.c1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [72, 4], 'label': '1728.34767.288.c1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '288.c1.b1', 'normal_contained_in': ['96.c1.b1', '96.d1.a1', '144.a1.b1'], 'normal_contains': ['576.a1.b1', '864.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '288.c1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.c1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301541
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '288.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2.e1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['96.c1.a1', '96.c1.b1', '96.k1.a1', '144.b1.a1', '144.n1.a1', '144.n1.b1', '144.x1.a1', '144.y1.a1', '144.y1.b1', '144.z1.a1', '144.ba1.a1', '144.bb1.a1', '144.bb1.b1'], 'contains': ['576.b1.a1', '864.b1.a1'], 'core': '288.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [72, 576], 'label': '1728.34767.288.d1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '288.d1.a1', 'normal_contained_in': ['96.c1.b1', '96.c1.a1', '144.b1.a1'], 'normal_contains': ['576.b1.a1', '864.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '288.d1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.d1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301542
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '288.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2.a1.b1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['96.e1.a1', '96.f1.a1', '96.m1.a1', '144.a1.a1', '144.bh1.b1', '144.bk1.a1', '144.bl1.a1', '144.bm1.a1', '144.bn1.a1', '144.bo1.a1', '144.bo1.b1', '144.bp1.a1'], 'contains': ['576.a1.a1', '864.c1.a1'], 'core': '288.e1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [864, 48], 'label': '1728.34767.288.e1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '288.e1.a1', 'normal_contained_in': ['96.e1.a1', '96.f1.a1', '144.a1.a1'], 'normal_contains': ['576.a1.a1', '864.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '288.e1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.e1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301543
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '2.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.b1.a1', '4.b1.b1', '4.e1.a1', '4.e1.b1', '4.g1.a1', '4.m1.a1', '4.u1.a1', '6.p1.a1', '6.p1.b1', '6.r1.a1'], 'core': '2.f1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [1, 864, 4, 6, 936, 576, 48, 36], 'label': '1728.34767.2.f1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.f1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.b1.b1', '4.b1.a1', '4.e1.b1', '4.e1.a1', '4.g1.a1', '4.m1.a1', '4.u1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.f1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2.f1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301544
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '8.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.d1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.g1.a1', '4.i1.a1', '4.m1.a1', '4.r1.a1', '4.s1.a1', '4.u1.a1', '4.v1.a1'], 'contains': ['16.a1.a1', '16.c1.a1', '16.c1.b1', '24.k1.a1', '24.q1.a1', '24.q1.b1', '24.bl1.a1'], 'core': '8.f1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [7, 48, 4, 864, 576, 936], 'label': '1728.34767.8.f1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.f1.a1', 'normal_contained_in': ['4.g1.a1', '4.i1.a1', '4.m1.a1', '4.r1.a1', '4.s1.a1', '4.v1.a1', '4.u1.a1'], 'normal_contains': ['16.a1.a1', '16.c1.b1', '16.c1.a1', '24.k1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.f1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.f1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301545
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '288.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['96.e1.b1', '96.f1.a1', '96.m1.b1', '144.a1.b1', '144.bh1.a1', '144.bk1.b1', '144.bl1.b1', '144.bm1.b1', '144.bn1.b1', '144.bo1.c1', '144.bo1.d1', '144.bp1.b1'], 'contains': ['576.a1.b1', '864.c1.a1'], 'core': '288.e1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [864, 4], 'label': '1728.34767.288.e1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '288.e1.b1', 'normal_contained_in': ['96.e1.b1', '96.f1.a1', '144.a1.b1'], 'normal_contains': ['576.a1.b1', '864.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '288.e1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.e1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301546
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '288.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2.e1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['96.e1.a1', '96.e1.b1', '96.n1.a1', '144.b1.a1', '144.bi1.a1', '144.bi1.b1', '144.bq1.a1', '144.br1.a1', '144.br1.b1', '144.bs1.a1', '144.bs1.b1', '144.bt1.a1'], 'contains': ['576.b1.a1', '864.c1.a1'], 'core': '288.f1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [864, 576], 'label': '1728.34767.288.f1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '288.f1.a1', 'normal_contained_in': ['96.e1.b1', '96.e1.a1', '144.b1.a1'], 'normal_contains': ['576.b1.a1', '864.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '288.f1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.f1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301547
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '288.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.a1.a1', '96.g1.b1', '96.i1.a1', '144.d1.a1', '144.i1.c1', '144.i1.d1'], 'contains': ['576.c1.a1', '864.a1.a1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [936, 1200], 'label': '1728.34767.288.g1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '96.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.b1', 'old_label': '288.g1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.g1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301548
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '288.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.a1.b1', '96.g1.a1', '96.i1.a1', '144.d1.b1', '144.i1.a1', '144.i1.b1'], 'contains': ['576.c1.b1', '864.a1.a1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [936, 1156], 'label': '1728.34767.288.g1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '96.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '288.g1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.g1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301549
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '288.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.b1.a1', '96.h1.a1', '96.i1.a1', '144.e1.a1', '144.l1.a1', '144.l1.b1'], 'contains': ['576.d1.a1', '864.a1.a1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [936, 100], 'label': '1728.34767.288.h1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '96.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.h1.a1', 'old_label': '288.h1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.h1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301550
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '288.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.g1.a1', '96.g1.b1', '96.h1.a1', '96.i1.a1', '144.f1.a1'], 'contains': ['576.e1.a1', '864.a1.a1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [936, 1204], 'label': '1728.34767.288.i1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '32.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.k1.a1', 'old_label': '288.i1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.i1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301551
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '288.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.c1.a1', '96.j1.b1', '96.l1.a1', '144.d1.a1', '144.o1.b1', '144.bc1.a1', '144.bd1.a1'], 'contains': ['576.c1.a1', '864.b1.a1'], 'core': '864.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [72, 1200], 'label': '1728.34767.288.j1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '96.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.b1', 'old_label': '288.j1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.j1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301552
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '288.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.c1.b1', '96.j1.a1', '96.l1.a1', '144.d1.b1', '144.o1.a1', '144.bc1.b1', '144.bd1.b1'], 'contains': ['576.c1.b1', '864.b1.a1'], 'core': '864.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [72, 1156], 'label': '1728.34767.288.j1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '96.c1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '288.j1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.j1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301553
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '288.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.d1.a1', '96.k1.a1', '96.l1.a1', '144.e1.a1', '144.be1.a1', '144.bf1.a1', '144.bg1.a1'], 'contains': ['576.d1.a1', '864.b1.a1'], 'core': '864.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [72, 100], 'label': '1728.34767.288.k1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '96.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.h1.a1', 'old_label': '288.k1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.k1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301554
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '288.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.j1.a1', '96.j1.b1', '96.k1.a1', '96.l1.a1', '144.f1.a1'], 'contains': ['576.e1.a1', '864.b1.a1'], 'core': '864.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [72, 1204], 'label': '1728.34767.288.l1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '32.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.k1.a1', 'old_label': '288.l1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.l1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301555
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '8.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.d1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.c1.a1', '4.c1.b1', '4.i1.a1', '4.n1.a1', '4.t1.a1', '4.w1.a1', '4.w1.b1'], 'contains': ['16.a1.a1', '16.i1.a1', '24.l1.a1', '24.r1.a1', '24.r1.b1', '24.bm1.a1'], 'core': '8.g1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [439, 48, 4, 864, 576, 72], 'label': '1728.34767.8.g1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.g1.a1', 'normal_contained_in': ['4.c1.b1', '4.c1.a1', '4.i1.a1', '4.n1.a1', '4.t1.a1', '4.w1.b1', '4.w1.a1'], 'normal_contains': ['16.a1.a1', '24.l1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.g1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.g1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301556
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '288.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.e1.a1', '96.m1.b1', '96.o1.a1', '144.d1.a1', '144.bj1.b1', '144.bu1.a1', '144.bv1.a1', '144.bw1.a1', '144.bw1.b1', '144.bx1.a1'], 'contains': ['576.c1.a1', '864.c1.a1'], 'core': '864.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [864, 1200], 'label': '1728.34767.288.m1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '96.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.b1', 'old_label': '288.m1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.m1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302234
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '48.bg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.i1.a1', '24.bm1.a1'], 'contains': ['96.k1.a1', '144.ba1.a1', '144.bg1.a1'], 'core': '288.d1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [439, 576, 72, 100], 'label': '1728.34767.48.bg1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.co1.a1', 'old_label': '48.bg1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bg1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301558
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '288.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.f1.a1', '96.n1.a1', '96.o1.a1', '144.e1.a1', '144.by1.a1', '144.by1.b1', '144.bz1.a1', '144.bz1.b1', '144.ca1.a1', '144.ca1.a2'], 'contains': ['576.d1.a1', '864.c1.a1'], 'core': '864.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [864, 100], 'label': '1728.34767.288.n1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '96.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.h1.a1', 'old_label': '288.n1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.n1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301559
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '288.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.m1.a1', '96.m1.b1', '96.n1.a1', '96.o1.a1', '144.f1.a1', '144.cb1.a1', '144.cb1.b1', '144.cc1.a1', '144.cc1.b1', '144.cd1.a1', '144.cd1.a2'], 'contains': ['576.e1.a1', '864.c1.a1'], 'core': '864.c1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [864, 1204], 'label': '1728.34767.288.o1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '32.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.k1.a1', 'old_label': '288.o1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.o1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301560
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '288.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12.n1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.p1.a1', '96.s1.a1', '144.g1.a1', '144.m1.a1', '144.bh1.a1'], 'contains': ['576.a1.b1', '864.d1.a1'], 'core': '576.a1.b1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [6, 4], 'label': '1728.34767.288.p1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '48.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.e1.a1', 'old_label': '288.p1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.p1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301561
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '288.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12.n1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.p1.b1', '96.s1.b1', '144.g1.b1', '144.m1.a1', '144.bh1.a1'], 'contains': ['576.a1.b1', '864.d1.b1'], 'core': '576.a1.b1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [870, 4], 'label': '1728.34767.288.p1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '48.d1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.e1.a1', 'old_label': '288.p1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.p1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301562
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '288.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12.n1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.p1.c1', '96.s1.c1', '144.g1.c1', '144.m1.b1', '144.bh1.b1'], 'contains': ['576.a1.a1', '864.d1.c1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [1, 48], 'label': '1728.34767.288.p1.c1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '48.d1.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.e1.b1', 'old_label': '288.p1.c1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.p1.c1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301563
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '288.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12.n1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.p1.d1', '96.s1.d1', '144.g1.d1', '144.m1.b1', '144.bh1.b1'], 'contains': ['576.a1.a1', '864.d1.d1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [865, 48], 'label': '1728.34767.288.p1.d1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '48.d1.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.e1.b1', 'old_label': '288.p1.d1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.p1.d1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301564
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '288.q1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12.o1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.p1.a1', '96.q1.a1', '144.h1.a1', '144.n1.a1', '144.bi1.a1'], 'contains': ['576.b1.a1', '864.d1.a1'], 'core': '576.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [6, 576], 'label': '1728.34767.288.q1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '48.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.e1.a1', 'old_label': '288.q1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.q1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301565
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '288.q1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12.o1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.p1.b1', '96.q1.b1', '144.h1.b1', '144.n1.a1', '144.bi1.a1'], 'contains': ['576.b1.a1', '864.d1.b1'], 'core': '576.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [870, 576], 'label': '1728.34767.288.q1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '48.c1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.e1.a1', 'old_label': '288.q1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.q1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301566
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '8.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.a1.b1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '4.e1.b1', '4.j1.a1', '4.o1.b1', '4.p1.a1', '4.u1.a1', '4.w1.a1'], 'contains': ['16.a1.a1', '16.j1.a1', '24.g1.a1', '24.s1.b1', '24.y1.b1', '24.be1.a1'], 'core': '8.h1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [42, 576, 48, 864, 4, 72], 'label': '1728.34767.8.h1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.h1.a1', 'normal_contained_in': ['4.b1.a1', '4.e1.b1', '4.j1.a1', '4.o1.b1', '4.p1.a1', '4.u1.a1', '4.w1.a1'], 'normal_contains': ['16.a1.a1', '24.g1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.h1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.h1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301567
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '288.q1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12.o1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.p1.c1', '96.q1.c1', '144.h1.c1', '144.n1.b1', '144.bi1.b1'], 'contains': ['576.b1.a1', '864.d1.c1'], 'core': '576.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [1, 576], 'label': '1728.34767.288.q1.c1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '48.c1.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.e1.b1', 'old_label': '288.q1.c1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.q1.c1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301568
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '288.q1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12.o1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.p1.d1', '96.q1.d1', '144.h1.d1', '144.n1.b1', '144.bi1.b1'], 'contains': ['576.b1.a1', '864.d1.d1'], 'core': '576.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [865, 576], 'label': '1728.34767.288.q1.d1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '48.c1.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.e1.b1', 'old_label': '288.q1.d1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.q1.d1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301569
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '288.r1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.n1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.p1.a1', '96.r1.a1', '144.i1.a1', '144.o1.a1', '144.bj1.a1'], 'contains': ['576.c1.b1', '864.d1.a1'], 'core': '1728.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [6, 1156], 'label': '1728.34767.288.r1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '16.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.r1.a1', 'old_label': '288.r1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.r1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301570
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '288.r1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.n1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.p1.b1', '96.r1.b1', '144.i1.b1', '144.o1.a1', '144.bj1.a1'], 'contains': ['576.c1.b1', '864.d1.b1'], 'core': '1728.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [870, 1156], 'label': '1728.34767.288.r1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '16.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.r1.a1', 'old_label': '288.r1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.r1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301571
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '288.r1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.n1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.p1.c1', '96.r1.c1', '144.i1.c1', '144.o1.b1', '144.bj1.b1'], 'contains': ['576.c1.a1', '864.d1.c1'], 'core': '1728.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [1, 1200], 'label': '1728.34767.288.r1.c1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '16.b1.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.r1.b1', 'old_label': '288.r1.c1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.r1.c1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301572
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '288.r1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.n1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.p1.d1', '96.r1.d1', '144.i1.d1', '144.o1.b1', '144.bj1.b1'], 'contains': ['576.c1.a1', '864.d1.d1'], 'core': '1728.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [865, 1200], 'label': '1728.34767.288.r1.d1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '16.b1.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.r1.b1', 'old_label': '288.r1.d1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.r1.d1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301573
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '288.s1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12.i1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.q1.a1', '96.r1.a1', '96.s1.a1', '144.c1.a1', '144.p1.a1', '144.bk1.a1'], 'contains': ['576.a1.a1', '864.d1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [6, 48], 'label': '1728.34767.288.s1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '144.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '288.s1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.s1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301574
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '288.s1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12.i1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.q1.b1', '96.r1.b1', '96.s1.b1', '144.c1.b1', '144.p1.a1', '144.bk1.a1'], 'contains': ['576.a1.a1', '864.d1.b1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [870, 48], 'label': '1728.34767.288.s1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '144.c1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '288.s1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.s1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301575
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '288.s1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.q1.c1', '96.r1.c1', '96.s1.c1', '144.c1.c1', '144.p1.b1', '144.bk1.b1'], 'contains': ['576.a1.b1', '864.d1.c1'], 'core': '576.a1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [1, 4], 'label': '1728.34767.288.s1.c1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '144.c1.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.b1', 'old_label': '288.s1.c1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.s1.c1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301576
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '288.s1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.q1.d1', '96.r1.d1', '96.s1.d1', '144.c1.d1', '144.p1.b1', '144.bk1.b1'], 'contains': ['576.a1.b1', '864.d1.d1'], 'core': '576.a1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [865, 4], 'label': '1728.34767.288.s1.d1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '144.c1.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.b1', 'old_label': '288.s1.d1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '288.s1.d1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301577
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '8.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.b1.b1', '4.e1.a1', '4.j1.b1', '4.o1.a1', '4.p1.b1', '4.u1.a1', '4.w1.b1'], 'contains': ['16.a1.a1', '16.j1.b1', '24.g1.b1', '24.s1.a1', '24.y1.a1', '24.be1.b1'], 'core': '8.h1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [37, 576, 4, 864, 48, 72], 'label': '1728.34767.8.h1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.h1.b1', 'normal_contained_in': ['4.b1.b1', '4.e1.a1', '4.j1.b1', '4.o1.a1', '4.p1.b1', '4.u1.a1', '4.w1.b1'], 'normal_contains': ['16.a1.a1', '24.g1.b1'], 'normalizer': '1.a1.a1', 'old_label': '8.h1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.h1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301598
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '432.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '36.w1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.bm1.a1', '144.bn1.b1', '144.br1.a1', '144.bv1.b1', '216.i1.a1', '216.p1.a1', '216.p1.b1'], 'contains': ['864.c1.a1'], 'core': '864.c1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [469], 'label': '1728.34767.432.l1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.h1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.o1.a1', 'old_label': '432.l1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.l1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301615
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '864.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.p1.a1', '288.q1.a1', '288.r1.a1', '288.s1.a1', '432.b1.a1', '432.d1.a1', '432.j1.a1'], 'contains': ['1728.a1.a1'], 'core': '1728.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [6], 'label': '1728.34767.864.d1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '144.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.e1.a1', 'old_label': '864.d1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.d1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301578
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '432.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['144.a1.a1', '144.a1.b1', '144.b1.a1', '144.d1.a1', '144.d1.b1', '144.e1.a1', '144.f1.a1', '216.a1.a1', '216.b1.a1', '216.b1.b1', '216.c1.a1', '216.d1.a1', '216.d1.b1', '216.e1.a1', '216.f1.a1', '216.g1.a1', '216.h1.a1', '216.h1.b1', '216.i1.a1', '216.i1.b1', '216.j1.a1', '216.k1.a1'], 'contains': ['864.a1.a1', '864.b1.a1', '864.c1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [936, 864], 'label': '1728.34767.432.a1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '432.a1.a1', 'normal_contained_in': ['144.a1.b1', '144.a1.a1', '144.b1.a1', '216.a1.a1'], 'normal_contains': ['864.a1.a1', '864.b1.a1', '864.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '432.a1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.a1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301579
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '432.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.c1.a1', '144.g1.a1', '144.h1.a1', '144.i1.a1', '216.b1.a1', '216.l1.a1', '216.l1.b1'], 'contains': ['864.a1.a1', '864.d1.a1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [6, 936], 'label': '1728.34767.432.b1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '144.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '432.b1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.b1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301580
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '432.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.c1.b1', '144.g1.b1', '144.h1.b1', '144.i1.b1', '216.b1.a1', '216.l1.c1', '216.l1.d1'], 'contains': ['864.a1.a1', '864.d1.b1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [870, 936], 'label': '1728.34767.432.b1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '144.c1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '432.b1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.b1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301581
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '432.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6.e1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.c1.c1', '144.g1.c1', '144.h1.c1', '144.i1.c1', '216.b1.b1', '216.l1.a1', '216.l1.c1'], 'contains': ['864.a1.a1', '864.d1.c1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [1, 936], 'label': '1728.34767.432.b1.c1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '144.c1.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.b1', 'old_label': '432.b1.c1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.b1.c1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301582
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '432.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6.e1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.c1.d1', '144.g1.d1', '144.h1.d1', '144.i1.d1', '216.b1.b1', '216.l1.b1', '216.l1.d1'], 'contains': ['864.a1.a1', '864.d1.d1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [865, 936], 'label': '1728.34767.432.b1.d1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '144.c1.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.b1', 'old_label': '432.b1.d1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.b1.d1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301583
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '432.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '18.x1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.j1.a1', '144.j1.c1', '144.k1.a1', '144.l1.a1', '216.f1.a1', '216.l1.a1', '216.l1.d1'], 'contains': ['864.a1.a1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [7], 'label': '1728.34767.432.c1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '48.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '432.c1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.c1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301584
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '432.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '18.x1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.j1.b1', '144.j1.d1', '144.k1.b1', '144.l1.b1', '216.f1.a1', '216.l1.b1', '216.l1.c1'], 'contains': ['864.a1.a1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [871], 'label': '1728.34767.432.c1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '48.e1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '432.c1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.c1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301585
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '432.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.m1.a1', '144.n1.a1', '144.o1.a1', '144.p1.a1', '216.b1.a1', '216.m1.a1', '216.n1.a1'], 'contains': ['864.b1.a1', '864.d1.a1', '864.d1.b1'], 'core': '864.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [6, 72], 'label': '1728.34767.432.d1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '72.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.e1.a1', 'old_label': '432.d1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.d1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301586
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '432.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6.e1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.m1.b1', '144.n1.b1', '144.o1.b1', '144.p1.b1', '216.b1.b1', '216.m1.b1', '216.n1.b1'], 'contains': ['864.b1.a1', '864.d1.c1', '864.d1.d1'], 'core': '864.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [1, 72], 'label': '1728.34767.432.d1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '72.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.e1.b1', 'old_label': '432.d1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.d1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301587
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '432.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6.r1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.q1.a1', '144.q1.b1', '144.x1.a1', '144.be1.a1', '216.c1.a1', '216.m1.a1', '216.m1.b1'], 'contains': ['864.b1.a1'], 'core': '864.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [36], 'label': '1728.34767.432.e1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '72.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.r1.a1', 'old_label': '432.e1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.e1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301588
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '8.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.d1.b1', '4.f1.a1', '4.j1.b1', '4.l1.a1', '4.q1.b1', '4.v1.a1', '4.w1.a1'], 'contains': ['16.a1.a1', '16.m1.a1', '24.h1.b1', '24.t1.a1', '24.z1.a1', '24.bf1.a1'], 'core': '8.i1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [469, 576, 4, 936, 48, 864], 'label': '1728.34767.8.i1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.i1.a1', 'normal_contained_in': ['4.d1.b1', '4.f1.a1', '4.j1.b1', '4.l1.a1', '4.q1.b1', '4.v1.a1', '4.w1.a1'], 'normal_contains': ['16.a1.a1', '24.h1.b1'], 'normalizer': '1.a1.a1', 'old_label': '8.i1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.i1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301589
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '432.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12.s1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.r1.a1', '144.s1.b1', '144.y1.a1', '144.bc1.a1', '216.d1.a1', '216.n1.a1', '216.o1.a1'], 'contains': ['864.b1.a1'], 'core': '864.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [433], 'label': '1728.34767.432.f1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '72.c1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.i1.a1', 'old_label': '432.f1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.f1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301590
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '432.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12.s1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.r1.b1', '144.s1.a1', '144.y1.b1', '144.bc1.b1', '216.d1.b1', '216.n1.b1', '216.o1.b1'], 'contains': ['864.b1.a1'], 'core': '864.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [438], 'label': '1728.34767.432.f1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '72.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.i1.b1', 'old_label': '432.f1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.f1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301591
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '432.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12.ci1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.t1.a1', '144.t1.b1', '144.z1.a1', '144.bf1.a1', '216.e1.a1', '216.o1.a1', '216.o1.b1'], 'contains': ['864.b1.a1'], 'core': '864.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [468], 'label': '1728.34767.432.g1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '72.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.ba1.a1', 'old_label': '432.g1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.g1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301592
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '432.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '18.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.u1.a1', '144.u1.b1', '144.ba1.a1', '144.bg1.a1', '216.g1.a1', '216.n1.a1', '216.n1.b1'], 'contains': ['864.b1.a1'], 'core': '864.b1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [439], 'label': '1728.34767.432.h1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.l1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.j1.a1', 'old_label': '432.h1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.h1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301593
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '432.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '36.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.v1.b1', '144.w1.a1', '144.bb1.a1', '144.bd1.a1', '216.h1.a1', '216.m1.a1', '216.o1.b1'], 'contains': ['864.b1.a1'], 'core': '864.b1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [42], 'label': '1728.34767.432.i1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1.a1', 'old_label': '432.i1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.i1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301594
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '432.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '36.d1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.v1.a1', '144.w1.b1', '144.bb1.b1', '144.bd1.b1', '216.h1.b1', '216.m1.b1', '216.o1.a1'], 'contains': ['864.b1.a1'], 'core': '864.b1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [37], 'label': '1728.34767.432.i1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.g1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1.b1', 'old_label': '432.i1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.i1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301595
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '432.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.bh1.a1', '144.bi1.a1', '144.bj1.a1', '144.bk1.a1', '216.b1.a1', '216.p1.a1', '216.p1.b1'], 'contains': ['864.c1.a1', '864.d1.a1', '864.d1.b1'], 'core': '864.c1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [6, 864], 'label': '1728.34767.432.j1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '72.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.e1.a1', 'old_label': '432.j1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.j1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301596
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '432.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6.e1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.bh1.b1', '144.bi1.b1', '144.bj1.b1', '144.bk1.b1', '216.b1.b1', '216.p1.c1', '216.p1.d1'], 'contains': ['864.c1.a1', '864.d1.c1', '864.d1.d1'], 'core': '864.c1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [1, 864], 'label': '1728.34767.432.j1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '72.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.e1.b1', 'old_label': '432.j1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.j1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301597
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '432.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.bl1.a1', '144.bl1.b1', '144.bq1.a1', '144.bu1.a1', '144.bu1.b1', '144.by1.a1', '144.by1.b1', '144.cb1.a1', '144.cb1.b1', '216.a1.a1', '216.q1.a1', '216.q1.b1'], 'contains': ['864.c1.a1'], 'core': '864.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [432], 'label': '1728.34767.432.k1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '216.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.h1.a1', 'old_label': '432.k1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.k1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301599
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '8.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.a1.b1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.d1.a1', '4.f1.b1', '4.j1.a1', '4.l1.b1', '4.q1.a1', '4.v1.a1', '4.w1.b1'], 'contains': ['16.a1.a1', '16.m1.b1', '24.h1.a1', '24.t1.b1', '24.z1.b1', '24.bf1.b1'], 'core': '8.i1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [474, 576, 48, 936, 4, 864], 'label': '1728.34767.8.i1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.i1.b1', 'normal_contained_in': ['4.d1.a1', '4.f1.b1', '4.j1.a1', '4.l1.b1', '4.q1.a1', '4.v1.a1', '4.w1.b1'], 'normal_contains': ['16.a1.a1', '24.h1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.i1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.i1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301600
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '432.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '36.w1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.bm1.b1', '144.bn1.a1', '144.br1.b1', '144.bv1.a1', '216.i1.b1', '216.p1.c1', '216.p1.d1'], 'contains': ['864.c1.a1'], 'core': '864.c1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [474], 'label': '1728.34767.432.l1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.h1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.o1.b1', 'old_label': '432.l1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.l1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301601
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '432.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '54.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.bo1.a1', '144.bo1.c1', '144.bs1.a1', '144.bw1.a1', '144.bw1.c1', '144.bz1.a1', '144.cc1.a1', '216.j1.a1', '216.p1.a1', '216.p1.c1', '216.q1.a1'], 'contains': ['864.c1.a1'], 'core': '864.c1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [1411], 'label': '1728.34767.432.m1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '16.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1.a1', 'old_label': '432.m1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.m1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301602
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '432.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '54.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.bo1.b1', '144.bo1.d1', '144.bs1.b1', '144.bw1.b1', '144.bw1.d1', '144.bz1.b1', '144.cc1.b1', '216.j1.a1', '216.p1.b1', '216.p1.d1', '216.q1.b1'], 'contains': ['864.c1.a1'], 'core': '864.c1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [475], 'label': '1728.34767.432.m1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '16.d1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1.a1', 'old_label': '432.m1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.m1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301603
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '432.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '108.m1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.bp1.a1', '144.bp1.b1', '144.bt1.a1', '144.bx1.a1', '144.bx1.b1', '144.ca1.a1', '144.ca1.a2', '144.cd1.a1', '144.cd1.a2', '216.k1.a1', '216.q1.a1', '216.q1.b1'], 'contains': ['864.c1.a1'], 'core': '864.c1.a1', 'coset_action_label': None, 'count': 54, 'diagramx': None, 'generators': [43], 'label': '1728.34767.432.n1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.k1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.h1.a1', 'old_label': '432.n1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.n1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301604
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '576.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2.a1.b1', 'complements': ['3.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['192.a1.a1', '192.b1.a1', '192.c1.a1', '288.a1.a1', '288.c1.a1', '288.e1.a1', '288.p1.c1', '288.p1.d1', '288.s1.a1', '288.s1.b1'], 'contains': ['1728.a1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [48], 'label': '1728.34767.576.a1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '576.a1.a1', 'normal_contained_in': ['192.a1.a1', '192.b1.a1', '288.a1.a1', '288.c1.a1', '288.e1.a1'], 'normal_contains': ['1728.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '576.a1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.a1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301605
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '576.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2.a1.a1', 'complements': ['3.a1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['192.a1.b1', '192.b1.a1', '192.c1.b1', '288.a1.b1', '288.c1.b1', '288.e1.b1', '288.p1.a1', '288.p1.b1', '288.s1.c1', '288.s1.d1'], 'contains': ['1728.a1.a1'], 'core': '576.a1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [4], 'label': '1728.34767.576.a1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '576.a1.b1', 'normal_contained_in': ['192.a1.b1', '192.b1.a1', '288.a1.b1', '288.c1.b1', '288.e1.b1'], 'normal_contains': ['1728.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '576.a1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.a1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301606
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '576.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2.e1.a1', 'complements': ['3.b1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['192.a1.a1', '192.a1.b1', '192.d1.a1', '288.b1.a1', '288.d1.a1', '288.f1.a1', '288.q1.a1', '288.q1.b1', '288.q1.c1', '288.q1.d1'], 'contains': ['1728.a1.a1'], 'core': '576.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [576], 'label': '1728.34767.576.b1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '576.b1.a1', 'normal_contained_in': ['192.a1.b1', '192.a1.a1', '288.b1.a1', '288.d1.a1', '288.f1.a1'], 'normal_contains': ['1728.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '576.b1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.b1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301607
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '576.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['192.a1.a1', '192.c1.b1', '192.e1.a1', '288.g1.a1', '288.j1.a1', '288.m1.a1', '288.r1.c1', '288.r1.d1'], 'contains': ['1728.a1.a1'], 'core': '1728.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [1200], 'label': '1728.34767.576.c1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '192.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.b1', 'old_label': '576.c1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.c1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301608
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '576.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['192.a1.b1', '192.c1.a1', '192.e1.a1', '288.g1.b1', '288.j1.b1', '288.m1.b1', '288.r1.a1', '288.r1.b1'], 'contains': ['1728.a1.a1'], 'core': '1728.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [1156], 'label': '1728.34767.576.c1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '192.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '576.c1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.c1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301609
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '576.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['192.b1.a1', '192.d1.a1', '192.e1.a1', '288.h1.a1', '288.k1.a1', '288.n1.a1'], 'contains': ['1728.a1.a1'], 'core': '1728.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [100], 'label': '1728.34767.576.d1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '192.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.h1.a1', 'old_label': '576.d1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.d1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301610
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '8.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.f1.a1', '4.f1.b1', '4.k1.a1', '4.n1.a1', '4.p1.a1', '4.p1.b1', '4.s1.a1'], 'contains': ['16.a1.a1', '16.d1.a1', '16.d1.b1', '24.u1.a1', '24.u1.b1', '24.ba1.a1', '24.ba1.b1', '24.bg1.a1', '24.bn1.a1', '24.bq1.a1'], 'core': '8.j1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [475, 576, 48, 936, 864, 4], 'label': '1728.34767.8.j1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.j1.a1', 'normal_contained_in': ['4.f1.b1', '4.f1.a1', '4.k1.a1', '4.n1.a1', '4.p1.b1', '4.p1.a1', '4.s1.a1'], 'normal_contains': ['16.a1.a1', '16.d1.a1', '16.d1.b1'], 'normalizer': '1.a1.a1', 'old_label': '8.j1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.j1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301611
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '576.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['192.c1.a1', '192.c1.b1', '192.d1.a1', '192.e1.a1', '288.i1.a1', '288.l1.a1', '288.o1.a1'], 'contains': ['1728.a1.a1'], 'core': '1728.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [1204], 'label': '1728.34767.576.e1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '64.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.k1.a1', 'old_label': '576.e1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '576.e1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301612
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '864.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['288.a1.a1', '288.a1.b1', '288.b1.a1', '288.g1.a1', '288.g1.b1', '288.h1.a1', '288.i1.a1', '432.a1.a1', '432.b1.a1', '432.b1.b1', '432.b1.c1', '432.b1.d1', '432.c1.a1', '432.c1.b1'], 'contains': ['1728.a1.a1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [936], 'label': '1728.34767.864.a1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '864.a1.a1', 'normal_contained_in': ['288.a1.b1', '288.a1.a1', '288.b1.a1', '432.a1.a1'], 'normal_contains': ['1728.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '864.a1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.a1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301613
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '864.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['288.c1.a1', '288.c1.b1', '288.d1.a1', '288.j1.a1', '288.j1.b1', '288.k1.a1', '288.l1.a1', '432.a1.a1', '432.d1.a1', '432.d1.b1', '432.e1.a1', '432.f1.a1', '432.f1.b1', '432.g1.a1', '432.h1.a1', '432.i1.a1', '432.i1.b1'], 'contains': ['1728.a1.a1'], 'core': '864.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [72], 'label': '1728.34767.864.b1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '864.b1.a1', 'normal_contained_in': ['288.c1.b1', '288.c1.a1', '288.d1.a1', '432.a1.a1'], 'normal_contains': ['1728.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '864.b1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.b1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301614
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '864.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['288.e1.a1', '288.e1.b1', '288.f1.a1', '288.m1.a1', '288.m1.b1', '288.n1.a1', '288.o1.a1', '432.a1.a1', '432.j1.a1', '432.j1.b1', '432.k1.a1', '432.l1.a1', '432.l1.b1', '432.m1.a1', '432.m1.b1', '432.n1.a1'], 'contains': ['1728.a1.a1'], 'core': '864.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [864], 'label': '1728.34767.864.c1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '864.c1.a1', 'normal_contained_in': ['288.e1.b1', '288.e1.a1', '288.f1.a1', '432.a1.a1'], 'normal_contains': ['1728.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '864.c1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.c1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301616
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '864.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.p1.b1', '288.q1.b1', '288.r1.b1', '288.s1.b1', '432.b1.b1', '432.d1.a1', '432.j1.a1'], 'contains': ['1728.a1.a1'], 'core': '1728.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [870], 'label': '1728.34767.864.d1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '144.c1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.e1.a1', 'old_label': '864.d1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.d1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301617
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '864.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6.e1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.p1.c1', '288.q1.c1', '288.r1.c1', '288.s1.c1', '432.b1.c1', '432.d1.b1', '432.j1.b1'], 'contains': ['1728.a1.a1'], 'core': '1728.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [1], 'label': '1728.34767.864.d1.c1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '144.c1.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.e1.b1', 'old_label': '864.d1.c1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.d1.c1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301618
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '864.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '6.e1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['288.p1.d1', '288.q1.d1', '288.r1.d1', '288.s1.d1', '432.b1.d1', '432.d1.b1', '432.j1.b1'], 'contains': ['1728.a1.a1'], 'core': '1728.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [865], 'label': '1728.34767.864.d1.d1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '144.c1.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.e1.b1', 'old_label': '864.d1.d1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '864.d1.d1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301619
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '1728.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1.a1.a1', 'complements': ['1.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['576.a1.a1', '576.a1.b1', '576.b1.a1', '576.c1.a1', '576.c1.b1', '576.d1.a1', '576.e1.a1', '864.a1.a1', '864.b1.a1', '864.c1.a1', '864.d1.a1', '864.d1.b1', '864.d1.c1', '864.d1.d1'], 'contains': [], 'core': '1728.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [], 'label': '1728.34767.1728.a1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1728.a1.a1', 'normal_contained_in': ['576.a1.b1', '576.a1.a1', '576.b1.a1', '864.a1.a1', '864.b1.a1', '864.c1.a1'], 'normal_contains': [], 'normalizer': '1.a1.a1', 'old_label': '1728.a1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1728.a1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301620
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '8.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.e1.a1', '4.e1.b1', '4.k1.a1', '4.m1.a1', '4.q1.a1', '4.q1.b1', '4.t1.a1'], 'contains': ['16.a1.a1', '16.n1.a1', '24.v1.a1', '24.v1.b1', '24.bb1.a1', '24.bb1.b1', '24.bh1.a1', '24.bo1.a1', '24.br1.a1'], 'core': '8.k1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [43, 576, 48, 936, 864, 4], 'label': '1728.34767.8.k1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.k1.a1', 'normal_contained_in': ['4.e1.b1', '4.e1.a1', '4.k1.a1', '4.m1.a1', '4.q1.b1', '4.q1.a1', '4.t1.a1'], 'normal_contains': ['16.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.k1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.k1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301621
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '8.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.b1.a1', 'complements': ['216.q1.b1', '216.q1.a1', '216.o1.a1', '216.o1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['4.g1.a1'], 'contains': ['16.b1.a1', '16.b1.c1', '16.c1.a1', '24.m1.a1', '24.bs1.a1', '24.bs1.c1'], 'core': '8.l1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [1, 48, 4, 6, 576, 936], 'label': '1728.34767.8.l1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.l1.a1', 'normal_contained_in': ['4.g1.a1'], 'normal_contains': ['16.b1.c1', '16.b1.a1', '16.c1.a1', '24.m1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.l1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.l1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301622
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '8.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.b1.a1', 'complements': ['216.q1.b1', '216.q1.a1', '216.o1.a1', '216.o1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['4.g1.a1'], 'contains': ['16.b1.a1', '16.b1.d1', '16.c1.b1', '24.m1.b1', '24.bs1.b1', '24.bs1.d1'], 'core': '8.l1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [865, 48, 4, 6, 576, 936], 'label': '1728.34767.8.l1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.l1.b1', 'normal_contained_in': ['4.g1.a1'], 'normal_contains': ['16.b1.a1', '16.b1.d1', '16.c1.b1', '24.m1.b1'], 'normalizer': '1.a1.a1', 'old_label': '8.l1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.l1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301623
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '2.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.d1.a1', '4.d1.b1', '4.f1.a1', '4.f1.b1', '4.g1.a1', '4.s1.a1', '4.v1.a1', '6.q1.a1', '6.q1.b1', '6.s1.a1'], 'core': '2.g1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [1, 864, 4, 6, 936, 576, 48, 468], 'label': '1728.34767.2.g1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.g1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.d1.b1', '4.d1.a1', '4.f1.b1', '4.f1.a1', '4.g1.a1', '4.s1.a1', '4.v1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.g1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2.g1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301624
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '8.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.b1.a1', 'complements': ['216.q1.b1', '216.q1.a1', '216.o1.a1', '216.o1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['4.g1.a1'], 'contains': ['16.b1.b1', '16.b1.c1', '16.c1.b1', '24.m1.c1', '24.bs1.e1', '24.bs1.g1'], 'core': '8.l1.c1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [1, 48, 4, 870, 576, 936], 'label': '1728.34767.8.l1.c1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.l1.c1', 'normal_contained_in': ['4.g1.a1'], 'normal_contains': ['16.b1.c1', '16.b1.b1', '16.c1.b1', '24.m1.c1'], 'normalizer': '1.a1.a1', 'old_label': '8.l1.c1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.l1.c1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301625
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '8.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.b1.a1', 'complements': ['216.q1.b1', '216.q1.a1', '216.o1.a1', '216.o1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['4.g1.a1'], 'contains': ['16.b1.b1', '16.b1.d1', '16.c1.a1', '24.m1.d1', '24.bs1.f1', '24.bs1.h1'], 'core': '8.l1.d1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [865, 48, 4, 870, 576, 936], 'label': '1728.34767.8.l1.d1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.l1.d1', 'normal_contained_in': ['4.g1.a1'], 'normal_contains': ['16.b1.d1', '16.b1.b1', '16.c1.a1', '24.m1.d1'], 'normalizer': '1.a1.a1', 'old_label': '8.l1.d1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.l1.d1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301626
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '8.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1'], 'contains': ['16.e1.a1', '16.f1.a1', '16.j1.a1', '24.bt1.a1', '24.bv1.a1', '24.bx1.a1'], 'core': '32.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [6, 576, 48, 36, 4, 72], 'label': '1728.34767.8.m1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.a1', 'old_label': '8.m1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.m1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301627
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '8.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1.b1'], 'contains': ['16.e1.b1', '16.f1.a1', '16.j1.b1', '24.bt1.b1', '24.bv1.b1', '24.bx1.b1'], 'core': '32.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [1, 576, 4, 36, 48, 72], 'label': '1728.34767.8.m1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.b1', 'old_label': '8.m1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.m1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301628
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '8.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.c1.a1'], 'contains': ['16.e1.a1', '16.g1.a1', '16.i1.a1', '24.bu1.a1', '24.bw1.a1', '24.by1.a1'], 'core': '32.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [433, 48, 4, 6, 576, 72], 'label': '1728.34767.8.n1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1.a1', 'old_label': '8.n1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.n1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301629
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '8.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.c1.b1'], 'contains': ['16.e1.b1', '16.g1.b1', '16.i1.a1', '24.bu1.b1', '24.bw1.b1', '24.by1.b1'], 'core': '32.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [1, 48, 4, 438, 576, 72], 'label': '1728.34767.8.n1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1.b1', 'old_label': '8.n1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.n1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301630
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '8.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.o1.a1'], 'contains': ['16.g1.a1', '16.h1.a1', '16.j1.b1', '24.bz1.a1', '24.ca1.b1', '24.cb1.a1'], 'core': '32.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [433, 576, 4, 468, 48, 72], 'label': '1728.34767.8.o1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.o1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.o1.a1', 'old_label': '8.o1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.o1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301631
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '8.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.o1.b1'], 'contains': ['16.g1.b1', '16.h1.a1', '16.j1.a1', '24.bz1.b1', '24.ca1.a1', '24.cb1.b1'], 'core': '32.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [438, 576, 48, 468, 4, 72], 'label': '1728.34767.8.o1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.o1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.o1.b1', 'old_label': '8.o1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.o1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301632
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '8.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.f1.a1'], 'contains': ['16.d1.a1', '16.k1.a1', '16.m1.a1', '24.cc1.a1', '24.cd1.a1', '24.ce1.a1', '24.cf1.a1'], 'core': '16.d1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [469, 576, 48, 6, 864, 4], 'label': '1728.34767.8.p1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '8.p1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.p1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301633
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '8.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.f1.a1'], 'contains': ['16.d1.b1', '16.k1.a1', '16.m1.a1', '24.cc1.b1', '24.cd1.b1', '24.ce1.b1', '24.cf1.b1'], 'core': '16.d1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [1405, 576, 48, 6, 864, 4], 'label': '1728.34767.8.p1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '8.p1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.p1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301686
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '12.v1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1.b1', '6.j1.b1'], 'contains': ['24.o1.b1', '24.w1.b1', '24.x1.b1', '36.a1.b1', '36.o1.b1'], 'core': '36.a1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [1, 4, 864, 432, 1200, 936], 'label': '1728.34767.12.v1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.b1', 'old_label': '12.v1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.v1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301634
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '2.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': ['864.d1.a1', '864.d1.b1', '864.d1.c1', '864.d1.d1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.h1.a1', '4.i1.a1', '4.k1.a1', '4.m1.a1', '4.n1.a1', '4.s1.a1', '4.t1.a1', '6.t1.a1', '6.t1.b1', '6.x1.a1', '6.bb1.a1'], 'core': '2.h1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [7, 864, 4, 36, 936, 576, 48, 432], 'label': '1728.34767.2.h1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.h1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.h1.a1', '4.i1.a1', '4.k1.a1', '4.m1.a1', '4.n1.a1', '4.s1.a1', '4.t1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.h1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2.h1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301635
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '8.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.f1.b1'], 'contains': ['16.d1.a1', '16.k1.b1', '16.m1.b1', '24.cc1.c1', '24.cd1.c1', '24.ce1.c1', '24.cf1.c1'], 'core': '16.d1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [937, 576, 48, 474, 864, 4], 'label': '1728.34767.8.p1.c1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.f1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.b1', 'old_label': '8.p1.c1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.p1.c1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301636
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '8.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.f1.b1'], 'contains': ['16.d1.b1', '16.k1.b1', '16.m1.b1', '24.cc1.d1', '24.cd1.d1', '24.ce1.d1', '24.cf1.d1'], 'core': '16.d1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [1, 576, 48, 474, 864, 4], 'label': '1728.34767.8.p1.d1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.f1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.b1', 'old_label': '8.p1.d1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.p1.d1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301637
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '8.q1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.k1.a1'], 'contains': ['16.d1.a1', '16.l1.a1', '16.n1.a1', '24.cg1.a1', '24.cg1.c1', '24.ch1.a1', '24.ch1.c1', '24.ci1.a1', '24.cj1.a1', '24.cj1.b1', '24.ck1.a1', '24.ck1.b1'], 'core': '16.d1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [979, 576, 48, 432, 864, 4], 'label': '1728.34767.8.q1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.k1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.h1.a1', 'old_label': '8.q1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.q1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301638
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '8.q1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.k1.a1'], 'contains': ['16.d1.b1', '16.l1.a1', '16.n1.a1', '24.cg1.b1', '24.cg1.d1', '24.ch1.b1', '24.ch1.d1', '24.ci1.b1', '24.cj1.c1', '24.cj1.d1', '24.ck1.c1', '24.ck1.d1'], 'core': '16.d1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [43, 576, 48, 432, 864, 4], 'label': '1728.34767.8.q1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.k1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.h1.a1', 'old_label': '8.q1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.q1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301639
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '9.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1.a1', '3.a1.b1'], 'contains': ['18.e1.a1', '18.e1.b1', '18.f1.a1', '18.f1.b1', '18.g1.a1', '18.g1.b1', '18.h1.a1', '18.h1.b1', '18.j1.a1', '18.k1.a1', '18.l1.a1', '18.x1.a1', '18.y1.a1', '18.z1.a1', '18.ba1.a1', '27.a1.a1'], 'core': '36.b1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [1, 864, 936, 6, 576, 36, 432], 'label': '1728.34767.9.a1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '9.a1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '9.a1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301640
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '9.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1.a1', '3.b1.a1'], 'contains': ['18.a1.a1', '18.b1.a1', '18.c1.a1', '18.d1.a1', '18.m1.b1', '18.n1.b1', '18.o1.b1', '18.p1.b1', '18.q1.a1', '18.r1.a1', '18.s1.a1', '18.t1.b1', '18.u1.b1', '18.v1.b1', '18.w1.b1', '27.a1.a1'], 'core': '36.a1.b1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [1, 864, 936, 6, 4, 36, 432], 'label': '1728.34767.9.b1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1.a1', 'old_label': '9.b1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '9.b1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301641
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '9.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1.b1', '3.b1.a1'], 'contains': ['18.a1.b1', '18.b1.b1', '18.c1.b1', '18.d1.b1', '18.m1.a1', '18.n1.a1', '18.o1.a1', '18.p1.a1', '18.q1.b1', '18.r1.b1', '18.s1.b1', '18.t1.a1', '18.u1.a1', '18.v1.a1', '18.w1.a1', '27.a1.a1'], 'core': '36.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [1, 864, 936, 6, 48, 36, 432], 'label': '1728.34767.9.b1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1.b1', 'old_label': '9.b1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '9.b1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301642
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '12.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.a1.b1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '6.a1.a1', '6.g1.a1', '6.o1.b1'], 'contains': ['24.a1.a1', '24.c1.a1', '24.e1.a1', '36.a1.a1', '36.i1.a1'], 'core': '12.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [6, 48, 864, 432, 576, 936], 'label': '1728.34767.12.a1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1.a1', 'normal_contained_in': ['4.a1.a1', '6.a1.a1'], 'normal_contains': ['24.a1.a1', '24.c1.a1', '24.e1.a1', '36.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '12.a1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.a1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301643
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '12.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.b1', '6.a1.b1', '6.g1.b1', '6.o1.a1'], 'contains': ['24.a1.b1', '24.c1.b1', '24.e1.b1', '36.a1.b1', '36.i1.b1'], 'core': '12.a1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [1, 4, 864, 432, 576, 936], 'label': '1728.34767.12.a1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1.b1', 'normal_contained_in': ['4.a1.b1', '6.a1.b1'], 'normal_contains': ['24.a1.b1', '24.c1.b1', '24.e1.b1', '36.a1.b1'], 'normalizer': '1.a1.a1', 'old_label': '12.a1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.a1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301644
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '12.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.a1.b1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '6.a1.a1', '6.h1.a1', '6.p1.b1'], 'contains': ['24.a1.a1', '24.d1.a1', '24.g1.a1', '24.bv1.a1', '36.j1.a1', '36.s1.a1'], 'core': '12.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [6, 576, 48, 36, 864, 72], 'label': '1728.34767.12.b1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.b1.a1', 'normal_contained_in': ['4.b1.a1', '6.a1.a1'], 'normal_contains': ['24.a1.a1', '24.d1.a1', '24.g1.a1'], 'normalizer': '1.a1.a1', 'old_label': '12.b1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.b1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301645
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '2.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': ['864.d1.c1', '864.d1.d1', '864.d1.a1', '864.d1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.i1.a1', '4.j1.a1', '4.j1.b1', '4.u1.a1', '4.v1.a1', '4.w1.a1', '4.w1.b1', '6.u1.a1', '6.u1.b1', '6.y1.a1'], 'core': '2.i1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [37, 864, 4, 42, 72, 576, 48, 432], 'label': '1728.34767.2.i1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.i1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.i1.a1', '4.j1.a1', '4.j1.b1', '4.v1.a1', '4.u1.a1', '4.w1.b1', '4.w1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.i1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2.i1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301646
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '12.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.b1.b1', '6.a1.b1', '6.h1.b1', '6.p1.a1'], 'contains': ['24.a1.b1', '24.d1.b1', '24.g1.b1', '24.bv1.b1', '36.j1.b1', '36.s1.b1'], 'core': '12.b1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [1, 576, 4, 36, 864, 72], 'label': '1728.34767.12.b1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.b1.b1', 'normal_contained_in': ['4.b1.b1', '6.a1.b1'], 'normal_contains': ['24.a1.b1', '24.d1.b1', '24.g1.b1'], 'normalizer': '1.a1.a1', 'old_label': '12.b1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.b1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301647
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '12.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.a1.b1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.d1.a1', '6.a1.a1', '6.i1.a1', '6.q1.b1'], 'contains': ['24.a1.a1', '24.f1.a1', '24.h1.a1', '36.l1.a1', '36.u1.a1'], 'core': '12.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [6, 576, 48, 468, 936, 864], 'label': '1728.34767.12.c1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.c1.a1', 'normal_contained_in': ['4.d1.a1', '6.a1.a1'], 'normal_contains': ['24.a1.a1', '24.f1.a1', '24.h1.a1'], 'normalizer': '1.a1.a1', 'old_label': '12.c1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.c1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301648
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '12.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.d1.b1', '6.a1.b1', '6.i1.b1', '6.q1.a1'], 'contains': ['24.a1.b1', '24.f1.b1', '24.h1.b1', '36.l1.b1', '36.u1.b1'], 'core': '12.c1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [1, 576, 4, 468, 936, 864], 'label': '1728.34767.12.c1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.c1.b1', 'normal_contained_in': ['4.d1.b1', '6.a1.b1'], 'normal_contains': ['24.a1.b1', '24.f1.b1', '24.h1.b1'], 'normalizer': '1.a1.a1', 'old_label': '12.c1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.c1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301649
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '12.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.a1.b1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '6.b1.a1', '6.k1.a1', '6.l1.a1'], 'contains': ['24.b1.a1', '24.i1.a1', '24.j1.b1', '36.a1.a1', '36.c1.a1'], 'core': '12.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [6, 48, 864, 432, 4, 936], 'label': '1728.34767.12.d1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.d1.a1', 'normal_contained_in': ['4.a1.a1', '6.b1.a1'], 'normal_contains': ['24.b1.a1', '24.i1.a1', '24.j1.b1', '36.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '12.d1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.d1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301687
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '12.w1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.e1.a1', '6.j1.a1'], 'contains': ['24.o1.a1', '24.y1.a1', '24.bb1.a1', '36.p1.a1', '36.v1.a1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [37, 48, 1156, 6, 72, 864], 'label': '1728.34767.12.w1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.j1.a1', 'old_label': '12.w1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.w1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301650
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '12.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.b1', '6.b1.a1', '6.k1.b1', '6.l1.b1'], 'contains': ['24.b1.b1', '24.i1.a1', '24.j1.a1', '36.a1.b1', '36.c1.b1'], 'core': '12.d1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [1, 4, 864, 432, 48, 936], 'label': '1728.34767.12.d1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.d1.b1', 'normal_contained_in': ['4.a1.b1', '6.b1.a1'], 'normal_contains': ['24.b1.b1', '24.i1.a1', '24.j1.a1', '36.a1.b1'], 'normalizer': '1.a1.a1', 'old_label': '12.d1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.d1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301651
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '12.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.c1.a1', '6.b1.a1', '6.m1.a1', '6.n1.a1'], 'contains': ['24.b1.a1', '24.j1.a1', '24.l1.a1', '24.by1.a1', '36.e1.a1', '36.t1.a1'], 'core': '12.e1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [433, 48, 4, 6, 864, 72], 'label': '1728.34767.12.e1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.e1.a1', 'normal_contained_in': ['4.c1.a1', '6.b1.a1'], 'normal_contains': ['24.b1.a1', '24.j1.a1', '24.l1.a1'], 'normalizer': '1.a1.a1', 'old_label': '12.e1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.e1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301652
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '12.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.c1.b1', '6.b1.a1', '6.m1.b1', '6.n1.b1'], 'contains': ['24.b1.b1', '24.j1.b1', '24.l1.a1', '24.by1.b1', '36.e1.b1', '36.t1.b1'], 'core': '12.e1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [1, 48, 4, 438, 864, 72], 'label': '1728.34767.12.e1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.e1.b1', 'normal_contained_in': ['4.c1.b1', '6.b1.a1'], 'normal_contains': ['24.b1.b1', '24.j1.b1', '24.l1.a1'], 'normalizer': '1.a1.a1', 'old_label': '12.e1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.e1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301653
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '12.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.e1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.g1.a1', '6.b1.a1', '6.r1.a1', '6.s1.a1'], 'contains': ['24.b1.a1', '24.b1.b1', '24.k1.a1', '24.m1.a1', '24.m1.b1', '24.m1.c1', '24.m1.d1', '36.x1.a1', '36.x1.b1'], 'core': '12.f1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [1, 48, 4, 6, 864, 936], 'label': '1728.34767.12.f1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.f1.a1', 'normal_contained_in': ['4.g1.a1', '6.b1.a1'], 'normal_contains': ['24.b1.b1', '24.b1.a1', '24.k1.a1', '24.m1.a1', '24.m1.c1', '24.m1.b1', '24.m1.d1'], 'normalizer': '1.a1.a1', 'old_label': '12.f1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.f1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301654
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '12.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.h1.a1', '6.a1.a1', '6.c1.b1', '6.t1.a1'], 'contains': ['24.c1.a1', '24.d1.a1', '24.f1.a1', '36.b1.a1', '36.y1.a1'], 'core': '12.g1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [36, 576, 864, 432, 48, 72], 'label': '1728.34767.12.g1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.g1.a1', 'normal_contained_in': ['4.h1.a1', '6.a1.a1'], 'normal_contains': ['24.c1.a1', '24.d1.a1', '24.f1.a1', '36.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '12.g1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.g1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301655
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '12.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.h1.a1', '6.a1.b1', '6.c1.a1', '6.t1.b1'], 'contains': ['24.c1.b1', '24.d1.b1', '24.f1.b1', '36.b1.a1', '36.y1.b1'], 'core': '12.g1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [36, 576, 864, 432, 4, 72], 'label': '1728.34767.12.g1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.g1.b1', 'normal_contained_in': ['4.h1.a1', '6.a1.b1'], 'normal_contains': ['24.c1.b1', '24.d1.b1', '24.f1.b1', '36.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '12.g1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.g1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301656
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '2.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': ['864.d1.c1', '864.d1.d1', '864.d1.a1', '864.d1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.l1.a1', '4.l1.b1', '4.m1.a1', '4.q1.a1', '4.q1.b1', '4.r1.a1', '4.v1.a1', '6.v1.a1', '6.v1.b1', '6.z1.a1'], 'core': '2.j1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [433, 864, 4, 438, 72, 576, 48, 36], 'label': '1728.34767.2.j1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.j1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.l1.b1', '4.l1.a1', '4.m1.a1', '4.q1.b1', '4.q1.a1', '4.r1.a1', '4.v1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.j1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2.j1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301657
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '12.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.a1.b1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.j1.a1', '6.a1.a1', '6.d1.b1', '6.u1.a1'], 'contains': ['24.c1.a1', '24.g1.a1', '24.h1.a1', '36.bb1.a1', '36.bv1.a1', '36.cj1.a1'], 'core': '12.h1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [42, 576, 48, 432, 72, 864], 'label': '1728.34767.12.h1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.h1.a1', 'normal_contained_in': ['4.j1.a1', '6.a1.a1'], 'normal_contains': ['24.c1.a1', '24.h1.a1', '24.g1.a1'], 'normalizer': '1.a1.a1', 'old_label': '12.h1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.h1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301658
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '12.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.j1.b1', '6.a1.b1', '6.d1.a1', '6.u1.b1'], 'contains': ['24.c1.b1', '24.g1.b1', '24.h1.b1', '36.bb1.b1', '36.bv1.b1', '36.cj1.b1'], 'core': '12.h1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [37, 576, 4, 432, 72, 864], 'label': '1728.34767.12.h1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.h1.b1', 'normal_contained_in': ['4.j1.b1', '6.a1.b1'], 'normal_contains': ['24.c1.b1', '24.h1.b1', '24.g1.b1'], 'normalizer': '1.a1.a1', 'old_label': '12.h1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.h1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301659
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '12.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.a1.b1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.l1.b1', '6.a1.a1', '6.e1.b1', '6.v1.a1'], 'contains': ['24.d1.a1', '24.e1.a1', '24.h1.a1', '36.be1.a1', '36.bx1.b1'], 'core': '12.i1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [438, 576, 48, 36, 72, 864], 'label': '1728.34767.12.i1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.i1.a1', 'normal_contained_in': ['4.l1.b1', '6.a1.a1'], 'normal_contains': ['24.d1.a1', '24.e1.a1', '24.h1.a1'], 'normalizer': '1.a1.a1', 'old_label': '12.i1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.i1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301660
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '12.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.l1.a1', '6.a1.b1', '6.e1.a1', '6.v1.b1'], 'contains': ['24.d1.b1', '24.e1.b1', '24.h1.b1', '36.be1.b1', '36.bx1.a1'], 'core': '12.i1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [433, 576, 4, 36, 72, 864], 'label': '1728.34767.12.i1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.i1.b1', 'normal_contained_in': ['4.l1.a1', '6.a1.b1'], 'normal_contains': ['24.d1.b1', '24.e1.b1', '24.h1.b1'], 'normalizer': '1.a1.a1', 'old_label': '12.i1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.i1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301661
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '12.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.a1.b1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.o1.b1', '6.a1.a1', '6.f1.b1', '6.w1.a1'], 'contains': ['24.e1.a1', '24.f1.a1', '24.g1.a1', '24.ca1.a1', '36.bk1.a1', '36.ca1.b1'], 'core': '12.j1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [438, 576, 48, 468, 864, 72], 'label': '1728.34767.12.j1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.j1.a1', 'normal_contained_in': ['4.o1.b1', '6.a1.a1'], 'normal_contains': ['24.e1.a1', '24.f1.a1', '24.g1.a1'], 'normalizer': '1.a1.a1', 'old_label': '12.j1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.j1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301662
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '12.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.o1.a1', '6.a1.b1', '6.f1.a1', '6.w1.b1'], 'contains': ['24.e1.b1', '24.f1.b1', '24.g1.b1', '24.ca1.b1', '36.bk1.b1', '36.ca1.a1'], 'core': '12.j1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [433, 576, 4, 468, 864, 72], 'label': '1728.34767.12.j1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.j1.b1', 'normal_contained_in': ['4.o1.a1', '6.a1.b1'], 'normal_contains': ['24.e1.b1', '24.f1.b1', '24.g1.b1'], 'normalizer': '1.a1.a1', 'old_label': '12.j1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.j1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301663
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '12.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.d1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.i1.a1', '6.b1.a1', '6.x1.a1', '6.y1.a1'], 'contains': ['24.i1.a1', '24.k1.a1', '24.l1.a1', '36.z1.a1', '36.z1.b1', '36.co1.a1'], 'core': '12.k1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [7, 48, 4, 432, 936, 864], 'label': '1728.34767.12.k1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.k1.a1', 'normal_contained_in': ['4.i1.a1', '6.b1.a1'], 'normal_contains': ['24.i1.a1', '24.k1.a1', '24.l1.a1'], 'normalizer': '1.a1.a1', 'old_label': '12.k1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.k1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301664
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '12.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.r1.a1', '6.b1.a1', '6.z1.a1', '6.ba1.a1'], 'contains': ['24.j1.a1', '24.j1.b1', '24.k1.a1', '36.bn1.a1', '36.bn1.b1'], 'core': '12.l1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [433, 48, 4, 438, 72, 864], 'label': '1728.34767.12.l1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.l1.a1', 'normal_contained_in': ['4.r1.a1', '6.b1.a1'], 'normal_contains': ['24.j1.b1', '24.j1.a1', '24.k1.a1'], 'normalizer': '1.a1.a1', 'old_label': '12.l1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.l1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301665
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '12.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '6.c1.a1', '6.d1.a1', '6.o1.a1'], 'contains': ['24.c1.b1', '24.n1.a1', '24.p1.b1', '36.c1.a1', '36.i1.a1', '36.o1.a1'], 'core': '24.c1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [6, 864, 936, 432, 4, 576], 'label': '1728.34767.12.m1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.m1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.m1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301666
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '12.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1.b1', '6.c1.b1', '6.d1.b1', '6.o1.b1'], 'contains': ['24.c1.a1', '24.n1.b1', '24.p1.a1', '36.c1.b1', '36.i1.b1', '36.o1.b1'], 'core': '24.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [1, 864, 936, 432, 48, 576], 'label': '1728.34767.12.m1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.b1', 'old_label': '12.m1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.m1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301667
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '2.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': ['864.d1.c1', '864.d1.d1', '864.d1.a1', '864.d1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.o1.a1', '4.o1.b1', '4.p1.a1', '4.p1.b1', '4.r1.a1', '4.s1.a1', '4.u1.a1', '6.w1.a1', '6.w1.b1', '6.ba1.a1'], 'core': '2.k1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [433, 864, 4, 438, 72, 576, 48, 468], 'label': '1728.34767.2.k1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.k1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.o1.b1', '4.o1.a1', '4.p1.b1', '4.p1.a1', '4.r1.a1', '4.s1.a1', '4.u1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.k1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2.k1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301668
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '12.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '6.c1.a1', '6.e1.a1', '6.p1.a1'], 'contains': ['24.d1.b1', '24.n1.a1', '24.s1.b1', '24.bt1.a1', '36.d1.a1', '36.j1.a1'], 'core': '24.d1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [6, 576, 72, 36, 864, 4], 'label': '1728.34767.12.n1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.n1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.n1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301669
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '12.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.g1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1.b1', '6.c1.b1', '6.e1.b1', '6.p1.b1'], 'contains': ['24.d1.a1', '24.n1.b1', '24.s1.a1', '24.bt1.b1', '36.d1.b1', '36.j1.b1'], 'core': '24.d1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [1, 576, 72, 36, 864, 48], 'label': '1728.34767.12.n1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.b1', 'old_label': '12.n1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.n1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301670
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '12.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.c1.a1', '6.e1.a1', '6.f1.a1', '6.o1.a1'], 'contains': ['24.e1.b1', '24.n1.a1', '24.r1.b1', '24.bu1.a1', '36.e1.a1', '36.k1.a1'], 'core': '24.e1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [433, 4, 72, 6, 864, 576], 'label': '1728.34767.12.o1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.o1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.o1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301671
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '12.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.h1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.c1.b1', '6.e1.b1', '6.f1.b1', '6.o1.b1'], 'contains': ['24.e1.a1', '24.n1.b1', '24.r1.a1', '24.bu1.b1', '36.e1.b1', '36.k1.b1'], 'core': '24.e1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [1, 48, 72, 438, 864, 576], 'label': '1728.34767.12.o1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.b1', 'old_label': '12.o1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.o1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301672
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '12.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.d1.a1', '6.c1.a1', '6.f1.a1', '6.q1.a1'], 'contains': ['24.f1.b1', '24.n1.a1', '24.t1.b1', '36.f1.a1', '36.l1.a1'], 'core': '24.f1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [6, 576, 864, 468, 4, 936], 'label': '1728.34767.12.p1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.p1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.p1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301673
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '12.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.d1.b1', '6.c1.b1', '6.f1.b1', '6.q1.b1'], 'contains': ['24.f1.a1', '24.n1.b1', '24.t1.a1', '36.f1.b1', '36.l1.b1'], 'core': '24.f1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [1, 576, 864, 468, 48, 936], 'label': '1728.34767.12.p1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.b1', 'old_label': '12.p1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.p1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301674
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '12.q1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.e1.a1', '6.d1.a1', '6.f1.a1', '6.p1.a1'], 'contains': ['24.g1.b1', '24.n1.a1', '24.v1.b1', '36.g1.a1', '36.m1.a1', '36.p1.a1'], 'core': '24.g1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [37, 576, 4, 6, 72, 864], 'label': '1728.34767.12.q1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.q1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.q1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301675
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '12.q1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.e1.b1', '6.d1.b1', '6.f1.b1', '6.p1.b1'], 'contains': ['24.g1.a1', '24.n1.b1', '24.v1.a1', '36.g1.b1', '36.m1.b1', '36.p1.b1'], 'core': '24.g1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [1, 576, 48, 42, 936, 864], 'label': '1728.34767.12.q1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.b1', 'old_label': '12.q1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.q1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301676
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '12.r1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.f1.a1', '6.d1.a1', '6.e1.a1', '6.q1.a1'], 'contains': ['24.h1.b1', '24.n1.a1', '24.u1.b1', '24.cc1.a1', '24.cc1.b1', '36.h1.a1', '36.n1.a1', '36.q1.a1'], 'core': '24.h1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [469, 576, 4, 6, 936, 864], 'label': '1728.34767.12.r1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.r1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.r1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301677
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '12.r1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.f1.b1', '6.d1.b1', '6.e1.b1', '6.q1.b1'], 'contains': ['24.h1.a1', '24.n1.b1', '24.u1.a1', '24.cc1.c1', '24.cc1.d1', '36.h1.b1', '36.n1.b1', '36.q1.b1'], 'core': '24.h1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [1, 576, 48, 474, 936, 864], 'label': '1728.34767.12.r1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.f1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.b1', 'old_label': '12.r1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.r1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301678
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '3.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['6.a1.b1', '6.c1.a1', '6.d1.a1', '6.e1.a1', '6.f1.a1', '6.g1.b1', '6.h1.b1', '6.i1.b1', '6.o1.a1', '6.p1.a1', '6.q1.a1', '6.t1.b1', '6.u1.b1', '6.v1.b1', '6.w1.b1', '9.a1.a1', '9.b1.a1'], 'core': '6.a1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [1, 936, 864, 6, 432, 576, 4, 36], 'label': '1728.34767.3.a1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '3.a1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3.a1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301679
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '12.s1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.u1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.c1.a1', '6.h1.a1', '6.i1.a1', '6.o1.b1'], 'contains': ['24.a1.a1', '24.p1.a1', '24.r1.a1', '24.bw1.a1', '36.k1.a1', '36.t1.a1'], 'core': '24.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [433, 48, 72, 6, 864, 576], 'label': '1728.34767.12.s1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.b1', 'old_label': '12.s1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.s1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301680
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '12.s1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.u1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.c1.b1', '6.h1.b1', '6.i1.b1', '6.o1.a1'], 'contains': ['24.a1.b1', '24.p1.b1', '24.r1.b1', '24.bw1.b1', '36.k1.b1', '36.t1.b1'], 'core': '24.a1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [1, 4, 72, 438, 864, 576], 'label': '1728.34767.12.s1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.s1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.s1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301681
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '12.t1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.e1.a1', '6.g1.a1', '6.i1.a1', '6.p1.b1'], 'contains': ['24.a1.a1', '24.s1.a1', '24.v1.a1', '36.m1.a1', '36.v1.a1'], 'core': '24.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [37, 576, 48, 6, 72, 864], 'label': '1728.34767.12.t1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.b1', 'old_label': '12.t1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.t1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301682
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '12.t1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.e1.b1', '6.g1.b1', '6.i1.b1', '6.p1.a1'], 'contains': ['24.a1.b1', '24.s1.b1', '24.v1.b1', '36.m1.b1', '36.v1.b1'], 'core': '24.a1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [1, 576, 4, 42, 936, 864], 'label': '1728.34767.12.t1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.t1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.t1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301683
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '12.u1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.f1.a1', '6.g1.a1', '6.h1.a1', '6.q1.b1'], 'contains': ['24.a1.a1', '24.t1.a1', '24.u1.a1', '24.cd1.a1', '24.cd1.b1', '36.n1.a1', '36.w1.a1'], 'core': '24.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [469, 576, 48, 6, 936, 864], 'label': '1728.34767.12.u1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.b1', 'old_label': '12.u1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.u1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301684
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '12.u1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.f1.b1', '6.g1.b1', '6.h1.b1', '6.q1.a1'], 'contains': ['24.a1.b1', '24.t1.b1', '24.u1.b1', '24.cd1.c1', '24.cd1.d1', '36.n1.b1', '36.w1.b1'], 'core': '24.a1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [1, 576, 4, 474, 936, 864], 'label': '1728.34767.12.u1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.f1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.u1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.u1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301685
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '12.v1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '6.j1.a1'], 'contains': ['24.o1.a1', '24.w1.a1', '24.x1.a1', '36.a1.a1', '36.o1.a1'], 'core': '36.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [6, 48, 864, 432, 1156, 936], 'label': '1728.34767.12.v1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '12.v1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.v1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301688
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '12.w1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.e1.b1', '6.j1.b1'], 'contains': ['24.o1.b1', '24.y1.b1', '24.bb1.b1', '36.p1.b1', '36.v1.b1'], 'core': '72.a1.b1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [1, 1200, 4, 42, 936, 864], 'label': '1728.34767.12.w1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.j1.b1', 'old_label': '12.w1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.w1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301689
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '3.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['6.a1.a1', '6.c1.b1', '6.d1.b1', '6.e1.b1', '6.f1.b1', '6.g1.a1', '6.h1.a1', '6.i1.a1', '6.o1.b1', '6.p1.b1', '6.q1.b1', '6.t1.a1', '6.u1.a1', '6.v1.a1', '6.w1.a1', '9.a1.a1', '9.b1.b1'], 'core': '6.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [1, 936, 864, 6, 432, 576, 48, 36], 'label': '1728.34767.3.a1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.b1', 'old_label': '3.a1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3.a1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301690
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '12.x1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.f1.a1', '6.j1.a1'], 'contains': ['24.o1.a1', '24.z1.a1', '24.ba1.a1', '24.ce1.a1', '24.ce1.b1', '36.q1.a1', '36.w1.a1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [469, 48, 1156, 6, 936, 864], 'label': '1728.34767.12.x1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.j1.a1', 'old_label': '12.x1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.x1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301691
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '12.x1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.f1.b1', '6.j1.b1'], 'contains': ['24.o1.b1', '24.z1.b1', '24.ba1.b1', '24.ce1.c1', '24.ce1.d1', '36.q1.b1', '36.w1.b1'], 'core': '72.a1.b1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [1, 1200, 4, 474, 936, 864], 'label': '1728.34767.12.x1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.f1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.j1.b1', 'old_label': '12.x1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.x1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301692
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '12.y1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.j1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '6.k1.a1', '6.m1.a1', '6.r1.a1'], 'contains': ['24.b1.a1', '24.bc1.a1', '24.be1.a1', '24.bx1.a1', '36.d1.a1', '36.s1.a1'], 'core': '24.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [6, 48, 72, 36, 864, 4], 'label': '1728.34767.12.y1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '12.y1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.y1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301693
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '12.y1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1.b1', '6.k1.b1', '6.m1.b1', '6.r1.a1'], 'contains': ['24.b1.b1', '24.bc1.a1', '24.be1.b1', '24.bx1.b1', '36.d1.b1', '36.s1.b1'], 'core': '24.b1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [1, 4, 72, 36, 864, 48], 'label': '1728.34767.12.y1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '12.y1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.y1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301694
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '12.z1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.d1.a1', '6.k1.a1', '6.n1.a1', '6.s1.a1'], 'contains': ['24.b1.a1', '24.bd1.a1', '24.bf1.b1', '36.f1.a1', '36.u1.a1'], 'core': '24.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [6, 48, 864, 468, 4, 936], 'label': '1728.34767.12.z1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '12.z1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.z1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301695
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '12.z1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.d1.b1', '6.k1.b1', '6.n1.b1', '6.s1.a1'], 'contains': ['24.b1.b1', '24.bd1.a1', '24.bf1.a1', '36.f1.b1', '36.u1.b1'], 'core': '24.b1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [1, 4, 864, 468, 48, 936], 'label': '1728.34767.12.z1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '12.z1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.z1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301696
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '12.ba1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.e1.a1', '6.l1.a1', '6.n1.a1', '6.r1.a1'], 'contains': ['24.b1.a1', '24.be1.b1', '24.bh1.a1', '36.g1.a1', '36.v1.a1'], 'core': '24.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [37, 48, 4, 6, 72, 864], 'label': '1728.34767.12.ba1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '12.ba1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.ba1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301697
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '12.ba1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.e1.b1', '6.l1.b1', '6.n1.b1', '6.r1.a1'], 'contains': ['24.b1.b1', '24.be1.a1', '24.bh1.a1', '36.g1.b1', '36.v1.b1'], 'core': '24.b1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [1, 48, 4, 42, 936, 864], 'label': '1728.34767.12.ba1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '12.ba1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.ba1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301698
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '12.bb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.f1.a1', '6.l1.a1', '6.m1.a1', '6.s1.a1'], 'contains': ['24.b1.a1', '24.bf1.a1', '24.bg1.a1', '24.cf1.a1', '24.cf1.b1', '36.h1.a1', '36.w1.a1'], 'core': '24.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [469, 48, 4, 6, 936, 864], 'label': '1728.34767.12.bb1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '12.bb1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bb1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301699
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '12.bb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.f1.b1', '6.l1.b1', '6.m1.b1', '6.s1.a1'], 'contains': ['24.b1.b1', '24.bf1.b1', '24.bg1.a1', '24.cf1.c1', '24.cf1.d1', '36.h1.b1', '36.w1.b1'], 'core': '24.b1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [1, 48, 4, 474, 936, 864], 'label': '1728.34767.12.bb1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.f1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '12.bb1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bb1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301700
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '3.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['6.b1.a1', '6.k1.a1', '6.k1.b1', '6.l1.a1', '6.l1.b1', '6.m1.a1', '6.m1.b1', '6.n1.a1', '6.n1.b1', '6.r1.a1', '6.s1.a1', '6.x1.a1', '6.y1.a1', '6.z1.a1', '6.ba1.a1', '9.b1.a1', '9.b1.b1'], 'core': '6.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [1, 936, 864, 6, 432, 48, 4, 36], 'label': '1728.34767.3.b1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '3.b1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3.b1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301701
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '12.bc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.g1.a1', '6.o1.a1', '6.p1.a1', '6.q1.a1'], 'contains': ['24.a1.b1', '24.n1.a1', '24.q1.b1', '24.bs1.a1', '24.bs1.b1', '24.bs1.e1', '24.bs1.f1', '36.r1.a1', '36.x1.a1'], 'core': '24.a1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [1, 4, 936, 6, 864, 576], 'label': '1728.34767.12.bc1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.bc1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bc1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301702
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '12.bc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.g1.a1', '6.o1.b1', '6.p1.b1', '6.q1.b1'], 'contains': ['24.a1.a1', '24.n1.b1', '24.q1.a1', '24.bs1.c1', '24.bs1.d1', '24.bs1.g1', '24.bs1.h1', '36.r1.a1', '36.x1.b1'], 'core': '24.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [1, 48, 936, 6, 864, 576], 'label': '1728.34767.12.bc1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.b1', 'old_label': '12.bc1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bc1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301703
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '12.bd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.i1.a1', '6.o1.b1', '6.t1.a1', '6.u1.a1'], 'contains': ['24.c1.a1', '24.q1.a1', '24.r1.a1', '36.z1.a1', '36.bu1.a1'], 'core': '24.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [7, 48, 864, 432, 576, 936], 'label': '1728.34767.12.bd1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.i1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.b1', 'old_label': '12.bd1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bd1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301704
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '12.bd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.i1.a1', '6.o1.a1', '6.t1.b1', '6.u1.b1'], 'contains': ['24.c1.b1', '24.q1.b1', '24.r1.b1', '36.z1.b1', '36.bu1.a1'], 'core': '24.c1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [7, 4, 864, 432, 576, 936], 'label': '1728.34767.12.bd1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.i1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.bd1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bd1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301705
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '12.be1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.j1.b1', '6.c1.b1', '6.g1.a1', '6.u1.a1'], 'contains': ['24.c1.a1', '24.s1.a1', '24.t1.a1', '36.ba1.a1', '36.bv1.b1'], 'core': '24.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [37, 576, 864, 432, 48, 72], 'label': '1728.34767.12.be1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.j1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.b1', 'old_label': '12.be1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.be1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301706
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '12.be1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.j1.a1', '6.c1.a1', '6.g1.b1', '6.u1.b1'], 'contains': ['24.c1.b1', '24.s1.b1', '24.t1.b1', '36.ba1.b1', '36.bv1.a1'], 'core': '24.c1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [42, 576, 864, 432, 4, 72], 'label': '1728.34767.12.be1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.j1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.be1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.be1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301707
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '12.bf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.k1.a1', '6.d1.b1', '6.g1.a1', '6.t1.a1'], 'contains': ['24.c1.a1', '24.u1.a1', '24.v1.a1', '24.cg1.a1', '24.cg1.b1', '36.bc1.a1', '36.bw1.a1', '36.ck1.a1'], 'core': '24.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [43, 576, 48, 432, 936, 864], 'label': '1728.34767.12.bf1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.k1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.b1', 'old_label': '12.bf1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bf1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301708
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '12.bf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.k1.a1', '6.d1.a1', '6.g1.b1', '6.t1.b1'], 'contains': ['24.c1.b1', '24.u1.b1', '24.v1.b1', '24.cg1.c1', '24.cg1.d1', '36.bc1.b1', '36.bw1.a1', '36.ck1.b1'], 'core': '24.c1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [43, 576, 4, 432, 936, 864], 'label': '1728.34767.12.bf1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.k1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.bf1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bf1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301709
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '12.bg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.l1.a1', '6.c1.b1', '6.h1.a1', '6.v1.a1'], 'contains': ['24.d1.a1', '24.p1.a1', '24.t1.a1', '36.bd1.a1', '36.bx1.a1'], 'core': '24.d1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [433, 576, 864, 36, 48, 72], 'label': '1728.34767.12.bg1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.l1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.b1', 'old_label': '12.bg1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bg1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301710
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '12.bg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.l1.b1', '6.c1.a1', '6.h1.b1', '6.v1.b1'], 'contains': ['24.d1.b1', '24.p1.b1', '24.t1.b1', '36.bd1.b1', '36.bx1.b1'], 'core': '24.d1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [438, 576, 864, 36, 4, 72], 'label': '1728.34767.12.bg1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.l1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.bg1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bg1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301711
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '2.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.a1.b1', 'complements': ['864.d1.c1', '864.d1.d1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1', '4.b1.a1', '4.d1.a1', '4.h1.a1', '4.j1.a1', '4.l1.b1', '4.o1.b1', '6.a1.a1', '6.c1.a1', '6.k1.a1'], 'core': '2.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [6, 72, 864, 36, 4, 576, 48, 432], 'label': '1728.34767.2.a1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.a1.a1', '4.b1.a1', '4.d1.a1', '4.h1.a1', '4.j1.a1', '4.l1.b1', '4.o1.b1', '6.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.a1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2.a1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301712
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '4.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.a1.b1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '2.b1.a1', '2.e1.a1'], 'contains': ['8.a1.a1', '8.b1.a1', '8.d1.b1', '12.a1.a1', '12.d1.a1', '12.m1.a1', '12.v1.a1'], 'core': '4.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [6, 864, 936, 432, 48, 4, 576], 'label': '1728.34767.4.a1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.a1.a1', 'normal_contained_in': ['2.a1.a1', '2.b1.a1', '2.e1.a1'], 'normal_contains': ['8.a1.a1', '8.b1.a1', '8.d1.b1', '12.a1.a1', '12.d1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.a1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.a1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301713
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '12.bh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.m1.a1', '6.p1.b1', '6.t1.a1', '6.v1.a1'], 'contains': ['24.d1.a1', '24.q1.a1', '24.v1.a1', '36.bf1.a1', '36.by1.a1'], 'core': '24.d1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [7, 576, 48, 36, 936, 864], 'label': '1728.34767.12.bh1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.m1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.b1', 'old_label': '12.bh1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bh1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301714
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '12.bh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.m1.a1', '6.p1.a1', '6.t1.b1', '6.v1.b1'], 'contains': ['24.d1.b1', '24.q1.b1', '24.v1.b1', '36.bf1.b1', '36.by1.a1'], 'core': '24.d1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [7, 576, 4, 36, 936, 864], 'label': '1728.34767.12.bh1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.m1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.bh1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bh1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301715
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '12.bi1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.n1.a1', '6.e1.b1', '6.h1.a1', '6.t1.a1'], 'contains': ['24.d1.a1', '24.r1.a1', '24.u1.a1', '36.bg1.a1', '36.bz1.a1'], 'core': '24.d1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [439, 576, 48, 36, 72, 864], 'label': '1728.34767.12.bi1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.n1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.b1', 'old_label': '12.bi1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bi1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301716
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '12.bi1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.n1.a1', '6.e1.a1', '6.h1.b1', '6.t1.b1'], 'contains': ['24.d1.b1', '24.r1.b1', '24.u1.b1', '36.bg1.b1', '36.bz1.a1'], 'core': '24.d1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [439, 576, 4, 36, 72, 864], 'label': '1728.34767.12.bi1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.n1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.bi1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bi1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301717
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '12.bj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.o1.a1', '6.c1.b1', '6.i1.a1', '6.w1.a1'], 'contains': ['24.f1.a1', '24.p1.a1', '24.s1.a1', '24.bz1.a1', '36.bh1.a1', '36.ca1.a1'], 'core': '24.f1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [433, 576, 72, 468, 864, 48], 'label': '1728.34767.12.bj1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.o1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.b1', 'old_label': '12.bj1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bj1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301718
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '12.bj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.o1.b1', '6.c1.a1', '6.i1.b1', '6.w1.b1'], 'contains': ['24.f1.b1', '24.p1.b1', '24.s1.b1', '24.bz1.b1', '36.bh1.b1', '36.ca1.b1'], 'core': '24.f1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [438, 576, 72, 468, 864, 4], 'label': '1728.34767.12.bj1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.o1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.bj1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bj1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301719
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '12.bk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.p1.a1', '6.d1.b1', '6.h1.a1', '6.w1.a1'], 'contains': ['24.g1.a1', '24.p1.a1', '24.u1.a1', '36.bi1.a1', '36.cb1.a1', '36.cl1.a1'], 'core': '24.g1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [433, 576, 48, 42, 72, 864], 'label': '1728.34767.12.bk1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.p1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.b1', 'old_label': '12.bk1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bk1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301720
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '12.bk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.p1.b1', '6.d1.a1', '6.h1.b1', '6.w1.b1'], 'contains': ['24.g1.b1', '24.p1.b1', '24.u1.b1', '36.bi1.b1', '36.cb1.b1', '36.cl1.b1'], 'core': '24.g1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [37, 576, 4, 438, 72, 864], 'label': '1728.34767.12.bk1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.p1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.bk1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bk1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301721
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '12.bl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.q1.a1', '6.d1.b1', '6.i1.a1', '6.v1.a1'], 'contains': ['24.h1.a1', '24.p1.a1', '24.v1.a1', '36.bj1.a1', '36.cc1.a1', '36.cm1.a1'], 'core': '24.h1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [433, 576, 48, 474, 72, 864], 'label': '1728.34767.12.bl1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.q1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.b1', 'old_label': '12.bl1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bl1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301722
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '12.bl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.q1.b1', '6.d1.a1', '6.i1.b1', '6.v1.b1'], 'contains': ['24.h1.b1', '24.p1.b1', '24.v1.b1', '36.bj1.b1', '36.cc1.b1', '36.cm1.b1'], 'core': '24.h1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [469, 576, 4, 438, 72, 864], 'label': '1728.34767.12.bl1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.q1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.bl1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bl1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301723
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '4.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.b1', '2.b1.b1', '2.e1.a1'], 'contains': ['8.a1.b1', '8.b1.a1', '8.d1.a1', '12.a1.b1', '12.d1.b1', '12.m1.b1', '12.v1.b1'], 'core': '4.a1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [1, 864, 936, 432, 4, 48, 576], 'label': '1728.34767.4.a1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.a1.b1', 'normal_contained_in': ['2.a1.b1', '2.b1.b1', '2.e1.a1'], 'normal_contains': ['8.a1.b1', '8.b1.a1', '8.d1.a1', '12.a1.b1', '12.d1.b1'], 'normalizer': '1.a1.a1', 'old_label': '4.a1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.a1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301724
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '12.bm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.p1.b1', '6.e1.b1', '6.g1.a1', '6.w1.a1'], 'contains': ['24.e1.a1', '24.s1.a1', '24.u1.a1', '36.bl1.a1', '36.cb1.b1'], 'core': '24.e1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [37, 576, 48, 438, 72, 864], 'label': '1728.34767.12.bm1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.p1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.b1', 'old_label': '12.bm1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bm1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301725
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '12.bm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.p1.a1', '6.e1.a1', '6.g1.b1', '6.w1.b1'], 'contains': ['24.e1.b1', '24.s1.b1', '24.u1.b1', '36.bl1.b1', '36.cb1.a1'], 'core': '24.e1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [433, 576, 4, 42, 72, 864], 'label': '1728.34767.12.bm1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.p1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.bm1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bm1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301726
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '12.bn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.q1.b1', '6.f1.b1', '6.g1.a1', '6.v1.a1'], 'contains': ['24.e1.a1', '24.t1.a1', '24.v1.a1', '36.bm1.a1', '36.cc1.b1'], 'core': '24.e1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [469, 576, 48, 438, 72, 864], 'label': '1728.34767.12.bn1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.q1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.b1', 'old_label': '12.bn1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bn1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301727
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '12.bn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.q1.a1', '6.f1.a1', '6.g1.b1', '6.v1.b1'], 'contains': ['24.e1.b1', '24.t1.b1', '24.v1.b1', '36.bm1.b1', '36.cc1.a1'], 'core': '24.e1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [433, 576, 4, 474, 72, 864], 'label': '1728.34767.12.bn1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.q1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.bn1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bn1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301728
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '12.bo1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.r1.a1', '6.o1.b1', '6.v1.a1', '6.w1.a1'], 'contains': ['24.e1.a1', '24.p1.a1', '24.q1.a1', '36.bn1.a1', '36.cd1.a1'], 'core': '24.e1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [433, 48, 864, 438, 576, 72], 'label': '1728.34767.12.bo1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.r1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.b1', 'old_label': '12.bo1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bo1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301729
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '12.bo1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.r1.a1', '6.o1.a1', '6.v1.b1', '6.w1.b1'], 'contains': ['24.e1.b1', '24.p1.b1', '24.q1.b1', '36.bn1.b1', '36.cd1.a1'], 'core': '24.e1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [433, 4, 864, 438, 576, 72], 'label': '1728.34767.12.bo1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.r1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.bo1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bo1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301730
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '12.bp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.s1.a1', '6.q1.b1', '6.t1.a1', '6.w1.a1'], 'contains': ['24.f1.a1', '24.q1.a1', '24.u1.a1', '36.bo1.a1', '36.ce1.a1'], 'core': '24.f1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [7, 576, 48, 468, 936, 864], 'label': '1728.34767.12.bp1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.s1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.b1', 'old_label': '12.bp1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bp1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301731
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '12.bp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.s1.a1', '6.q1.a1', '6.t1.b1', '6.w1.b1'], 'contains': ['24.f1.b1', '24.q1.b1', '24.u1.b1', '36.bo1.b1', '36.ce1.a1'], 'core': '24.f1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [7, 576, 4, 468, 936, 864], 'label': '1728.34767.12.bp1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.s1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.bp1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bp1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301732
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '12.bq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.t1.a1', '6.f1.b1', '6.i1.a1', '6.t1.a1'], 'contains': ['24.f1.a1', '24.r1.a1', '24.v1.a1', '36.bp1.a1', '36.cf1.a1'], 'core': '24.f1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [439, 576, 48, 468, 72, 864], 'label': '1728.34767.12.bq1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.t1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.b1', 'old_label': '12.bq1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bq1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301733
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '12.bq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.t1.a1', '6.f1.a1', '6.i1.b1', '6.t1.b1'], 'contains': ['24.f1.b1', '24.r1.b1', '24.v1.b1', '36.bp1.b1', '36.cf1.a1'], 'core': '24.f1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [439, 576, 4, 468, 72, 864], 'label': '1728.34767.12.bq1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.t1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.bq1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bq1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301734
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '4.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.a1.b1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '2.c1.a1', '2.f1.a1'], 'contains': ['8.a1.a1', '8.c1.a1', '8.h1.a1', '8.m1.a1', '12.b1.a1', '12.n1.a1', '12.y1.a1'], 'core': '4.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [6, 48, 72, 36, 576, 864, 4], 'label': '1728.34767.4.b1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1.a1', 'normal_contained_in': ['2.a1.a1', '2.c1.a1', '2.f1.a1'], 'normal_contains': ['8.a1.a1', '8.c1.a1', '8.h1.a1', '12.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.b1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.b1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301735
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '12.br1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.u1.a1', '6.p1.b1', '6.u1.a1', '6.w1.a1'], 'contains': ['24.g1.a1', '24.q1.a1', '24.s1.a1', '36.bq1.a1', '36.cg1.a1'], 'core': '24.g1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [37, 576, 48, 42, 72, 864], 'label': '1728.34767.12.br1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.u1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.b1', 'old_label': '12.br1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.br1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301736
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '12.br1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.u1.a1', '6.p1.a1', '6.u1.b1', '6.w1.b1'], 'contains': ['24.g1.b1', '24.q1.b1', '24.s1.b1', '36.bq1.b1', '36.cg1.a1'], 'core': '24.g1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [37, 576, 4, 42, 72, 864], 'label': '1728.34767.12.br1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.u1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.br1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.br1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301737
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '12.bs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.v1.a1', '6.q1.b1', '6.u1.a1', '6.v1.a1'], 'contains': ['24.h1.a1', '24.q1.a1', '24.t1.a1', '36.br1.a1', '36.ch1.a1'], 'core': '24.h1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [469, 576, 48, 474, 936, 864], 'label': '1728.34767.12.bs1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.v1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.b1', 'old_label': '12.bs1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bs1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301738
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '12.bs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.v1.a1', '6.q1.a1', '6.u1.b1', '6.v1.b1'], 'contains': ['24.h1.b1', '24.q1.b1', '24.t1.b1', '36.br1.b1', '36.ch1.a1'], 'core': '24.h1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [469, 576, 4, 474, 936, 864], 'label': '1728.34767.12.bs1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.v1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.bs1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bs1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301739
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '12.bt1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.w1.b1', '6.e1.b1', '6.i1.a1', '6.u1.a1'], 'contains': ['24.h1.a1', '24.r1.a1', '24.s1.a1', '36.bs1.a1', '36.ci1.b1'], 'core': '24.h1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [37, 576, 48, 474, 72, 864], 'label': '1728.34767.12.bt1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.w1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.b1', 'old_label': '12.bt1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bt1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301740
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '12.bt1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.w1.a1', '6.e1.a1', '6.i1.b1', '6.u1.b1'], 'contains': ['24.h1.b1', '24.r1.b1', '24.s1.b1', '36.bs1.b1', '36.ci1.a1'], 'core': '24.h1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [469, 576, 4, 42, 72, 864], 'label': '1728.34767.12.bt1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.w1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.bt1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bt1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301741
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '12.bu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.w1.a1', '6.f1.b1', '6.h1.a1', '6.u1.a1'], 'contains': ['24.g1.a1', '24.r1.a1', '24.t1.a1', '36.bt1.a1', '36.ci1.a1'], 'core': '24.g1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [469, 576, 48, 42, 72, 864], 'label': '1728.34767.12.bu1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.w1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.b1', 'old_label': '12.bu1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bu1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301742
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '12.bu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.w1.b1', '6.f1.a1', '6.h1.b1', '6.u1.b1'], 'contains': ['24.g1.b1', '24.r1.b1', '24.t1.b1', '36.bt1.b1', '36.ci1.b1'], 'core': '24.g1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [37, 576, 4, 474, 72, 864], 'label': '1728.34767.12.bu1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.w1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.bu1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bu1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301743
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '12.bv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.j1.b1', '6.j1.a1'], 'contains': ['24.w1.a1', '24.y1.a1', '24.z1.a1', '36.ba1.a1', '36.cj1.b1'], 'core': '72.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [37, 1156, 864, 432, 48, 72], 'label': '1728.34767.12.bv1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.j1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.j1.a1', 'old_label': '12.bv1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bv1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301744
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '12.bv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.j1.a1', '6.j1.b1'], 'contains': ['24.w1.b1', '24.y1.b1', '24.z1.b1', '36.ba1.b1', '36.cj1.a1'], 'core': '72.b1.b1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [42, 1200, 864, 432, 4, 72], 'label': '1728.34767.12.bv1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.j1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.j1.b1', 'old_label': '12.bv1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bv1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301745
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '4.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.b1', '2.c1.b1', '2.f1.a1'], 'contains': ['8.a1.b1', '8.c1.a1', '8.h1.b1', '8.m1.b1', '12.b1.b1', '12.n1.b1', '12.y1.b1'], 'core': '4.b1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [1, 4, 72, 36, 576, 864, 48], 'label': '1728.34767.4.b1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1.b1', 'normal_contained_in': ['2.a1.b1', '2.c1.b1', '2.f1.a1'], 'normal_contains': ['8.a1.b1', '8.c1.a1', '8.h1.b1', '12.b1.b1'], 'normalizer': '1.a1.a1', 'old_label': '4.b1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.b1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301746
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '12.bw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.k1.a1', '6.j1.a1'], 'contains': ['24.w1.a1', '24.ba1.a1', '24.bb1.a1', '24.ch1.a1', '24.ch1.b1', '36.bc1.a1', '36.ck1.b1', '36.cu1.a1'], 'core': '72.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [43, 48, 1156, 432, 936, 864], 'label': '1728.34767.12.bw1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.k1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.j1.a1', 'old_label': '12.bw1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bw1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301747
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '12.bw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.k1.a1', '6.j1.b1'], 'contains': ['24.w1.b1', '24.ba1.b1', '24.bb1.b1', '24.ch1.c1', '24.ch1.d1', '36.bc1.b1', '36.ck1.a1', '36.cu1.a1'], 'core': '72.b1.b1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [43, 1200, 4, 432, 936, 864], 'label': '1728.34767.12.bw1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.k1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.j1.b1', 'old_label': '12.bw1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bw1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301748
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '12.bx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.p1.b1', '6.j1.a1'], 'contains': ['24.x1.a1', '24.y1.a1', '24.ba1.a1', '36.bl1.a1', '36.cl1.b1'], 'core': '72.c1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [37, 48, 1156, 438, 72, 864], 'label': '1728.34767.12.bx1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.p1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.j1.a1', 'old_label': '12.bx1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bx1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301749
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '12.bx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.p1.a1', '6.j1.b1'], 'contains': ['24.x1.b1', '24.y1.b1', '24.ba1.b1', '36.bl1.b1', '36.cl1.a1'], 'core': '72.c1.b1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [433, 1200, 4, 42, 72, 864], 'label': '1728.34767.12.bx1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.p1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.j1.b1', 'old_label': '12.bx1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bx1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301750
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '12.by1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.q1.b1', '6.j1.a1'], 'contains': ['24.x1.a1', '24.z1.a1', '24.bb1.a1', '36.bm1.a1', '36.cm1.b1'], 'core': '72.c1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [469, 48, 1156, 438, 72, 864], 'label': '1728.34767.12.by1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.q1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.j1.a1', 'old_label': '12.by1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.by1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301751
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '12.by1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.q1.a1', '6.j1.b1'], 'contains': ['24.x1.b1', '24.z1.b1', '24.bb1.b1', '36.bm1.b1', '36.cm1.a1'], 'core': '72.c1.b1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [433, 1200, 4, 474, 72, 864], 'label': '1728.34767.12.by1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.q1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.j1.b1', 'old_label': '12.by1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.by1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301752
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '12.bz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.h1.a1', '6.k1.a1', '6.k1.b1', '6.x1.a1'], 'contains': ['24.i1.a1', '24.bc1.a1', '24.bd1.a1', '36.y1.a1', '36.y1.b1', '36.cn1.a1'], 'core': '24.i1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [36, 864, 72, 432, 4, 48], 'label': '1728.34767.12.bz1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.h1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '12.bz1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.bz1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301753
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '12.ca1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.j1.a1', '6.k1.a1', '6.l1.b1', '6.y1.a1'], 'contains': ['24.i1.a1', '24.be1.a1', '24.bf1.b1', '36.ba1.b1', '36.bb1.a1'], 'core': '24.i1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [42, 48, 864, 432, 4, 72], 'label': '1728.34767.12.ca1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.j1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '12.ca1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.ca1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301754
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '12.ca1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.j1.b1', '6.k1.b1', '6.l1.a1', '6.y1.a1'], 'contains': ['24.i1.a1', '24.be1.b1', '24.bf1.a1', '36.ba1.a1', '36.bb1.b1'], 'core': '24.i1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [37, 4, 864, 432, 48, 72], 'label': '1728.34767.12.ca1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.j1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '12.ca1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.ca1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301755
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '12.cb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.k1.a1', '6.l1.a1', '6.l1.b1', '6.x1.a1'], 'contains': ['24.i1.a1', '24.bg1.a1', '24.bh1.a1', '24.ci1.a1', '24.ci1.b1', '36.bc1.a1', '36.bc1.b1', '36.cp1.a1'], 'core': '24.i1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [43, 48, 4, 432, 936, 864], 'label': '1728.34767.12.cb1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.k1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '12.cb1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.cb1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301756
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '4.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1', '2.d1.a1', '2.e1.a1'], 'contains': ['8.a1.a1', '8.d1.a1', '8.g1.a1', '8.n1.a1', '12.e1.a1', '12.o1.a1', '12.s1.a1'], 'core': '4.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [433, 4, 72, 6, 48, 864, 576], 'label': '1728.34767.4.c1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1.a1', 'normal_contained_in': ['2.c1.a1', '2.d1.a1', '2.e1.a1'], 'normal_contains': ['8.a1.a1', '8.d1.a1', '8.g1.a1', '12.e1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.c1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.c1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301757
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '12.cc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.l1.a1', '6.k1.b1', '6.m1.a1', '6.z1.a1'], 'contains': ['24.j1.a1', '24.bc1.a1', '24.bf1.a1', '36.bd1.a1', '36.be1.b1'], 'core': '24.j1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [433, 4, 864, 36, 48, 72], 'label': '1728.34767.12.cc1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.l1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '12.cc1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.cc1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301758
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '12.cc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.l1.b1', '6.k1.a1', '6.m1.b1', '6.z1.a1'], 'contains': ['24.j1.b1', '24.bc1.a1', '24.bf1.b1', '36.bd1.b1', '36.be1.a1'], 'core': '24.j1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [438, 48, 864, 36, 4, 72], 'label': '1728.34767.12.cc1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.l1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '12.cc1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.cc1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301759
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '12.cd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.m1.a1', '6.r1.a1', '6.x1.a1', '6.z1.a1'], 'contains': ['24.k1.a1', '24.bc1.a1', '24.bh1.a1', '36.bf1.a1', '36.bf1.b1', '36.cq1.a1'], 'core': '24.k1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [7, 48, 4, 36, 936, 864], 'label': '1728.34767.12.cd1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.m1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '12.cd1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.cd1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301760
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '12.ce1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.n1.a1', '6.m1.a1', '6.m1.b1', '6.x1.a1'], 'contains': ['24.l1.a1', '24.bc1.a1', '24.bg1.a1', '36.bg1.a1', '36.bg1.b1', '36.cr1.a1'], 'core': '24.l1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [439, 48, 4, 36, 72, 864], 'label': '1728.34767.12.ce1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.n1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '12.ce1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.ce1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301761
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '12.cf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.o1.a1', '6.k1.b1', '6.n1.a1', '6.ba1.a1'], 'contains': ['24.j1.a1', '24.bd1.a1', '24.be1.b1', '24.cb1.a1', '36.bh1.a1', '36.bk1.b1'], 'core': '24.j1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [433, 4, 72, 468, 864, 48], 'label': '1728.34767.12.cf1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.o1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '12.cf1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.cf1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301762
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '12.cf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.o1.b1', '6.k1.a1', '6.n1.b1', '6.ba1.a1'], 'contains': ['24.j1.b1', '24.bd1.a1', '24.be1.a1', '24.cb1.b1', '36.bh1.b1', '36.bk1.a1'], 'core': '24.j1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [438, 48, 72, 468, 864, 4], 'label': '1728.34767.12.cf1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.o1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '12.cf1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.cf1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301763
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '12.cg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.p1.a1', '6.l1.b1', '6.m1.a1', '6.ba1.a1'], 'contains': ['24.j1.a1', '24.be1.a1', '24.bg1.a1', '36.bi1.a1', '36.bl1.b1'], 'core': '24.j1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [433, 48, 4, 42, 72, 864], 'label': '1728.34767.12.cg1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.p1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '12.cg1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.cg1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301764
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '12.cg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.p1.b1', '6.l1.a1', '6.m1.b1', '6.ba1.a1'], 'contains': ['24.j1.b1', '24.be1.b1', '24.bg1.a1', '36.bi1.b1', '36.bl1.a1'], 'core': '24.j1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [37, 48, 4, 438, 72, 864], 'label': '1728.34767.12.cg1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.p1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '12.cg1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.cg1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301765
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '12.ch1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.q1.a1', '6.l1.b1', '6.n1.a1', '6.z1.a1'], 'contains': ['24.j1.a1', '24.bf1.b1', '24.bh1.a1', '36.bj1.a1', '36.bm1.b1'], 'core': '24.j1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [433, 48, 4, 474, 72, 864], 'label': '1728.34767.12.ch1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.q1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '12.ch1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.ch1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301766
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '12.ch1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.q1.b1', '6.l1.a1', '6.n1.b1', '6.z1.a1'], 'contains': ['24.j1.b1', '24.bf1.a1', '24.bh1.a1', '36.bj1.b1', '36.bm1.a1'], 'core': '24.j1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [469, 48, 4, 438, 72, 864], 'label': '1728.34767.12.ch1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.q1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '12.ch1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.ch1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301767
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '4.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.c1.b1', '2.d1.b1', '2.e1.a1'], 'contains': ['8.a1.b1', '8.d1.b1', '8.g1.a1', '8.n1.b1', '12.e1.b1', '12.o1.b1', '12.s1.b1'], 'core': '4.c1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [1, 4, 72, 438, 48, 864, 576], 'label': '1728.34767.4.c1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1.b1', 'normal_contained_in': ['2.c1.b1', '2.d1.b1', '2.e1.a1'], 'normal_contains': ['8.a1.b1', '8.d1.b1', '8.g1.a1', '12.e1.b1'], 'normalizer': '1.a1.a1', 'old_label': '4.c1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.c1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301768
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '12.ci1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.s1.a1', '6.s1.a1', '6.x1.a1', '6.ba1.a1'], 'contains': ['24.k1.a1', '24.bd1.a1', '24.bg1.a1', '36.bo1.a1', '36.bo1.b1', '36.cs1.a1'], 'core': '24.k1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [7, 48, 4, 468, 936, 864], 'label': '1728.34767.12.ci1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.s1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '12.ci1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.ci1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301769
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '12.cj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.t1.a1', '6.n1.a1', '6.n1.b1', '6.x1.a1'], 'contains': ['24.l1.a1', '24.bd1.a1', '24.bh1.a1', '36.bp1.a1', '36.bp1.b1', '36.ct1.a1'], 'core': '24.l1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [439, 48, 4, 468, 72, 864], 'label': '1728.34767.12.cj1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.t1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '12.cj1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.cj1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301770
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '12.ck1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.u1.a1', '6.r1.a1', '6.y1.a1', '6.ba1.a1'], 'contains': ['24.k1.a1', '24.be1.a1', '24.be1.b1', '36.bq1.a1', '36.bq1.b1'], 'core': '24.k1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [37, 48, 4, 42, 72, 864], 'label': '1728.34767.12.ck1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.u1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '12.ck1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.ck1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301771
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '12.cl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.v1.a1', '6.s1.a1', '6.y1.a1', '6.z1.a1'], 'contains': ['24.k1.a1', '24.bf1.a1', '24.bf1.b1', '36.br1.a1', '36.br1.b1'], 'core': '24.k1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [469, 48, 4, 474, 936, 864], 'label': '1728.34767.12.cl1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.v1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '12.cl1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.cl1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301772
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '12.cm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.w1.a1', '6.m1.a1', '6.n1.b1', '6.y1.a1'], 'contains': ['24.l1.a1', '24.be1.a1', '24.bf1.a1', '36.bs1.b1', '36.bt1.a1'], 'core': '24.l1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [469, 48, 4, 42, 72, 864], 'label': '1728.34767.12.cm1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.w1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '12.cm1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.cm1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301773
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '12.cm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.w1.b1', '6.m1.b1', '6.n1.a1', '6.y1.a1'], 'contains': ['24.l1.a1', '24.be1.b1', '24.bf1.b1', '36.bs1.a1', '36.bt1.b1'], 'core': '24.l1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [37, 48, 4, 474, 72, 864], 'label': '1728.34767.12.cm1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.w1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '12.cm1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.cm1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301774
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '12.cn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.h1.a1', '6.bb1.a1'], 'contains': ['24.bi1.a1', '24.bj1.a1', '24.bk1.a1', '36.b1.a1', '36.cn1.a1'], 'core': '36.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [36, 576, 864, 432, 100, 72], 'label': '1728.34767.12.cn1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.h1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.h1.a1', 'old_label': '12.cn1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.cn1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301775
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '12.co1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.i1.a1', '6.bb1.a1'], 'contains': ['24.bi1.a1', '24.bl1.a1', '24.bm1.a1', '36.bu1.a1', '36.co1.a1'], 'core': '72.d1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [7, 100, 864, 432, 576, 936], 'label': '1728.34767.12.co1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.i1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.bb1.a1', 'old_label': '12.co1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.co1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301776
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '12.cp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.k1.a1', '6.bb1.a1'], 'contains': ['24.bi1.a1', '24.bn1.a1', '24.bo1.a1', '24.cj1.a1', '24.cj1.b1', '24.cj1.c1', '24.cj1.d1', '36.bw1.a1', '36.cp1.a1', '36.cu1.a1'], 'core': '72.d1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [43, 576, 100, 432, 936, 864], 'label': '1728.34767.12.cp1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.k1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.bb1.a1', 'old_label': '12.cp1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.cp1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301777
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '12.cq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.m1.a1', '6.bb1.a1'], 'contains': ['24.bj1.a1', '24.bl1.a1', '24.bo1.a1', '36.by1.a1', '36.cq1.a1'], 'core': '72.e1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [7, 576, 100, 36, 936, 864], 'label': '1728.34767.12.cq1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.m1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.bb1.a1', 'old_label': '12.cq1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.cq1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301778
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '4.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.a1.b1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '2.d1.a1', '2.g1.a1'], 'contains': ['8.a1.a1', '8.e1.a1', '8.i1.b1', '12.c1.a1', '12.p1.a1', '12.z1.a1'], 'core': '4.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [6, 48, 864, 468, 576, 4, 936], 'label': '1728.34767.4.d1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1.a1', 'normal_contained_in': ['2.a1.a1', '2.d1.a1', '2.g1.a1'], 'normal_contains': ['8.a1.a1', '8.e1.a1', '8.i1.b1', '12.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.d1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.d1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301779
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '12.cr1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.n1.a1', '6.bb1.a1'], 'contains': ['24.bj1.a1', '24.bm1.a1', '24.bn1.a1', '36.bz1.a1', '36.cr1.a1'], 'core': '72.e1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [439, 576, 100, 36, 72, 864], 'label': '1728.34767.12.cr1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.n1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.bb1.a1', 'old_label': '12.cr1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.cr1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301780
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '12.cs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.s1.a1', '6.bb1.a1'], 'contains': ['24.bk1.a1', '24.bl1.a1', '24.bn1.a1', '36.ce1.a1', '36.cs1.a1'], 'core': '72.f1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [7, 576, 100, 468, 936, 864], 'label': '1728.34767.12.cs1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.s1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.bb1.a1', 'old_label': '12.cs1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.cs1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301781
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '12.ct1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.t1.a1', '6.bb1.a1'], 'contains': ['24.bk1.a1', '24.bm1.a1', '24.bo1.a1', '36.cf1.a1', '36.ct1.a1'], 'core': '72.f1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [439, 576, 100, 468, 72, 864], 'label': '1728.34767.12.ct1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.t1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.bb1.a1', 'old_label': '12.ct1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.ct1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301782
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '12.cu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.k1.a1'], 'contains': ['24.bp1.a1', '24.bq1.a1', '24.br1.a1', '24.ck1.a1', '24.ck1.b1', '24.ck1.c1', '24.ck1.d1', '36.ck1.a1', '36.ck1.b1', '36.cp1.a1', '36.cu1.a1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [43, 1200, 1156, 432, 936, 864], 'label': '1728.34767.12.cu1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.k1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.cu1.a1', 'old_label': '12.cu1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.cu1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301783
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '16.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '8.a1.b1', '8.b1.a1', '8.c1.a1', '8.d1.a1', '8.d1.b1', '8.e1.a1', '8.f1.a1', '8.g1.a1', '8.h1.a1', '8.h1.b1', '8.i1.a1', '8.i1.b1', '8.j1.a1', '8.k1.a1'], 'contains': ['32.a1.a1', '32.b1.a1', '32.c1.a1', '48.a1.a1', '48.a1.b1', '48.b1.a1', '48.f1.a1', '48.f1.b1', '48.g1.a1', '48.h1.a1'], 'core': '16.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [936, 576, 864, 4, 48], 'label': '1728.34767.16.a1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '16.a1.a1', 'normal_contained_in': ['8.a1.b1', '8.a1.a1', '8.b1.a1', '8.c1.a1', '8.d1.b1', '8.d1.a1', '8.e1.a1', '8.f1.a1', '8.g1.a1', '8.i1.b1', '8.i1.a1', '8.h1.a1', '8.h1.b1', '8.j1.a1', '8.k1.a1'], 'normal_contains': ['32.a1.a1', '32.b1.a1', '32.c1.a1', '48.a1.b1', '48.a1.a1', '48.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.a1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.a1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301784
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '16.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.a1.b1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '8.l1.a1', '8.l1.b1'], 'contains': ['32.a1.a1', '32.d1.a1', '48.c1.a1', '48.d1.a1', '48.i1.a1', '48.j1.a1'], 'core': '16.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [6, 48, 936, 4, 576], 'label': '1728.34767.16.b1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '16.b1.a1', 'normal_contained_in': ['8.a1.a1', '8.l1.a1', '8.l1.b1'], 'normal_contains': ['32.a1.a1', '48.c1.a1', '48.d1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.b1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.b1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302185
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '48.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.b1.b1', '24.o1.a1'], 'contains': ['96.g1.a1', '96.r1.b1', '144.c1.b1', '144.i1.b1'], 'core': '144.c1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [870, 936, 1156, 48], 'label': '1728.34767.48.j1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '16.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '48.j1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.j1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301785
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '16.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.a1.b1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '8.l1.c1', '8.l1.d1'], 'contains': ['32.a1.a1', '32.d1.b1', '48.c1.b1', '48.d1.b1', '48.i1.b1', '48.j1.b1'], 'core': '16.b1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [870, 48, 936, 4, 576], 'label': '1728.34767.16.b1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '16.b1.b1', 'normal_contained_in': ['8.a1.a1', '8.l1.c1', '8.l1.d1'], 'normal_contains': ['32.a1.a1', '48.c1.b1', '48.d1.b1'], 'normalizer': '1.a1.a1', 'old_label': '16.b1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.b1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301786
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '16.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.b1', '8.l1.a1', '8.l1.c1'], 'contains': ['32.a1.a1', '32.d1.c1', '48.c1.c1', '48.d1.c1', '48.i1.c1', '48.j1.c1'], 'core': '16.b1.c1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [1, 4, 936, 48, 576], 'label': '1728.34767.16.b1.c1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '16.b1.c1', 'normal_contained_in': ['8.a1.b1', '8.l1.a1', '8.l1.c1'], 'normal_contains': ['32.a1.a1', '48.c1.c1', '48.d1.c1'], 'normalizer': '1.a1.a1', 'old_label': '16.b1.c1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.b1.c1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301787
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '16.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.b1', '8.l1.b1', '8.l1.d1'], 'contains': ['32.a1.a1', '32.d1.d1', '48.c1.d1', '48.d1.d1', '48.i1.d1', '48.j1.d1'], 'core': '16.b1.d1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [865, 4, 936, 48, 576], 'label': '1728.34767.16.b1.d1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '16.b1.d1', 'normal_contained_in': ['8.a1.b1', '8.l1.b1', '8.l1.d1'], 'normal_contains': ['32.a1.a1', '48.c1.d1', '48.d1.d1'], 'normalizer': '1.a1.a1', 'old_label': '16.b1.d1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.b1.d1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301788
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '16.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.d1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.f1.a1', '8.l1.a1', '8.l1.d1'], 'contains': ['32.a1.a1', '48.e1.a1', '48.k1.a1', '48.k1.c1', '48.l1.a1'], 'core': '16.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [7, 48, 576, 936, 4], 'label': '1728.34767.16.c1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '16.c1.a1', 'normal_contained_in': ['8.f1.a1', '8.l1.a1', '8.l1.d1'], 'normal_contains': ['32.a1.a1', '48.e1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.c1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.c1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301789
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '4.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.b1', '2.d1.b1', '2.g1.a1'], 'contains': ['8.a1.b1', '8.e1.a1', '8.i1.a1', '12.c1.b1', '12.p1.b1', '12.z1.b1'], 'core': '4.d1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [1, 4, 864, 468, 576, 48, 936], 'label': '1728.34767.4.d1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1.b1', 'normal_contained_in': ['2.a1.b1', '2.d1.b1', '2.g1.a1'], 'normal_contains': ['8.a1.b1', '8.e1.a1', '8.i1.a1', '12.c1.b1'], 'normalizer': '1.a1.a1', 'old_label': '4.d1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.d1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301790
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '16.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.d1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.f1.a1', '8.l1.b1', '8.l1.c1'], 'contains': ['32.a1.a1', '48.e1.b1', '48.k1.b1', '48.k1.d1', '48.l1.b1'], 'core': '16.c1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [871, 48, 576, 936, 4], 'label': '1728.34767.16.c1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '16.c1.b1', 'normal_contained_in': ['8.f1.a1', '8.l1.c1', '8.l1.b1'], 'normal_contains': ['32.a1.a1', '48.e1.b1'], 'normalizer': '1.a1.a1', 'old_label': '16.c1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.c1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301791
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '16.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.j1.a1', '8.p1.a1', '8.p1.c1', '8.q1.a1'], 'contains': ['32.c1.a1', '48.bo1.a1', '48.bo1.c1', '48.bs1.a1', '48.bs1.c1', '48.bw1.a1', '48.bz1.a1', '48.cc1.a1'], 'core': '16.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [1411, 576, 864, 4, 48], 'label': '1728.34767.16.d1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '16.d1.a1', 'normal_contained_in': ['8.j1.a1'], 'normal_contains': ['32.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.d1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.d1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301792
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '16.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.j1.a1', '8.p1.b1', '8.p1.d1', '8.q1.b1'], 'contains': ['32.c1.a1', '48.bo1.b1', '48.bo1.d1', '48.bs1.b1', '48.bs1.d1', '48.bw1.b1', '48.bz1.b1', '48.cc1.b1'], 'core': '16.d1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [475, 576, 864, 4, 48], 'label': '1728.34767.16.d1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '16.d1.b1', 'normal_contained_in': ['8.j1.a1'], 'normal_contains': ['32.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.d1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.d1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301793
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '16.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '8.m1.a1', '8.n1.a1'], 'contains': ['32.b1.a1', '32.d1.a1', '32.d1.b1', '48.m1.a1', '48.n1.a1', '48.o1.a1', '48.p1.a1'], 'core': '32.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [6, 48, 72, 4, 576], 'label': '1728.34767.16.e1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '16.e1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.e1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301794
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '16.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.a1.b1', '8.m1.b1', '8.n1.b1'], 'contains': ['32.b1.a1', '32.d1.c1', '32.d1.d1', '48.m1.b1', '48.n1.b1', '48.o1.b1', '48.p1.b1'], 'core': '32.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [1, 4, 72, 48, 576], 'label': '1728.34767.16.e1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.b1', 'old_label': '16.e1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.e1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301795
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '16.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.c1.a1', '8.m1.a1', '8.m1.b1'], 'contains': ['32.b1.a1', '48.q1.a1', '48.q1.b1', '48.z1.a1', '48.be1.a1'], 'core': '32.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [36, 576, 4, 48, 72], 'label': '1728.34767.16.f1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.f1.a1', 'old_label': '16.f1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.f1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301796
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '16.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.d1.a1', '8.n1.a1', '8.o1.a1'], 'contains': ['32.b1.a1', '48.r1.a1', '48.s1.b1', '48.x1.b1', '48.ba1.a1'], 'core': '32.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [433, 4, 48, 576, 72], 'label': '1728.34767.16.g1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.a1', 'old_label': '16.g1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.g1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301797
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '16.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.d1.b1', '8.n1.b1', '8.o1.b1'], 'contains': ['32.b1.a1', '48.r1.b1', '48.s1.a1', '48.x1.a1', '48.ba1.b1'], 'core': '32.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [438, 48, 4, 576, 72], 'label': '1728.34767.16.g1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.d1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.b1', 'old_label': '16.g1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.g1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301798
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '16.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.e1.a1', '8.o1.a1', '8.o1.b1'], 'contains': ['32.b1.a1', '48.t1.a1', '48.t1.b1', '48.bb1.a1', '48.bf1.a1'], 'core': '32.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [468, 576, 4, 48, 72], 'label': '1728.34767.16.h1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.k1.a1', 'old_label': '16.h1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.h1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301799
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '16.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.g1.a1', '8.n1.a1', '8.n1.b1'], 'contains': ['32.b1.a1', '48.u1.a1', '48.u1.b1', '48.bc1.a1', '48.bg1.a1'], 'core': '32.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [439, 48, 576, 72, 4], 'label': '1728.34767.16.i1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.e1.a1', 'old_label': '16.i1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.i1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301800
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '4.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '2.d1.a1', '2.f1.a1'], 'contains': ['8.a1.a1', '8.h1.b1', '8.k1.a1', '12.q1.a1', '12.t1.a1', '12.w1.a1', '12.ba1.a1'], 'core': '4.e1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [37, 48, 4, 6, 576, 72, 864], 'label': '1728.34767.4.e1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1.a1', 'normal_contained_in': ['2.b1.a1', '2.d1.a1', '2.f1.a1'], 'normal_contains': ['8.a1.a1', '8.h1.b1', '8.k1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.e1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.e1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301801
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '16.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.h1.a1', '8.m1.a1', '8.o1.b1'], 'contains': ['32.b1.a1', '48.v1.b1', '48.w1.a1', '48.y1.b1', '48.bd1.a1'], 'core': '32.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [42, 576, 4, 72, 48], 'label': '1728.34767.16.j1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.h1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '16.j1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.j1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301802
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '16.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.h1.b1', '8.m1.b1', '8.o1.a1'], 'contains': ['32.b1.a1', '48.v1.a1', '48.w1.b1', '48.y1.a1', '48.bd1.b1'], 'core': '32.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [37, 576, 48, 72, 4], 'label': '1728.34767.16.j1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.h1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.b1', 'old_label': '16.j1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.j1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301803
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '16.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '8.p1.a1', '8.p1.b1'], 'contains': ['32.c1.a1', '32.d1.a1', '32.d1.b1', '48.bh1.a1', '48.bi1.a1', '48.bj1.a1', '48.bk1.a1'], 'core': '32.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [6, 48, 864, 4, 576], 'label': '1728.34767.16.k1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '16.k1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.k1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301804
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '16.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.a1.b1', '8.p1.c1', '8.p1.d1'], 'contains': ['32.c1.a1', '32.d1.c1', '32.d1.d1', '48.bh1.b1', '48.bi1.b1', '48.bj1.b1', '48.bk1.b1'], 'core': '32.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [1, 4, 864, 48, 576], 'label': '1728.34767.16.k1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.b1', 'old_label': '16.k1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.k1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301805
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '16.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.b1.a1', '8.q1.a1', '8.q1.b1'], 'contains': ['32.c1.a1', '48.bl1.a1', '48.bl1.b1', '48.bq1.a1', '48.bq1.b1', '48.bu1.a1', '48.by1.a1', '48.by1.b1', '48.cb1.a1', '48.cb1.b1'], 'core': '32.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [432, 864, 4, 48, 576], 'label': '1728.34767.16.l1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.h1.a1', 'old_label': '16.l1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.l1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301806
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '16.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.i1.a1', '8.p1.a1', '8.p1.b1'], 'contains': ['32.c1.a1', '48.bm1.a1', '48.bn1.b1', '48.br1.a1', '48.bv1.a1'], 'core': '32.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [469, 576, 48, 864, 4], 'label': '1728.34767.16.m1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.i1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '16.m1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.m1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301807
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '16.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.i1.b1', '8.p1.c1', '8.p1.d1'], 'contains': ['32.c1.a1', '48.bm1.b1', '48.bn1.a1', '48.br1.b1', '48.bv1.b1'], 'core': '32.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [474, 576, 4, 864, 48], 'label': '1728.34767.16.m1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.i1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.b1', 'old_label': '16.m1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.m1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301808
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '16.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.k1.a1', '8.q1.a1', '8.q1.b1'], 'contains': ['32.c1.a1', '48.bp1.a1', '48.bp1.b1', '48.bt1.a1', '48.bt1.b1', '48.bx1.a1', '48.ca1.a1', '48.ca1.a2', '48.cd1.a1', '48.cd1.a2'], 'core': '32.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [43, 576, 864, 4, 48], 'label': '1728.34767.16.n1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.k1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.h1.a1', 'old_label': '16.n1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.n1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301809
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '18.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.c1.a1', '6.k1.a1', '9.b1.a1'], 'contains': ['36.c1.a1', '36.d1.a1', '36.f1.a1', '36.y1.b1', '36.ba1.b1', '36.bd1.b1', '36.bh1.b1', '54.a1.a1'], 'core': '72.b1.b1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [6, 864, 72, 36, 432, 4], 'label': '1728.34767.18.a1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1.a1', 'old_label': '18.a1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.a1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301810
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '18.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.c1.b1', '6.k1.b1', '9.b1.b1'], 'contains': ['36.c1.b1', '36.d1.b1', '36.f1.b1', '36.y1.a1', '36.ba1.a1', '36.bd1.a1', '36.bh1.a1', '54.a1.b1'], 'core': '72.b1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [1, 864, 72, 36, 432, 48], 'label': '1728.34767.18.a1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1.b1', 'old_label': '18.a1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.a1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301811
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '4.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.b1.b1', '2.d1.b1', '2.f1.a1'], 'contains': ['8.a1.b1', '8.h1.a1', '8.k1.a1', '12.q1.b1', '12.t1.b1', '12.w1.b1', '12.ba1.b1'], 'core': '4.e1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [1, 48, 4, 42, 576, 936, 864], 'label': '1728.34767.4.e1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1.b1', 'normal_contained_in': ['2.b1.b1', '2.d1.b1', '2.f1.a1'], 'normal_contains': ['8.a1.b1', '8.h1.a1', '8.k1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.e1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.e1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301812
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '18.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.d1.a1', '6.l1.a1', '9.b1.a1'], 'contains': ['36.c1.a1', '36.g1.a1', '36.h1.a1', '36.bb1.b1', '36.bc1.b1', '36.bi1.b1', '36.bj1.b1', '54.b1.a1'], 'core': '72.b1.b1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [37, 4, 864, 6, 432, 72], 'label': '1728.34767.18.b1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1.a1', 'old_label': '18.b1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.b1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301813
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '18.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.d1.b1', '6.l1.b1', '9.b1.b1'], 'contains': ['36.c1.b1', '36.g1.b1', '36.h1.b1', '36.bb1.a1', '36.bc1.a1', '36.bi1.a1', '36.bj1.a1', '54.b1.b1'], 'core': '72.b1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [1, 48, 864, 42, 432, 936], 'label': '1728.34767.18.b1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1.b1', 'old_label': '18.b1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.b1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301814
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '18.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.e1.a1', '6.m1.a1', '9.b1.a1'], 'contains': ['36.d1.a1', '36.e1.a1', '36.h1.a1', '36.be1.b1', '36.bg1.b1', '36.bl1.b1', '36.bs1.b1', '54.c1.a1'], 'core': '72.c1.b1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [433, 4, 864, 6, 36, 72], 'label': '1728.34767.18.c1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1.a1', 'old_label': '18.c1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.c1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301815
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '18.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.e1.b1', '6.m1.b1', '9.b1.b1'], 'contains': ['36.d1.b1', '36.e1.b1', '36.h1.b1', '36.be1.a1', '36.bg1.a1', '36.bl1.a1', '36.bs1.a1', '54.c1.b1'], 'core': '72.c1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [1, 48, 864, 438, 36, 72], 'label': '1728.34767.18.c1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1.b1', 'old_label': '18.c1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.c1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301816
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '18.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.f1.a1', '6.n1.a1', '9.b1.a1'], 'contains': ['36.e1.a1', '36.f1.a1', '36.g1.a1', '36.bk1.b1', '36.bm1.b1', '36.bp1.b1', '36.bt1.b1', '54.d1.a1'], 'core': '72.c1.b1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [433, 4, 864, 6, 468, 72], 'label': '1728.34767.18.d1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1.a1', 'old_label': '18.d1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.d1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301817
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '18.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.f1.b1', '6.n1.b1', '9.b1.b1'], 'contains': ['36.e1.b1', '36.f1.b1', '36.g1.b1', '36.bk1.a1', '36.bm1.a1', '36.bp1.a1', '36.bt1.a1', '54.d1.b1'], 'core': '72.c1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [1, 48, 864, 438, 468, 72], 'label': '1728.34767.18.d1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1.b1', 'old_label': '18.d1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.d1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301818
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '18.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.a1.a1', '6.c1.a1', '9.a1.a1'], 'contains': ['36.b1.a1', '36.i1.a1', '36.j1.a1', '36.l1.a1', '36.bv1.a1', '36.bx1.b1', '36.ca1.b1', '54.a1.a1'], 'core': '36.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [6, 576, 864, 36, 432, 72], 'label': '1728.34767.18.e1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '18.e1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.e1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301819
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '18.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.a1.b1', '6.c1.b1', '9.a1.a1'], 'contains': ['36.b1.a1', '36.i1.b1', '36.j1.b1', '36.l1.b1', '36.bv1.b1', '36.bx1.a1', '36.ca1.a1', '54.a1.b1'], 'core': '36.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [1, 576, 864, 36, 432, 72], 'label': '1728.34767.18.e1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.b1', 'old_label': '18.e1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.e1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301820
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '18.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.d1.a1', '6.g1.a1', '9.a1.a1'], 'contains': ['36.i1.a1', '36.m1.a1', '36.n1.a1', '36.bv1.b1', '36.bw1.a1', '36.cb1.b1', '36.cc1.b1', '54.b1.a1'], 'core': '72.d1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [37, 576, 864, 6, 432, 72], 'label': '1728.34767.18.f1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '18.f1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.f1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301821
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '18.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.d1.b1', '6.g1.b1', '9.a1.a1'], 'contains': ['36.i1.b1', '36.m1.b1', '36.n1.b1', '36.bv1.a1', '36.bw1.a1', '36.cb1.a1', '36.cc1.a1', '54.b1.b1'], 'core': '72.d1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [1, 576, 864, 42, 432, 936], 'label': '1728.34767.18.f1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '18.f1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.f1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301822
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '2.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.a1.a1', 'complements': ['864.d1.a1', '864.d1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.b1', '4.b1.b1', '4.d1.b1', '4.h1.a1', '4.j1.b1', '4.l1.a1', '4.o1.a1', '6.a1.b1', '6.c1.b1', '6.k1.b1'], 'core': '2.a1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [1, 72, 864, 36, 48, 576, 4, 432], 'label': '1728.34767.2.a1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1.b1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.a1.b1', '4.b1.b1', '4.d1.b1', '4.h1.a1', '4.j1.b1', '4.l1.a1', '4.o1.a1', '6.a1.b1'], 'normalizer': '1.a1.a1', 'old_label': '2.a1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2.a1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301823
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '4.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '2.c1.a1', '2.g1.a1'], 'contains': ['8.a1.a1', '8.i1.a1', '8.j1.a1', '8.p1.a1', '8.p1.b1', '12.r1.a1', '12.u1.a1', '12.x1.a1', '12.bb1.a1'], 'core': '4.f1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [469, 48, 4, 6, 576, 936, 864], 'label': '1728.34767.4.f1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.f1.a1', 'normal_contained_in': ['2.b1.a1', '2.c1.a1', '2.g1.a1'], 'normal_contains': ['8.a1.a1', '8.i1.a1', '8.j1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.f1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.f1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301824
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '18.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.e1.a1', '6.h1.a1', '9.a1.a1'], 'contains': ['36.j1.a1', '36.k1.a1', '36.n1.a1', '36.bx1.a1', '36.bz1.a1', '36.cb1.a1', '36.ci1.a1', '54.c1.a1'], 'core': '72.e1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [433, 576, 864, 6, 36, 72], 'label': '1728.34767.18.g1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '18.g1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.g1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301825
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '18.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.e1.b1', '6.h1.b1', '9.a1.a1'], 'contains': ['36.j1.b1', '36.k1.b1', '36.n1.b1', '36.bx1.b1', '36.bz1.a1', '36.cb1.b1', '36.ci1.b1', '54.c1.b1'], 'core': '72.e1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [1, 576, 864, 438, 36, 72], 'label': '1728.34767.18.g1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '18.g1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.g1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301826
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '18.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.f1.a1', '6.i1.a1', '9.a1.a1'], 'contains': ['36.k1.a1', '36.l1.a1', '36.m1.a1', '36.ca1.a1', '36.cc1.a1', '36.cf1.a1', '36.ci1.b1', '54.d1.a1'], 'core': '72.f1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [433, 576, 864, 6, 468, 72], 'label': '1728.34767.18.h1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '18.h1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.h1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301827
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '18.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.f1.b1', '6.i1.b1', '9.a1.a1'], 'contains': ['36.k1.b1', '36.l1.b1', '36.m1.b1', '36.ca1.b1', '36.cc1.b1', '36.cf1.a1', '36.ci1.a1', '54.d1.b1'], 'core': '72.f1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [1, 576, 864, 438, 468, 72], 'label': '1728.34767.18.h1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '18.h1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.h1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301828
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '18.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.d1.a1', '6.j1.a1'], 'contains': ['36.o1.a1', '36.p1.a1', '36.q1.a1', '36.cj1.b1', '36.ck1.b1', '36.cl1.b1', '36.cm1.b1', '54.b1.a1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [37, 1156, 864, 6, 432, 72], 'label': '1728.34767.18.i1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.i1.a1', 'old_label': '18.i1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.i1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301829
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '18.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.d1.b1', '6.j1.b1'], 'contains': ['36.o1.b1', '36.p1.b1', '36.q1.b1', '36.cj1.a1', '36.ck1.a1', '36.cl1.a1', '36.cm1.a1', '54.b1.b1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [1, 1200, 864, 42, 432, 936], 'label': '1728.34767.18.i1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.i1.b1', 'old_label': '18.i1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.i1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301830
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '18.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.w1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.o1.a1', '6.o1.b1', '9.a1.a1'], 'contains': ['36.i1.a1', '36.i1.b1', '36.k1.a1', '36.k1.b1', '36.r1.a1', '36.bu1.a1', '36.cd1.a1', '54.e1.a1'], 'core': '72.d1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [1, 864, 936, 6, 432, 576], 'label': '1728.34767.18.j1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '18.j1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.j1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301831
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '18.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.p1.a1', '6.p1.b1', '9.a1.a1'], 'contains': ['36.j1.a1', '36.j1.b1', '36.m1.a1', '36.m1.b1', '36.r1.a1', '36.by1.a1', '36.cg1.a1', '54.f1.a1'], 'core': '72.e1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [1, 576, 864, 6, 36, 936], 'label': '1728.34767.18.k1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '18.k1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.k1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301832
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '18.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.q1.a1', '6.q1.b1', '9.a1.a1'], 'contains': ['36.l1.a1', '36.l1.b1', '36.n1.a1', '36.n1.b1', '36.r1.a1', '36.ce1.a1', '36.ch1.a1', '54.g1.a1'], 'core': '72.f1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [1, 576, 864, 6, 468, 936], 'label': '1728.34767.18.l1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '18.l1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.l1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301833
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '18.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.a1.a1', '6.k1.a1', '9.b1.b1'], 'contains': ['36.a1.a1', '36.s1.a1', '36.u1.a1', '36.y1.a1', '36.bb1.a1', '36.be1.a1', '36.bk1.a1', '54.a1.a1'], 'core': '36.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [6, 48, 864, 36, 432, 72], 'label': '1728.34767.18.m1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '18.m1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.m1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301834
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '4.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.b1.b1', '2.c1.b1', '2.g1.a1'], 'contains': ['8.a1.b1', '8.i1.b1', '8.j1.a1', '8.p1.c1', '8.p1.d1', '12.r1.b1', '12.u1.b1', '12.x1.b1', '12.bb1.b1'], 'core': '4.f1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [1, 48, 4, 474, 576, 936, 864], 'label': '1728.34767.4.f1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.f1.b1', 'normal_contained_in': ['2.b1.b1', '2.c1.b1', '2.g1.a1'], 'normal_contains': ['8.a1.b1', '8.i1.b1', '8.j1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.f1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.f1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301835
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '18.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.a1.b1', '6.k1.b1', '9.b1.a1'], 'contains': ['36.a1.b1', '36.s1.b1', '36.u1.b1', '36.y1.b1', '36.bb1.b1', '36.be1.b1', '36.bk1.b1', '54.a1.b1'], 'core': '36.a1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [1, 4, 864, 36, 432, 72], 'label': '1728.34767.18.m1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '18.m1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.m1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301836
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '18.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.g1.a1', '6.j1.a1', '6.l1.a1', '9.b1.b1'], 'contains': ['36.a1.a1', '36.v1.a1', '36.w1.a1', '36.ba1.a1', '36.bc1.a1', '36.bl1.a1', '36.bm1.a1', '54.b1.a1'], 'core': '36.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [37, 48, 864, 6, 432, 72], 'label': '1728.34767.18.n1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1.b1', 'old_label': '18.n1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.n1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301837
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '18.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.g1.b1', '6.j1.b1', '6.l1.b1', '9.b1.a1'], 'contains': ['36.a1.b1', '36.v1.b1', '36.w1.b1', '36.ba1.b1', '36.bc1.b1', '36.bl1.b1', '36.bm1.b1', '54.b1.b1'], 'core': '36.a1.b1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [1, 4, 864, 42, 432, 936], 'label': '1728.34767.18.n1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1.a1', 'old_label': '18.n1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.n1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301838
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '18.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.h1.a1', '6.m1.a1', '9.b1.b1'], 'contains': ['36.s1.a1', '36.t1.a1', '36.w1.a1', '36.bd1.a1', '36.bg1.a1', '36.bi1.a1', '36.bt1.a1', '54.c1.a1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [433, 48, 864, 6, 36, 72], 'label': '1728.34767.18.o1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1.b1', 'old_label': '18.o1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.o1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301839
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '18.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.h1.b1', '6.m1.b1', '9.b1.a1'], 'contains': ['36.s1.b1', '36.t1.b1', '36.w1.b1', '36.bd1.b1', '36.bg1.b1', '36.bi1.b1', '36.bt1.b1', '54.c1.b1'], 'core': '72.a1.b1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [1, 4, 864, 438, 36, 72], 'label': '1728.34767.18.o1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1.a1', 'old_label': '18.o1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.o1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301840
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '18.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.i1.a1', '6.n1.a1', '9.b1.b1'], 'contains': ['36.t1.a1', '36.u1.a1', '36.v1.a1', '36.bh1.a1', '36.bj1.a1', '36.bp1.a1', '36.bs1.a1', '54.d1.a1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [433, 48, 864, 6, 468, 72], 'label': '1728.34767.18.p1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1.b1', 'old_label': '18.p1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.p1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301841
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '18.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.i1.b1', '6.n1.b1', '9.b1.a1'], 'contains': ['36.t1.b1', '36.u1.b1', '36.v1.b1', '36.bh1.b1', '36.bj1.b1', '36.bp1.b1', '36.bs1.b1', '54.d1.b1'], 'core': '72.a1.b1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [1, 4, 864, 438, 468, 72], 'label': '1728.34767.18.p1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1.a1', 'old_label': '18.p1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.p1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301842
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '18.q1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1.a1', '6.o1.a1', '9.b1.a1'], 'contains': ['36.a1.b1', '36.c1.a1', '36.e1.a1', '36.t1.b1', '36.x1.a1', '36.z1.b1', '36.bn1.b1', '54.e1.a1'], 'core': '36.a1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [1, 4, 864, 6, 432, 936], 'label': '1728.34767.18.q1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '18.q1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.q1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301843
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '18.q1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1.a1', '6.o1.b1', '9.b1.b1'], 'contains': ['36.a1.a1', '36.c1.b1', '36.e1.b1', '36.t1.a1', '36.x1.b1', '36.z1.a1', '36.bn1.a1', '54.e1.a1'], 'core': '36.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [1, 48, 864, 6, 432, 936], 'label': '1728.34767.18.q1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.b1', 'old_label': '18.q1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.q1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301844
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '18.r1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.p1.a1', '6.r1.a1', '9.b1.a1'], 'contains': ['36.d1.a1', '36.g1.a1', '36.s1.b1', '36.v1.b1', '36.x1.a1', '36.bf1.b1', '36.bq1.b1', '54.f1.a1'], 'core': '72.a1.b1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [1, 4, 864, 6, 36, 936], 'label': '1728.34767.18.r1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1.a1', 'old_label': '18.r1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.r1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301845
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '4.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.e1.a1', '2.f1.a1', '2.g1.a1'], 'contains': ['8.a1.a1', '8.a1.b1', '8.f1.a1', '8.l1.a1', '8.l1.b1', '8.l1.c1', '8.l1.d1', '12.f1.a1', '12.bc1.a1', '12.bc1.b1'], 'core': '4.g1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [1, 4, 936, 6, 48, 864, 576], 'label': '1728.34767.4.g1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.g1.a1', 'normal_contained_in': ['2.e1.a1', '2.f1.a1', '2.g1.a1'], 'normal_contains': ['8.a1.b1', '8.a1.a1', '8.f1.a1', '8.l1.a1', '8.l1.c1', '8.l1.b1', '8.l1.d1', '12.f1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.g1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.g1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301846
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '18.r1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.p1.b1', '6.r1.a1', '9.b1.b1'], 'contains': ['36.d1.b1', '36.g1.b1', '36.s1.a1', '36.v1.a1', '36.x1.b1', '36.bf1.a1', '36.bq1.a1', '54.f1.a1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [1, 48, 864, 6, 36, 936], 'label': '1728.34767.18.r1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1.b1', 'old_label': '18.r1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.r1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301847
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '18.s1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.q1.a1', '6.s1.a1', '9.b1.a1'], 'contains': ['36.f1.a1', '36.h1.a1', '36.u1.b1', '36.w1.b1', '36.x1.a1', '36.bo1.b1', '36.br1.b1', '54.g1.a1'], 'core': '72.a1.b1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [1, 4, 864, 6, 468, 936], 'label': '1728.34767.18.s1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1.a1', 'old_label': '18.s1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.s1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301848
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '18.s1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.q1.b1', '6.s1.a1', '9.b1.b1'], 'contains': ['36.f1.b1', '36.h1.b1', '36.u1.a1', '36.w1.a1', '36.x1.b1', '36.bo1.a1', '36.br1.a1', '54.g1.a1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [1, 48, 864, 6, 468, 936], 'label': '1728.34767.18.s1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1.b1', 'old_label': '18.s1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.s1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301849
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '18.t1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.t1.a1', '6.x1.a1', '9.b1.b1'], 'contains': ['36.y1.a1', '36.z1.a1', '36.bc1.a1', '36.bf1.a1', '36.bg1.a1', '36.bo1.a1', '36.bp1.a1', '54.h1.a1'], 'core': '72.b1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [7, 48, 864, 36, 432, 936], 'label': '1728.34767.18.t1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.h1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1.b1', 'old_label': '18.t1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.t1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301850
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '18.t1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.t1.b1', '6.x1.a1', '9.b1.a1'], 'contains': ['36.y1.b1', '36.z1.b1', '36.bc1.b1', '36.bf1.b1', '36.bg1.b1', '36.bo1.b1', '36.bp1.b1', '54.h1.a1'], 'core': '72.b1.b1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [7, 4, 864, 36, 432, 936], 'label': '1728.34767.18.t1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.h1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1.a1', 'old_label': '18.t1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.t1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301851
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '18.u1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.u1.a1', '6.y1.a1', '9.b1.b1'], 'contains': ['36.z1.a1', '36.ba1.a1', '36.bb1.a1', '36.bq1.a1', '36.br1.a1', '36.bs1.a1', '36.bt1.a1', '54.i1.a1'], 'core': '72.b1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [37, 48, 864, 42, 432, 72], 'label': '1728.34767.18.u1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.i1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1.b1', 'old_label': '18.u1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.u1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301852
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '18.u1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.u1.b1', '6.y1.a1', '9.b1.a1'], 'contains': ['36.z1.b1', '36.ba1.b1', '36.bb1.b1', '36.bq1.b1', '36.br1.b1', '36.bs1.b1', '36.bt1.b1', '54.i1.a1'], 'core': '72.b1.b1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [37, 4, 864, 42, 432, 72], 'label': '1728.34767.18.u1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.i1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1.a1', 'old_label': '18.u1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.u1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301853
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '18.v1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.v1.a1', '6.z1.a1', '9.b1.b1'], 'contains': ['36.bd1.a1', '36.be1.a1', '36.bf1.a1', '36.bj1.a1', '36.bm1.a1', '36.bn1.a1', '36.br1.a1', '54.j1.a1'], 'core': '72.c1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [433, 48, 864, 438, 36, 72], 'label': '1728.34767.18.v1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.j1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1.b1', 'old_label': '18.v1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.v1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301854
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '18.v1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.v1.b1', '6.z1.a1', '9.b1.a1'], 'contains': ['36.bd1.b1', '36.be1.b1', '36.bf1.b1', '36.bj1.b1', '36.bm1.b1', '36.bn1.b1', '36.br1.b1', '54.j1.a1'], 'core': '72.c1.b1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [433, 4, 864, 438, 36, 72], 'label': '1728.34767.18.v1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.j1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1.a1', 'old_label': '18.v1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.v1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301855
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '18.w1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.w1.a1', '6.ba1.a1', '9.b1.b1'], 'contains': ['36.bh1.a1', '36.bi1.a1', '36.bk1.a1', '36.bl1.a1', '36.bn1.a1', '36.bo1.a1', '36.bq1.a1', '54.k1.a1'], 'core': '72.c1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [433, 48, 864, 438, 468, 72], 'label': '1728.34767.18.w1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.k1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1.b1', 'old_label': '18.w1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.w1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301856
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '4.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '2.a1.b1', '2.h1.a1'], 'contains': ['8.b1.a1', '8.c1.a1', '8.e1.a1', '12.g1.a1', '12.g1.b1', '12.bz1.a1', '12.cn1.a1'], 'core': '4.h1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [36, 864, 72, 432, 576, 4, 48], 'label': '1728.34767.4.h1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.h1.a1', 'normal_contained_in': ['2.a1.b1', '2.a1.a1', '2.h1.a1'], 'normal_contains': ['8.b1.a1', '8.c1.a1', '8.e1.a1', '12.g1.b1', '12.g1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.h1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.h1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301857
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '18.w1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.w1.b1', '6.ba1.a1', '9.b1.a1'], 'contains': ['36.bh1.b1', '36.bi1.b1', '36.bk1.b1', '36.bl1.b1', '36.bn1.b1', '36.bo1.b1', '36.bq1.b1', '54.k1.a1'], 'core': '72.c1.b1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [433, 4, 864, 438, 468, 72], 'label': '1728.34767.18.w1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.k1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1.a1', 'old_label': '18.w1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.w1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301858
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '18.x1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.t1.a1', '6.t1.b1', '6.bb1.a1', '9.a1.a1'], 'contains': ['36.b1.a1', '36.bu1.a1', '36.bw1.a1', '36.by1.a1', '36.bz1.a1', '36.ce1.a1', '36.cf1.a1', '54.h1.a1'], 'core': '36.b1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [7, 576, 864, 36, 432, 936], 'label': '1728.34767.18.x1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.h1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '18.x1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.x1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301859
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '18.y1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.u1.a1', '6.u1.b1', '9.a1.a1'], 'contains': ['36.bu1.a1', '36.bv1.a1', '36.bv1.b1', '36.cg1.a1', '36.ch1.a1', '36.ci1.a1', '36.ci1.b1', '54.i1.a1'], 'core': '72.d1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [37, 576, 864, 42, 432, 72], 'label': '1728.34767.18.y1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.i1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '18.y1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.y1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301860
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '18.z1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.v1.a1', '6.v1.b1', '9.a1.a1'], 'contains': ['36.bx1.a1', '36.bx1.b1', '36.by1.a1', '36.cc1.a1', '36.cc1.b1', '36.cd1.a1', '36.ch1.a1', '54.j1.a1'], 'core': '72.e1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [433, 576, 864, 438, 36, 72], 'label': '1728.34767.18.z1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.j1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '18.z1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.z1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301861
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '18.ba1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.w1.a1', '6.w1.b1', '9.a1.a1'], 'contains': ['36.ca1.a1', '36.ca1.b1', '36.cb1.a1', '36.cb1.b1', '36.cd1.a1', '36.ce1.a1', '36.cg1.a1', '54.k1.a1'], 'core': '72.f1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [433, 576, 864, 438, 468, 72], 'label': '1728.34767.18.ba1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.k1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '18.ba1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.ba1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301862
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '18.bb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.x1.a1', '6.bb1.a1'], 'contains': ['36.cn1.a1', '36.co1.a1', '36.cp1.a1', '36.cq1.a1', '36.cr1.a1', '36.cs1.a1', '36.ct1.a1', '54.h1.a1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [7, 100, 864, 36, 432, 936], 'label': '1728.34767.18.bb1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.h1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bb1.a1', 'old_label': '18.bb1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.bb1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301863
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '24.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.e1.b1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '12.a1.a1', '12.b1.a1', '12.c1.a1', '12.s1.a1', '12.t1.a1', '12.u1.a1', '12.bc1.b1'], 'contains': ['48.a1.a1', '48.c1.a1', '48.c1.b1', '48.n1.a1', '48.bi1.a1', '72.a1.a1', '72.h1.a1'], 'core': '24.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [6, 48, 936, 864, 576], 'label': '1728.34767.24.a1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.a1.a1', 'normal_contained_in': ['8.a1.a1', '12.a1.a1', '12.b1.a1', '12.c1.a1'], 'normal_contains': ['48.a1.a1', '48.c1.a1', '48.c1.b1', '72.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '24.a1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.a1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301864
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '24.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.e1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.b1', '12.a1.b1', '12.b1.b1', '12.c1.b1', '12.s1.b1', '12.t1.b1', '12.u1.b1', '12.bc1.a1'], 'contains': ['48.a1.b1', '48.c1.c1', '48.c1.d1', '48.n1.b1', '48.bi1.b1', '72.a1.b1', '72.h1.b1'], 'core': '24.a1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [1, 4, 936, 864, 576], 'label': '1728.34767.24.a1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.a1.b1', 'normal_contained_in': ['8.a1.b1', '12.a1.b1', '12.b1.b1', '12.c1.b1'], 'normal_contains': ['48.a1.b1', '48.c1.c1', '48.c1.d1', '72.a1.b1'], 'normalizer': '1.a1.a1', 'old_label': '24.a1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.a1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301865
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '24.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.d1.b1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '12.d1.a1', '12.e1.a1', '12.f1.a1', '12.y1.a1', '12.z1.a1', '12.ba1.a1', '12.bb1.a1'], 'contains': ['48.b1.a1', '48.d1.a1', '48.d1.b1', '48.p1.a1', '48.bk1.a1', '72.a1.a1', '72.g1.a1'], 'core': '24.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [6, 48, 936, 864, 4], 'label': '1728.34767.24.b1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.b1.a1', 'normal_contained_in': ['8.a1.a1', '12.d1.a1', '12.e1.a1', '12.f1.a1'], 'normal_contains': ['48.b1.a1', '48.d1.a1', '48.d1.b1', '72.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '24.b1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.b1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301866
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '24.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.d1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.b1', '12.d1.b1', '12.e1.b1', '12.f1.a1', '12.y1.b1', '12.z1.b1', '12.ba1.b1', '12.bb1.b1'], 'contains': ['48.b1.a1', '48.d1.c1', '48.d1.d1', '48.p1.b1', '48.bk1.b1', '72.a1.b1', '72.g1.b1'], 'core': '24.b1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [1, 4, 936, 864, 48], 'label': '1728.34767.24.b1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.b1.b1', 'normal_contained_in': ['8.a1.b1', '12.d1.b1', '12.e1.b1', '12.f1.a1'], 'normal_contains': ['48.b1.a1', '48.d1.c1', '48.d1.d1', '72.a1.b1'], 'normalizer': '1.a1.a1', 'old_label': '24.b1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.b1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301867
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '4.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.d1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.e1.a1', '2.h1.a1', '2.i1.a1'], 'contains': ['8.b1.a1', '8.f1.a1', '8.g1.a1', '12.k1.a1', '12.bd1.a1', '12.bd1.b1', '12.co1.a1'], 'core': '4.i1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [7, 4, 864, 432, 48, 576, 936], 'label': '1728.34767.4.i1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.i1.a1', 'normal_contained_in': ['2.e1.a1', '2.h1.a1', '2.i1.a1'], 'normal_contains': ['8.b1.a1', '8.f1.a1', '8.g1.a1', '12.k1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.i1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.i1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301868
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '24.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.b1.a1', '12.a1.a1', '12.g1.a1', '12.h1.a1', '12.m1.b1', '12.bd1.a1', '12.be1.a1', '12.bf1.a1'], 'contains': ['48.a1.a1', '48.bl1.a1', '72.b1.a1', '72.d1.a1', '72.bb1.a1'], 'core': '24.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [432, 864, 936, 48, 576], 'label': '1728.34767.24.c1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.c1.a1', 'normal_contained_in': ['8.b1.a1', '12.a1.a1', '12.g1.a1', '12.h1.a1'], 'normal_contains': ['48.a1.a1', '72.b1.a1', '72.d1.a1'], 'normalizer': '1.a1.a1', 'old_label': '24.c1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.c1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301869
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '24.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.b1.a1', '12.a1.b1', '12.g1.b1', '12.h1.b1', '12.m1.a1', '12.bd1.b1', '12.be1.b1', '12.bf1.b1'], 'contains': ['48.a1.b1', '48.bl1.b1', '72.b1.b1', '72.d1.a1', '72.bb1.b1'], 'core': '24.c1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [432, 864, 936, 4, 576], 'label': '1728.34767.24.c1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.c1.b1', 'normal_contained_in': ['8.b1.a1', '12.a1.b1', '12.g1.b1', '12.h1.b1'], 'normal_contains': ['48.a1.b1', '72.b1.b1', '72.d1.a1'], 'normalizer': '1.a1.a1', 'old_label': '24.c1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.c1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301870
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '24.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.b1.b1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.c1.a1', '12.b1.a1', '12.g1.a1', '12.i1.a1', '12.n1.b1', '12.bg1.a1', '12.bh1.a1', '12.bi1.a1'], 'contains': ['48.a1.a1', '48.q1.a1', '72.e1.a1', '72.j1.a1'], 'core': '24.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [36, 576, 864, 48, 72], 'label': '1728.34767.24.d1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.d1.a1', 'normal_contained_in': ['8.c1.a1', '12.b1.a1', '12.g1.a1', '12.i1.a1'], 'normal_contains': ['48.a1.a1', '72.e1.a1'], 'normalizer': '1.a1.a1', 'old_label': '24.d1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.d1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301871
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '24.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.c1.a1', '12.b1.b1', '12.g1.b1', '12.i1.b1', '12.n1.a1', '12.bg1.b1', '12.bh1.b1', '12.bi1.b1'], 'contains': ['48.a1.b1', '48.q1.b1', '72.e1.a1', '72.j1.b1'], 'core': '24.d1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [36, 576, 864, 4, 72], 'label': '1728.34767.24.d1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.d1.b1', 'normal_contained_in': ['8.c1.a1', '12.b1.b1', '12.g1.b1', '12.i1.b1'], 'normal_contains': ['48.a1.b1', '72.e1.a1'], 'normalizer': '1.a1.a1', 'old_label': '24.d1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.d1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301872
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '24.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.a1.b1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.d1.b1', '12.a1.a1', '12.i1.a1', '12.j1.a1', '12.o1.b1', '12.bm1.a1', '12.bn1.a1', '12.bo1.a1'], 'contains': ['48.a1.a1', '48.s1.a1', '72.c1.a1', '72.u1.b1'], 'core': '24.e1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [438, 48, 864, 576, 72], 'label': '1728.34767.24.e1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.e1.a1', 'normal_contained_in': ['8.d1.b1', '12.a1.a1', '12.i1.a1', '12.j1.a1'], 'normal_contains': ['48.a1.a1', '72.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '24.e1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.e1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301873
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '24.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.d1.a1', '12.a1.b1', '12.i1.b1', '12.j1.b1', '12.o1.a1', '12.bm1.b1', '12.bn1.b1', '12.bo1.b1'], 'contains': ['48.a1.b1', '48.s1.b1', '72.c1.b1', '72.u1.a1'], 'core': '24.e1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [433, 4, 864, 576, 72], 'label': '1728.34767.24.e1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.e1.b1', 'normal_contained_in': ['8.d1.a1', '12.a1.b1', '12.i1.b1', '12.j1.b1'], 'normal_contains': ['48.a1.b1', '72.c1.b1'], 'normalizer': '1.a1.a1', 'old_label': '24.e1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.e1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301874
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '24.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.e1.a1', '12.c1.a1', '12.g1.a1', '12.j1.a1', '12.p1.b1', '12.bj1.a1', '12.bp1.a1', '12.bq1.a1'], 'contains': ['48.a1.a1', '48.t1.a1', '72.f1.a1', '72.l1.a1'], 'core': '24.f1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [468, 576, 864, 48, 72], 'label': '1728.34767.24.f1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.f1.a1', 'normal_contained_in': ['8.e1.a1', '12.c1.a1', '12.g1.a1', '12.j1.a1'], 'normal_contains': ['48.a1.a1', '72.f1.a1'], 'normalizer': '1.a1.a1', 'old_label': '24.f1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.f1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301875
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '24.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.e1.a1', '12.c1.b1', '12.g1.b1', '12.j1.b1', '12.p1.a1', '12.bj1.b1', '12.bp1.b1', '12.bq1.b1'], 'contains': ['48.a1.b1', '48.t1.b1', '72.f1.a1', '72.l1.b1'], 'core': '24.f1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [468, 576, 864, 4, 72], 'label': '1728.34767.24.f1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.f1.b1', 'normal_contained_in': ['8.e1.a1', '12.c1.b1', '12.g1.b1', '12.j1.b1'], 'normal_contains': ['48.a1.b1', '72.f1.a1'], 'normalizer': '1.a1.a1', 'old_label': '24.f1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.f1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301876
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '24.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.a1.b1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.h1.a1', '12.b1.a1', '12.h1.a1', '12.j1.a1', '12.q1.b1', '12.bk1.a1', '12.br1.a1', '12.bu1.a1'], 'contains': ['48.a1.a1', '48.w1.a1', '72.p1.a1', '72.x1.a1', '72.bd1.a1'], 'core': '24.g1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [42, 576, 864, 72, 48], 'label': '1728.34767.24.g1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.g1.a1', 'normal_contained_in': ['8.h1.a1', '12.b1.a1', '12.h1.a1', '12.j1.a1'], 'normal_contains': ['48.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '24.g1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.g1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301877
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '24.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.h1.b1', '12.b1.b1', '12.h1.b1', '12.j1.b1', '12.q1.a1', '12.bk1.b1', '12.br1.b1', '12.bu1.b1'], 'contains': ['48.a1.b1', '48.w1.b1', '72.p1.b1', '72.x1.b1', '72.bd1.b1'], 'core': '24.g1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [37, 576, 864, 72, 4], 'label': '1728.34767.24.g1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.g1.b1', 'normal_contained_in': ['8.h1.b1', '12.b1.b1', '12.h1.b1', '12.j1.b1'], 'normal_contains': ['48.a1.b1'], 'normalizer': '1.a1.a1', 'old_label': '24.g1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.g1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301878
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '4.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.a1.b1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '2.b1.b1', '2.i1.a1'], 'contains': ['8.b1.a1', '8.h1.a1', '8.i1.b1', '12.h1.a1', '12.be1.b1', '12.bv1.b1', '12.ca1.a1'], 'core': '4.j1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [42, 48, 864, 432, 576, 4, 72], 'label': '1728.34767.4.j1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.j1.a1', 'normal_contained_in': ['2.a1.a1', '2.b1.b1', '2.i1.a1'], 'normal_contains': ['8.b1.a1', '8.i1.b1', '8.h1.a1', '12.h1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.j1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.j1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301879
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '24.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.a1.b1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.i1.b1', '12.c1.a1', '12.h1.a1', '12.i1.a1', '12.r1.b1', '12.bl1.a1', '12.bs1.a1', '12.bt1.a1'], 'contains': ['48.a1.a1', '48.bn1.a1', '72.r1.a1', '72.y1.b1', '72.be1.a1'], 'core': '24.h1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [474, 576, 936, 864, 48], 'label': '1728.34767.24.h1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.h1.a1', 'normal_contained_in': ['8.i1.b1', '12.c1.a1', '12.h1.a1', '12.i1.a1'], 'normal_contains': ['48.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '24.h1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.h1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301880
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '24.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.i1.a1', '12.c1.b1', '12.h1.b1', '12.i1.b1', '12.r1.a1', '12.bl1.b1', '12.bs1.b1', '12.bt1.b1'], 'contains': ['48.a1.b1', '48.bn1.b1', '72.r1.b1', '72.y1.a1', '72.be1.b1'], 'core': '24.h1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [469, 576, 936, 864, 4], 'label': '1728.34767.24.h1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.h1.b1', 'normal_contained_in': ['8.i1.a1', '12.c1.b1', '12.h1.b1', '12.i1.b1'], 'normal_contains': ['48.a1.b1'], 'normalizer': '1.a1.a1', 'old_label': '24.h1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.h1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301881
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '24.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.b1.a1', '12.d1.a1', '12.d1.b1', '12.k1.a1', '12.bz1.a1', '12.ca1.a1', '12.ca1.b1', '12.cb1.a1'], 'contains': ['48.b1.a1', '48.bu1.a1', '72.b1.a1', '72.b1.b1', '72.bh1.a1'], 'core': '24.i1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [432, 864, 936, 4, 48], 'label': '1728.34767.24.i1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.i1.a1', 'normal_contained_in': ['8.b1.a1', '12.d1.b1', '12.d1.a1', '12.k1.a1'], 'normal_contains': ['48.b1.a1', '72.b1.b1', '72.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '24.i1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.i1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301882
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '24.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.d1.a1', '12.d1.b1', '12.e1.a1', '12.l1.a1', '12.cc1.a1', '12.cf1.a1', '12.cg1.a1', '12.ch1.a1'], 'contains': ['48.b1.a1', '48.ba1.a1', '72.c1.b1', '72.k1.a1'], 'core': '24.j1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [433, 4, 864, 48, 72], 'label': '1728.34767.24.j1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.j1.a1', 'normal_contained_in': ['8.d1.a1', '12.d1.b1', '12.e1.a1', '12.l1.a1'], 'normal_contains': ['48.b1.a1', '72.c1.b1'], 'normalizer': '1.a1.a1', 'old_label': '24.j1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.j1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301883
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '24.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.a1.b1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.d1.b1', '12.d1.a1', '12.e1.b1', '12.l1.a1', '12.cc1.b1', '12.cf1.b1', '12.cg1.b1', '12.ch1.b1'], 'contains': ['48.b1.a1', '48.ba1.b1', '72.c1.a1', '72.k1.b1'], 'core': '24.j1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [438, 48, 864, 4, 72], 'label': '1728.34767.24.j1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.j1.b1', 'normal_contained_in': ['8.d1.b1', '12.d1.a1', '12.e1.b1', '12.l1.a1'], 'normal_contains': ['48.b1.a1', '72.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '24.j1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.j1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301884
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '24.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '36.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.f1.a1', '12.f1.a1', '12.k1.a1', '12.l1.a1', '12.cd1.a1', '12.ci1.a1', '12.ck1.a1', '12.cl1.a1'], 'contains': ['48.b1.a1', '48.e1.a1', '48.e1.b1', '72.m1.a1', '72.m1.b1', '72.bk1.a1'], 'core': '24.k1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [7, 48, 864, 936, 4], 'label': '1728.34767.24.k1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.k1.a1', 'normal_contained_in': ['8.f1.a1', '12.f1.a1', '12.k1.a1', '12.l1.a1'], 'normal_contains': ['48.b1.a1', '48.e1.b1', '48.e1.a1'], 'normalizer': '1.a1.a1', 'old_label': '24.k1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.k1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301885
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '24.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.d1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.g1.a1', '12.e1.a1', '12.e1.b1', '12.k1.a1', '12.ce1.a1', '12.cj1.a1', '12.cm1.a1', '12.cm1.b1'], 'contains': ['48.b1.a1', '48.bc1.a1', '72.n1.a1', '72.n1.b1', '72.bl1.a1'], 'core': '24.l1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [439, 48, 864, 72, 4], 'label': '1728.34767.24.l1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.l1.a1', 'normal_contained_in': ['8.g1.a1', '12.e1.b1', '12.e1.a1', '12.k1.a1'], 'normal_contains': ['48.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '24.l1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.l1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301886
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '24.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.e1.a1', 'complements': ['72.ch1.b1', '72.ci1.d1', '72.ci1.b1', '72.ck1.c1', '72.ck1.d1', '72.ch1.a1', '72.ci1.c1', '72.ci1.a1', '72.ck1.a1', '72.ck1.b1', '72.cb1.a1', '72.cb1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['8.l1.a1', '12.f1.a1'], 'contains': ['48.d1.a1', '48.d1.c1', '48.e1.a1', '72.bs1.a1', '72.bs1.c1'], 'core': '24.m1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [1, 48, 6, 936, 4], 'label': '1728.34767.24.m1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.m1.a1', 'normal_contained_in': ['8.l1.a1', '12.f1.a1'], 'normal_contains': ['48.d1.c1', '48.d1.a1', '48.e1.a1'], 'normalizer': '1.a1.a1', 'old_label': '24.m1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.m1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301887
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '24.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.e1.a1', 'complements': ['72.ch1.b1', '72.ci1.d1', '72.ci1.b1', '72.ck1.c1', '72.ck1.d1', '72.ch1.a1', '72.ci1.c1', '72.ci1.a1', '72.ck1.a1', '72.ck1.b1', '72.cb1.a1', '72.cb1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['8.l1.b1', '12.f1.a1'], 'contains': ['48.d1.a1', '48.d1.d1', '48.e1.b1', '72.bs1.b1', '72.bs1.d1'], 'core': '24.m1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [865, 48, 6, 936, 4], 'label': '1728.34767.24.m1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.m1.b1', 'normal_contained_in': ['8.l1.b1', '12.f1.a1'], 'normal_contains': ['48.d1.a1', '48.d1.d1', '48.e1.b1'], 'normalizer': '1.a1.a1', 'old_label': '24.m1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.m1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301888
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '24.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.e1.a1', 'complements': ['72.ch1.b1', '72.ci1.d1', '72.ci1.b1', '72.ck1.c1', '72.ck1.d1', '72.ch1.a1', '72.ci1.c1', '72.ci1.a1', '72.ck1.a1', '72.ck1.b1', '72.cb1.a1', '72.cb1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['8.l1.c1', '12.f1.a1'], 'contains': ['48.d1.b1', '48.d1.c1', '48.e1.b1', '72.bs1.e1', '72.bs1.g1'], 'core': '24.m1.c1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [1, 48, 870, 936, 4], 'label': '1728.34767.24.m1.c1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.m1.c1', 'normal_contained_in': ['8.l1.c1', '12.f1.a1'], 'normal_contains': ['48.d1.c1', '48.d1.b1', '48.e1.b1'], 'normalizer': '1.a1.a1', 'old_label': '24.m1.c1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.m1.c1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301889
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '4.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.b1', '2.b1.a1', '2.i1.a1'], 'contains': ['8.b1.a1', '8.h1.b1', '8.i1.a1', '12.h1.b1', '12.be1.a1', '12.bv1.a1', '12.ca1.b1'], 'core': '4.j1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [37, 4, 864, 432, 576, 48, 72], 'label': '1728.34767.4.j1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.j1.b1', 'normal_contained_in': ['2.a1.b1', '2.b1.a1', '2.i1.a1'], 'normal_contains': ['8.b1.a1', '8.i1.a1', '8.h1.b1', '12.h1.b1'], 'normalizer': '1.a1.a1', 'old_label': '4.j1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.j1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301890
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '24.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.e1.a1', 'complements': ['72.ch1.b1', '72.ci1.d1', '72.ci1.b1', '72.ck1.c1', '72.ck1.d1', '72.ch1.a1', '72.ci1.c1', '72.ci1.a1', '72.ck1.a1', '72.ck1.b1', '72.cb1.a1', '72.cb1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['8.l1.d1', '12.f1.a1'], 'contains': ['48.d1.b1', '48.d1.d1', '48.e1.a1', '72.bs1.f1', '72.bs1.h1'], 'core': '24.m1.d1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [865, 48, 870, 936, 4], 'label': '1728.34767.24.m1.d1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.m1.d1', 'normal_contained_in': ['8.l1.d1', '12.f1.a1'], 'normal_contains': ['48.d1.d1', '48.d1.b1', '48.e1.a1'], 'normalizer': '1.a1.a1', 'old_label': '24.m1.d1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.m1.d1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301891
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '24.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.n1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '12.m1.a1', '12.n1.a1', '12.o1.a1', '12.p1.a1', '12.q1.a1', '12.r1.a1', '12.bc1.a1'], 'contains': ['48.a1.b1', '48.i1.a1', '48.i1.b1', '48.m1.a1', '48.bh1.a1', '72.g1.a1', '72.h1.a1', '72.i1.a1'], 'core': '48.a1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [6, 576, 936, 864, 4], 'label': '1728.34767.24.n1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '24.n1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.n1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301892
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '24.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.n1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.a1.b1', '12.m1.b1', '12.n1.b1', '12.o1.b1', '12.p1.b1', '12.q1.b1', '12.r1.b1', '12.bc1.b1'], 'contains': ['48.a1.a1', '48.i1.c1', '48.i1.d1', '48.m1.b1', '48.bh1.b1', '72.g1.b1', '72.h1.b1', '72.i1.b1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [1, 576, 936, 864, 48], 'label': '1728.34767.24.n1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.b1', 'old_label': '24.n1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.n1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301893
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '24.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '12.v1.a1', '12.w1.a1', '12.x1.a1'], 'contains': ['48.f1.a1', '48.j1.a1', '48.j1.b1', '48.o1.a1', '48.bj1.a1', '72.a1.a1', '72.i1.a1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [6, 48, 936, 864, 1156], 'label': '1728.34767.24.o1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '24.o1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.o1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301894
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '24.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.a1.b1', '12.v1.b1', '12.w1.b1', '12.x1.b1'], 'contains': ['48.f1.b1', '48.j1.c1', '48.j1.d1', '48.o1.b1', '48.bj1.b1', '72.a1.b1', '72.i1.b1'], 'core': '72.a1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [1, 4, 936, 864, 1200], 'label': '1728.34767.24.o1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.b1', 'old_label': '24.o1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.o1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301895
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '24.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.p1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.d1.a1', '12.m1.b1', '12.s1.a1', '12.bg1.a1', '12.bj1.a1', '12.bk1.a1', '12.bl1.a1', '12.bo1.a1'], 'contains': ['48.a1.a1', '48.r1.a1', '72.k1.a1', '72.u1.a1', '72.bc1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [433, 72, 864, 48, 576], 'label': '1728.34767.24.p1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.b1', 'old_label': '24.p1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.p1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301896
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '24.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.p1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.d1.b1', '12.m1.a1', '12.s1.b1', '12.bg1.b1', '12.bj1.b1', '12.bk1.b1', '12.bl1.b1', '12.bo1.b1'], 'contains': ['48.a1.b1', '48.r1.b1', '72.k1.b1', '72.u1.b1', '72.bc1.b1'], 'core': '48.a1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [438, 72, 864, 4, 576], 'label': '1728.34767.24.p1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.d1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '24.p1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.p1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301897
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '24.q1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.f1.a1', '12.bc1.b1', '12.bd1.a1', '12.bh1.a1', '12.bo1.a1', '12.bp1.a1', '12.br1.a1', '12.bs1.a1'], 'contains': ['48.a1.a1', '48.k1.a1', '48.k1.b1', '72.m1.a1', '72.v1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [7, 48, 864, 576, 936], 'label': '1728.34767.24.q1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.b1', 'old_label': '24.q1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.q1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301898
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '24.q1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.f1.a1', '12.bc1.a1', '12.bd1.b1', '12.bh1.b1', '12.bo1.b1', '12.bp1.b1', '12.br1.b1', '12.bs1.b1'], 'contains': ['48.a1.b1', '48.k1.c1', '48.k1.d1', '72.m1.b1', '72.v1.a1'], 'core': '48.a1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [7, 4, 864, 576, 936], 'label': '1728.34767.24.q1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '24.q1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.q1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301899
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '24.r1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '36.i1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.g1.a1', '12.o1.b1', '12.s1.a1', '12.bd1.a1', '12.bi1.a1', '12.bq1.a1', '12.bt1.a1', '12.bu1.a1'], 'contains': ['48.a1.a1', '48.u1.a1', '72.n1.a1', '72.w1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [439, 48, 864, 576, 72], 'label': '1728.34767.24.r1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.b1', 'old_label': '24.r1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.r1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301900
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '4.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '2.b1.b1', '2.h1.a1'], 'contains': ['8.b1.a1', '8.j1.a1', '8.k1.a1', '8.q1.a1', '8.q1.b1', '12.bf1.a1', '12.bf1.b1', '12.bw1.a1', '12.bw1.b1', '12.cb1.a1', '12.cp1.a1', '12.cu1.a1'], 'core': '4.k1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [43, 48, 4, 432, 576, 936, 864], 'label': '1728.34767.4.k1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.k1.a1', 'normal_contained_in': ['2.b1.b1', '2.b1.a1', '2.h1.a1'], 'normal_contains': ['8.b1.a1', '8.j1.a1', '8.k1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.k1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.k1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301901
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '24.r1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '36.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.g1.a1', '12.o1.a1', '12.s1.b1', '12.bd1.b1', '12.bi1.b1', '12.bq1.b1', '12.bt1.b1', '12.bu1.b1'], 'contains': ['48.a1.b1', '48.u1.b1', '72.n1.b1', '72.w1.a1'], 'core': '48.a1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [439, 4, 864, 576, 72], 'label': '1728.34767.24.r1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '24.r1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.r1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301902
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '24.s1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.g1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.h1.b1', '12.n1.b1', '12.t1.a1', '12.be1.a1', '12.bj1.a1', '12.bm1.a1', '12.br1.a1', '12.bt1.a1'], 'contains': ['48.a1.a1', '48.v1.a1', '72.o1.a1', '72.x1.b1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [37, 576, 864, 48, 72], 'label': '1728.34767.24.s1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.h1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.b1', 'old_label': '24.s1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.s1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301903
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '24.s1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.h1.a1', '12.n1.a1', '12.t1.b1', '12.be1.b1', '12.bj1.b1', '12.bm1.b1', '12.br1.b1', '12.bt1.b1'], 'contains': ['48.a1.b1', '48.v1.b1', '72.o1.b1', '72.x1.a1'], 'core': '48.a1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [42, 576, 864, 4, 72], 'label': '1728.34767.24.s1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.h1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '24.s1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.s1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301904
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '24.t1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.i1.a1', '12.p1.b1', '12.u1.a1', '12.be1.a1', '12.bg1.a1', '12.bn1.a1', '12.bs1.a1', '12.bu1.a1'], 'contains': ['48.a1.a1', '48.bm1.a1', '72.q1.a1', '72.y1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [469, 576, 936, 48, 864], 'label': '1728.34767.24.t1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.i1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.b1', 'old_label': '24.t1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.t1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301905
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '24.t1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.i1.b1', '12.p1.a1', '12.u1.b1', '12.be1.b1', '12.bg1.b1', '12.bn1.b1', '12.bs1.b1', '12.bu1.b1'], 'contains': ['48.a1.b1', '48.bm1.b1', '72.q1.b1', '72.y1.b1'], 'core': '48.a1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [474, 576, 936, 4, 864], 'label': '1728.34767.24.t1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.i1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '24.t1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.t1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301906
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '24.u1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.j1.a1', '12.r1.b1', '12.u1.a1', '12.bf1.a1', '12.bi1.a1', '12.bk1.a1', '12.bm1.a1', '12.bp1.a1'], 'contains': ['48.a1.a1', '48.bo1.a1', '48.bo1.b1', '72.s1.a1', '72.z1.a1', '72.bf1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [475, 576, 936, 864, 48], 'label': '1728.34767.24.u1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.j1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.b1', 'old_label': '24.u1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.u1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301907
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '24.u1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.j1.a1', '12.r1.a1', '12.u1.b1', '12.bf1.b1', '12.bi1.b1', '12.bk1.b1', '12.bm1.b1', '12.bp1.b1'], 'contains': ['48.a1.b1', '48.bo1.c1', '48.bo1.d1', '72.s1.b1', '72.z1.a1', '72.bf1.b1'], 'core': '48.a1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [475, 576, 936, 864, 4], 'label': '1728.34767.24.u1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.j1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '24.u1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.u1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301908
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '24.v1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.k1.a1', '12.q1.b1', '12.t1.a1', '12.bf1.a1', '12.bh1.a1', '12.bl1.a1', '12.bn1.a1', '12.bq1.a1'], 'contains': ['48.a1.a1', '48.bp1.a1', '72.t1.a1', '72.ba1.a1', '72.bg1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [43, 576, 936, 864, 48], 'label': '1728.34767.24.v1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.k1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.b1', 'old_label': '24.v1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.v1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301909
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '24.v1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.k1.a1', '12.q1.a1', '12.t1.b1', '12.bf1.b1', '12.bh1.b1', '12.bl1.b1', '12.bn1.b1', '12.bq1.b1'], 'contains': ['48.a1.b1', '48.bp1.b1', '72.t1.b1', '72.ba1.a1', '72.bg1.b1'], 'core': '48.a1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [43, 576, 936, 864, 4], 'label': '1728.34767.24.v1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.k1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '24.v1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.v1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301910
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '24.w1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.b1.a1', '12.v1.a1', '12.bv1.a1', '12.bw1.a1'], 'contains': ['48.f1.a1', '48.bq1.a1', '72.b1.a1', '72.bb1.b1', '72.bo1.a1'], 'core': '72.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [432, 864, 936, 1156, 48], 'label': '1728.34767.24.w1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '24.w1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.w1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301911
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '4.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.b1', '2.c1.a1', '2.j1.a1'], 'contains': ['8.c1.a1', '8.d1.a1', '8.i1.a1', '12.i1.b1', '12.bg1.a1', '12.cc1.a1'], 'core': '4.l1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [433, 4, 864, 36, 576, 48, 72], 'label': '1728.34767.4.l1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.l1.a1', 'normal_contained_in': ['2.a1.b1', '2.c1.a1', '2.j1.a1'], 'normal_contains': ['8.c1.a1', '8.d1.a1', '8.i1.a1', '12.i1.b1'], 'normalizer': '1.a1.a1', 'old_label': '4.l1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.l1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301912
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '24.w1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.b1.a1', '12.v1.b1', '12.bv1.b1', '12.bw1.b1'], 'contains': ['48.f1.b1', '48.bq1.b1', '72.b1.b1', '72.bb1.a1', '72.bo1.a1'], 'core': '72.b1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [432, 864, 936, 4, 1200], 'label': '1728.34767.24.w1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.b1', 'old_label': '24.w1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.w1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301913
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '24.x1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.d1.b1', '12.v1.a1', '12.bx1.a1', '12.by1.a1'], 'contains': ['48.f1.a1', '48.x1.a1', '72.c1.a1', '72.bc1.b1'], 'core': '72.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [438, 48, 864, 1156, 72], 'label': '1728.34767.24.x1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.d1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '24.x1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.x1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301914
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '24.x1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.d1.a1', '12.v1.b1', '12.bx1.b1', '12.by1.b1'], 'contains': ['48.f1.b1', '48.x1.b1', '72.c1.b1', '72.bc1.a1'], 'core': '72.c1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [433, 4, 864, 1200, 72], 'label': '1728.34767.24.x1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.b1', 'old_label': '24.x1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.x1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301915
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '24.y1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.h1.b1', '12.w1.a1', '12.bv1.a1', '12.bx1.a1'], 'contains': ['48.f1.a1', '48.y1.a1', '72.o1.a1', '72.bd1.b1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [37, 1156, 864, 48, 72], 'label': '1728.34767.24.y1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.h1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.j1.a1', 'old_label': '24.y1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.y1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301916
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '24.y1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.h1.a1', '12.w1.b1', '12.bv1.b1', '12.bx1.b1'], 'contains': ['48.f1.b1', '48.y1.b1', '72.o1.b1', '72.bd1.a1'], 'core': '144.a1.b1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [42, 1200, 864, 4, 72], 'label': '1728.34767.24.y1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.h1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.j1.b1', 'old_label': '24.y1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.y1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301917
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '24.z1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.i1.a1', '12.x1.a1', '12.bv1.a1', '12.by1.a1'], 'contains': ['48.f1.a1', '48.br1.a1', '72.q1.a1', '72.be1.b1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [469, 1156, 936, 48, 864], 'label': '1728.34767.24.z1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.i1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.j1.a1', 'old_label': '24.z1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.z1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301918
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '24.z1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.i1.b1', '12.x1.b1', '12.bv1.b1', '12.by1.b1'], 'contains': ['48.f1.b1', '48.br1.b1', '72.q1.b1', '72.be1.a1'], 'core': '144.a1.b1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [474, 1200, 936, 4, 864], 'label': '1728.34767.24.z1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.i1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.j1.b1', 'old_label': '24.z1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.z1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301919
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '24.ba1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.j1.a1', '12.x1.a1', '12.bw1.a1', '12.bx1.a1'], 'contains': ['48.f1.a1', '48.bs1.a1', '48.bs1.b1', '72.s1.a1', '72.bf1.b1', '72.bp1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [475, 48, 936, 864, 1156], 'label': '1728.34767.24.ba1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.j1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.j1.a1', 'old_label': '24.ba1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.ba1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301920
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '24.ba1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.j1.a1', '12.x1.b1', '12.bw1.b1', '12.bx1.b1'], 'contains': ['48.f1.b1', '48.bs1.c1', '48.bs1.d1', '72.s1.b1', '72.bf1.a1', '72.bp1.a1'], 'core': '144.a1.b1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [475, 1200, 936, 864, 4], 'label': '1728.34767.24.ba1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.j1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.j1.b1', 'old_label': '24.ba1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.ba1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301921
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '24.bb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.k1.a1', '12.w1.a1', '12.bw1.a1', '12.by1.a1'], 'contains': ['48.f1.a1', '48.bt1.a1', '72.t1.a1', '72.bg1.b1', '72.bq1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [43, 48, 936, 864, 1156], 'label': '1728.34767.24.bb1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.k1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.j1.a1', 'old_label': '24.bb1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bb1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301922
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '4.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.a1.b1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '2.c1.b1', '2.j1.a1'], 'contains': ['8.c1.a1', '8.d1.b1', '8.i1.b1', '12.i1.a1', '12.bg1.b1', '12.cc1.b1'], 'core': '4.l1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [438, 48, 864, 36, 576, 4, 72], 'label': '1728.34767.4.l1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.l1.b1', 'normal_contained_in': ['2.a1.a1', '2.c1.b1', '2.j1.a1'], 'normal_contains': ['8.c1.a1', '8.d1.b1', '8.i1.b1', '12.i1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.l1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.l1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301923
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '24.bb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.k1.a1', '12.w1.b1', '12.bw1.b1', '12.by1.b1'], 'contains': ['48.f1.b1', '48.bt1.b1', '72.t1.b1', '72.bg1.a1', '72.bq1.a1'], 'core': '144.a1.b1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [43, 1200, 936, 864, 4], 'label': '1728.34767.24.bb1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.k1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.j1.b1', 'old_label': '24.bb1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bb1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301924
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '24.bc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.bc1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.c1.a1', '12.y1.a1', '12.y1.b1', '12.bz1.a1', '12.cc1.a1', '12.cc1.b1', '12.cd1.a1', '12.ce1.a1'], 'contains': ['48.b1.a1', '48.z1.a1', '72.j1.a1', '72.j1.b1', '72.bi1.a1'], 'core': '48.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [36, 72, 864, 4, 48], 'label': '1728.34767.24.bc1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '24.bc1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bc1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301925
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '24.bd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.bd1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.e1.a1', '12.z1.a1', '12.z1.b1', '12.bz1.a1', '12.cf1.a1', '12.cf1.b1', '12.ci1.a1', '12.cj1.a1'], 'contains': ['48.b1.a1', '48.bb1.a1', '72.l1.a1', '72.l1.b1', '72.bj1.a1'], 'core': '48.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [468, 72, 864, 4, 48], 'label': '1728.34767.24.bd1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '24.bd1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bd1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301926
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '24.be1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.j1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.h1.a1', '12.y1.a1', '12.ba1.b1', '12.ca1.a1', '12.cf1.b1', '12.cg1.a1', '12.ck1.a1', '12.cm1.a1'], 'contains': ['48.b1.a1', '48.bd1.a1', '72.o1.b1', '72.p1.a1'], 'core': '48.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [42, 48, 864, 4, 72], 'label': '1728.34767.24.be1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.h1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '24.be1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.be1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301927
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '24.be1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.h1.b1', '12.y1.b1', '12.ba1.a1', '12.ca1.b1', '12.cf1.a1', '12.cg1.b1', '12.ck1.a1', '12.cm1.b1'], 'contains': ['48.b1.a1', '48.bd1.b1', '72.o1.a1', '72.p1.b1'], 'core': '48.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [37, 4, 864, 48, 72], 'label': '1728.34767.24.be1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.h1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '24.be1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.be1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301928
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '24.bf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.i1.a1', '12.z1.b1', '12.bb1.a1', '12.ca1.b1', '12.cc1.a1', '12.ch1.b1', '12.cl1.a1', '12.cm1.a1'], 'contains': ['48.b1.a1', '48.bv1.a1', '72.q1.a1', '72.r1.b1'], 'core': '48.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [469, 4, 936, 48, 864], 'label': '1728.34767.24.bf1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.i1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '24.bf1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bf1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301929
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '24.bf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.i1.b1', '12.z1.a1', '12.bb1.b1', '12.ca1.a1', '12.cc1.b1', '12.ch1.a1', '12.cl1.a1', '12.cm1.b1'], 'contains': ['48.b1.a1', '48.bv1.b1', '72.q1.b1', '72.r1.a1'], 'core': '48.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [474, 48, 936, 4, 864], 'label': '1728.34767.24.bf1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.i1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '24.bf1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bf1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301930
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '24.bg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.j1.a1', '12.bb1.a1', '12.bb1.b1', '12.cb1.a1', '12.ce1.a1', '12.cg1.a1', '12.cg1.b1', '12.ci1.a1'], 'contains': ['48.b1.a1', '48.bw1.a1', '48.bw1.b1', '72.s1.a1', '72.s1.b1', '72.bm1.a1'], 'core': '48.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [475, 48, 936, 864, 4], 'label': '1728.34767.24.bg1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.j1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '24.bg1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bg1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301931
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '24.bh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.k1.a1', '12.ba1.a1', '12.ba1.b1', '12.cb1.a1', '12.cd1.a1', '12.ch1.a1', '12.ch1.b1', '12.cj1.a1'], 'contains': ['48.b1.a1', '48.bx1.a1', '72.t1.a1', '72.t1.b1', '72.bn1.a1'], 'core': '48.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [43, 48, 936, 864, 4], 'label': '1728.34767.24.bh1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.k1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '24.bh1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bh1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301932
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '24.bi1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.b1.a1', '12.cn1.a1', '12.co1.a1', '12.cp1.a1'], 'contains': ['48.g1.a1', '48.by1.a1', '48.by1.b1', '72.d1.a1', '72.bh1.a1', '72.bo1.a1'], 'core': '72.d1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [432, 864, 936, 100, 576], 'label': '1728.34767.24.bi1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.h1.a1', 'old_label': '24.bi1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bi1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301933
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '2.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': ['864.d1.c1', '864.d1.d1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1', '4.e1.a1', '4.f1.a1', '4.j1.b1', '4.k1.a1', '4.p1.b1', '4.q1.b1', '6.d1.a1', '6.g1.a1', '6.j1.a1', '6.l1.a1'], 'core': '2.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [37, 864, 4, 6, 72, 576, 48, 432], 'label': '1728.34767.2.b1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.a1.a1', '4.f1.a1', '4.e1.a1', '4.j1.b1', '4.k1.a1', '4.q1.b1', '4.p1.b1'], 'normalizer': '1.a1.a1', 'old_label': '2.b1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2.b1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301934
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '4.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.f1.a1', '2.h1.a1', '2.j1.a1'], 'contains': ['8.c1.a1', '8.f1.a1', '8.k1.a1', '12.bh1.a1', '12.bh1.b1', '12.cd1.a1', '12.cq1.a1'], 'core': '4.m1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [7, 48, 4, 36, 576, 936, 864], 'label': '1728.34767.4.m1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.m1.a1', 'normal_contained_in': ['2.f1.a1', '2.h1.a1', '2.j1.a1'], 'normal_contains': ['8.c1.a1', '8.f1.a1', '8.k1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.m1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.m1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301935
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '24.bj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.c1.a1', '12.cn1.a1', '12.cq1.a1', '12.cr1.a1'], 'contains': ['48.g1.a1', '48.be1.a1', '72.e1.a1', '72.bi1.a1'], 'core': '72.e1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [36, 576, 864, 100, 72], 'label': '1728.34767.24.bj1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.h1.a1', 'old_label': '24.bj1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bj1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301936
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '24.bk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.e1.a1', '12.cn1.a1', '12.cs1.a1', '12.ct1.a1'], 'contains': ['48.g1.a1', '48.bf1.a1', '72.f1.a1', '72.bj1.a1'], 'core': '72.f1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [468, 576, 864, 100, 72], 'label': '1728.34767.24.bk1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.h1.a1', 'old_label': '24.bk1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bk1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301937
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '24.bl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.f1.a1', '12.co1.a1', '12.cq1.a1', '12.cs1.a1'], 'contains': ['48.g1.a1', '48.l1.a1', '48.l1.b1', '72.v1.a1', '72.bk1.a1'], 'core': '144.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [7, 100, 864, 576, 936], 'label': '1728.34767.24.bl1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.bb1.a1', 'old_label': '24.bl1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bl1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301938
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '24.bm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.g1.a1', '12.co1.a1', '12.cr1.a1', '12.ct1.a1'], 'contains': ['48.g1.a1', '48.bg1.a1', '72.w1.a1', '72.bl1.a1'], 'core': '144.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [439, 100, 864, 576, 72], 'label': '1728.34767.24.bm1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.bb1.a1', 'old_label': '24.bm1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bm1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301939
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '24.bn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.j1.a1', '12.cp1.a1', '12.cr1.a1', '12.cs1.a1'], 'contains': ['48.g1.a1', '48.bz1.a1', '48.bz1.b1', '72.z1.a1', '72.bm1.a1', '72.bp1.a1'], 'core': '144.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [475, 576, 936, 864, 100], 'label': '1728.34767.24.bn1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.j1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.bb1.a1', 'old_label': '24.bn1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bn1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301940
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '24.bo1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.k1.a1', '12.cp1.a1', '12.cq1.a1', '12.ct1.a1'], 'contains': ['48.g1.a1', '48.ca1.a1', '48.ca1.a2', '72.ba1.a1', '72.bn1.a1', '72.bq1.a1'], 'core': '144.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [43, 576, 936, 864, 100], 'label': '1728.34767.24.bo1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.k1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.bb1.a1', 'old_label': '24.bo1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bo1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301941
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '24.bp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.b1.a1', '12.cu1.a1'], 'contains': ['48.h1.a1', '48.cb1.a1', '48.cb1.b1', '72.bb1.a1', '72.bb1.b1', '72.bh1.a1', '72.bo1.a1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [432, 864, 936, 1156, 1200], 'label': '1728.34767.24.bp1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.k1.a1', 'old_label': '24.bp1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bp1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301942
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '24.bq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.j1.a1', '12.cu1.a1'], 'contains': ['48.h1.a1', '48.cc1.a1', '48.cc1.b1', '72.bf1.a1', '72.bf1.b1', '72.bm1.a1', '72.bp1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [475, 1200, 936, 864, 1156], 'label': '1728.34767.24.bq1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.j1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.cu1.a1', 'old_label': '24.bq1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bq1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301943
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '24.br1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.k1.a1', '12.cu1.a1'], 'contains': ['48.h1.a1', '48.cd1.a1', '48.cd1.a2', '72.bg1.a1', '72.bg1.b1', '72.bn1.a1', '72.bq1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [43, 1200, 936, 864, 1156], 'label': '1728.34767.24.br1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.k1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.cu1.a1', 'old_label': '24.br1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.br1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301944
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '24.bs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.l1.a1', '12.bc1.a1'], 'contains': ['48.c1.c1', '48.i1.a1', '48.k1.c1', '72.br1.a1', '72.bs1.a1'], 'core': '48.c1.c1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [1, 4, 6, 576, 936], 'label': '1728.34767.24.bs1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.l1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '24.bs1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bs1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301945
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '4.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1', '2.c1.b1', '2.h1.a1'], 'contains': ['8.c1.a1', '8.g1.a1', '8.j1.a1', '12.bi1.a1', '12.bi1.b1', '12.ce1.a1', '12.cr1.a1'], 'core': '4.n1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [439, 48, 4, 36, 576, 72, 864], 'label': '1728.34767.4.n1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.n1.a1', 'normal_contained_in': ['2.c1.b1', '2.c1.a1', '2.h1.a1'], 'normal_contains': ['8.c1.a1', '8.g1.a1', '8.j1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.n1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.n1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301946
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '24.bs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.l1.b1', '12.bc1.a1'], 'contains': ['48.c1.d1', '48.i1.a1', '48.k1.d1', '72.br1.b1', '72.bs1.b1'], 'core': '48.c1.d1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [865, 4, 6, 576, 936], 'label': '1728.34767.24.bs1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.l1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '24.bs1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bs1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301947
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '24.bs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.l1.a1', '12.bc1.b1'], 'contains': ['48.c1.a1', '48.i1.c1', '48.k1.a1', '72.br1.a1', '72.bs1.c1'], 'core': '48.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [1, 48, 6, 576, 936], 'label': '1728.34767.24.bs1.c1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.l1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.b1', 'old_label': '24.bs1.c1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bs1.c1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301948
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '24.bs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.l1.b1', '12.bc1.b1'], 'contains': ['48.c1.a1', '48.i1.d1', '48.k1.b1', '72.br1.b1', '72.bs1.d1'], 'core': '48.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [865, 48, 6, 576, 936], 'label': '1728.34767.24.bs1.d1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.l1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.b1', 'old_label': '24.bs1.d1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bs1.d1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301949
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '24.bs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.l1.c1', '12.bc1.a1'], 'contains': ['48.c1.c1', '48.i1.b1', '48.k1.d1', '72.br1.c1', '72.bs1.e1'], 'core': '48.c1.c1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [1, 4, 870, 576, 936], 'label': '1728.34767.24.bs1.e1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.l1.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '24.bs1.e1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bs1.e1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301950
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '24.bs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.l1.d1', '12.bc1.a1'], 'contains': ['48.c1.d1', '48.i1.b1', '48.k1.c1', '72.br1.d1', '72.bs1.f1'], 'core': '48.c1.d1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [865, 4, 870, 576, 936], 'label': '1728.34767.24.bs1.f1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.l1.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '24.bs1.f1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bs1.f1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301951
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '24.bs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.l1.c1', '12.bc1.b1'], 'contains': ['48.c1.b1', '48.i1.c1', '48.k1.b1', '72.br1.c1', '72.bs1.g1'], 'core': '48.c1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [1, 48, 870, 576, 936], 'label': '1728.34767.24.bs1.g1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.l1.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.b1', 'old_label': '24.bs1.g1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bs1.g1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301952
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '24.bs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.l1.d1', '12.bc1.b1'], 'contains': ['48.c1.b1', '48.i1.d1', '48.k1.a1', '72.br1.d1', '72.bs1.h1'], 'core': '48.c1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [865, 48, 870, 576, 936], 'label': '1728.34767.24.bs1.h1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.l1.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.b1', 'old_label': '24.bs1.h1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bs1.h1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301953
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '24.bt1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.m1.a1', '12.n1.a1'], 'contains': ['48.m1.a1', '48.q1.b1', '48.v1.b1', '72.bt1.a1', '72.bv1.a1'], 'core': '96.c1.b1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [6, 576, 36, 4, 72], 'label': '1728.34767.24.bt1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.n1.a1', 'old_label': '24.bt1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bt1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301954
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '24.bt1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.g1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.m1.b1', '12.n1.b1'], 'contains': ['48.m1.b1', '48.q1.a1', '48.v1.a1', '72.bt1.b1', '72.bv1.b1'], 'core': '96.c1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [1, 576, 36, 48, 72], 'label': '1728.34767.24.bt1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.n1.b1', 'old_label': '24.bt1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bt1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301955
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '24.bu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.n1.a1', '12.o1.a1'], 'contains': ['48.m1.a1', '48.s1.b1', '48.u1.b1', '72.bu1.a1', '72.bw1.a1'], 'core': '96.c1.b1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [433, 4, 6, 576, 72], 'label': '1728.34767.24.bu1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.o1.a1', 'old_label': '24.bu1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bu1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301956
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '4.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.b1', '2.d1.a1', '2.k1.a1'], 'contains': ['8.d1.a1', '8.e1.a1', '8.h1.b1', '8.o1.a1', '12.j1.b1', '12.bj1.a1', '12.cf1.a1'], 'core': '4.o1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [433, 4, 72, 468, 576, 864, 48], 'label': '1728.34767.4.o1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.o1.a1', 'normal_contained_in': ['2.a1.b1', '2.d1.a1', '2.k1.a1'], 'normal_contains': ['8.d1.a1', '8.e1.a1', '8.h1.b1', '12.j1.b1'], 'normalizer': '1.a1.a1', 'old_label': '4.o1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.o1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301957
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '24.bu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.h1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.n1.b1', '12.o1.b1'], 'contains': ['48.m1.b1', '48.s1.a1', '48.u1.a1', '72.bu1.b1', '72.bw1.b1'], 'core': '96.c1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [1, 48, 438, 576, 72], 'label': '1728.34767.24.bu1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.o1.b1', 'old_label': '24.bu1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bu1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301958
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '24.bv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.m1.a1', '12.b1.a1'], 'contains': ['48.n1.a1', '48.q1.a1', '48.w1.a1', '72.bv1.a1', '72.bx1.a1'], 'core': '96.c1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [6, 576, 36, 72, 48], 'label': '1728.34767.24.bv1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.a1', 'old_label': '24.bv1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bv1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301959
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '24.bv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.m1.b1', '12.b1.b1'], 'contains': ['48.n1.b1', '48.q1.b1', '48.w1.b1', '72.bv1.b1', '72.bx1.b1'], 'core': '96.c1.b1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [1, 576, 36, 72, 4], 'label': '1728.34767.24.bv1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.b1', 'old_label': '24.bv1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bv1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301960
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '24.bw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.u1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.n1.a1', '12.s1.a1'], 'contains': ['48.n1.a1', '48.r1.a1', '48.u1.a1', '72.bw1.a1', '72.by1.a1'], 'core': '96.c1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [433, 48, 6, 576, 72], 'label': '1728.34767.24.bw1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.s1.a1', 'old_label': '24.bw1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bw1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301961
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '24.bw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.u1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.n1.b1', '12.s1.b1'], 'contains': ['48.n1.b1', '48.r1.b1', '48.u1.b1', '72.bw1.b1', '72.by1.b1'], 'core': '96.c1.b1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [1, 4, 438, 576, 72], 'label': '1728.34767.24.bw1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.s1.b1', 'old_label': '24.bw1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bw1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301962
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '24.bx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.j1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.m1.a1', '12.y1.a1'], 'contains': ['48.p1.a1', '48.z1.a1', '48.bd1.a1', '72.bt1.a1', '72.bx1.a1'], 'core': '96.d1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [6, 48, 36, 4, 72], 'label': '1728.34767.24.bx1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.y1.a1', 'old_label': '24.bx1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bx1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301963
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '24.bx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.m1.b1', '12.y1.b1'], 'contains': ['48.p1.b1', '48.z1.a1', '48.bd1.b1', '72.bt1.b1', '72.bx1.b1'], 'core': '96.d1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [1, 4, 36, 48, 72], 'label': '1728.34767.24.bx1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.y1.b1', 'old_label': '24.bx1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bx1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301964
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '24.by1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.n1.a1', '12.e1.a1'], 'contains': ['48.p1.a1', '48.ba1.a1', '48.bc1.a1', '72.bu1.a1', '72.by1.a1'], 'core': '96.d1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [433, 48, 6, 72, 4], 'label': '1728.34767.24.by1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1.a1', 'old_label': '24.by1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.by1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301965
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '24.by1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.n1.b1', '12.e1.b1'], 'contains': ['48.p1.b1', '48.ba1.b1', '48.bc1.a1', '72.bu1.b1', '72.by1.b1'], 'core': '96.d1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [1, 48, 438, 72, 4], 'label': '1728.34767.24.by1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.e1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1.b1', 'old_label': '24.by1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.by1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301966
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '24.bz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.o1.a1', '12.bj1.a1'], 'contains': ['48.r1.a1', '48.t1.a1', '48.v1.a1', '72.bz1.a1', '72.cb1.a1'], 'core': '96.c1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [433, 576, 468, 48, 72], 'label': '1728.34767.24.bz1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.o1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bj1.a1', 'old_label': '24.bz1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bz1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301967
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '4.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.a1.b1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '2.d1.b1', '2.k1.a1'], 'contains': ['8.d1.b1', '8.e1.a1', '8.h1.a1', '8.o1.b1', '12.j1.a1', '12.bj1.b1', '12.cf1.b1'], 'core': '4.o1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [438, 48, 72, 468, 576, 864, 4], 'label': '1728.34767.4.o1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.o1.b1', 'normal_contained_in': ['2.a1.a1', '2.d1.b1', '2.k1.a1'], 'normal_contains': ['8.d1.b1', '8.e1.a1', '8.h1.a1', '12.j1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.o1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.o1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301968
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '24.bz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.o1.b1', '12.bj1.b1'], 'contains': ['48.r1.b1', '48.t1.b1', '48.v1.b1', '72.bz1.b1', '72.cb1.b1'], 'core': '96.c1.b1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [438, 576, 468, 4, 72], 'label': '1728.34767.24.bz1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.o1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bj1.b1', 'old_label': '24.bz1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bz1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301969
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '24.ca1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.o1.b1', '12.j1.a1'], 'contains': ['48.s1.a1', '48.t1.a1', '48.w1.a1', '72.ca1.a1', '72.cb1.b1'], 'core': '96.c1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [438, 576, 468, 72, 48], 'label': '1728.34767.24.ca1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.j1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.o1.b1', 'old_label': '24.ca1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.ca1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301970
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '24.ca1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.o1.a1', '12.j1.b1'], 'contains': ['48.s1.b1', '48.t1.b1', '48.w1.b1', '72.ca1.b1', '72.cb1.a1'], 'core': '96.c1.b1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [433, 576, 468, 72, 4], 'label': '1728.34767.24.ca1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.j1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.o1.a1', 'old_label': '24.ca1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.ca1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301971
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '24.cb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.o1.a1', '12.cf1.a1'], 'contains': ['48.ba1.a1', '48.bb1.a1', '48.bd1.b1', '72.bz1.a1', '72.ca1.b1'], 'core': '96.d1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [433, 4, 468, 48, 72], 'label': '1728.34767.24.cb1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.o1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.cf1.a1', 'old_label': '24.cb1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.cb1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301972
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '24.cb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.o1.b1', '12.cf1.b1'], 'contains': ['48.ba1.b1', '48.bb1.a1', '48.bd1.a1', '72.bz1.b1', '72.ca1.a1'], 'core': '96.d1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [438, 48, 468, 4, 72], 'label': '1728.34767.24.cb1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.o1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.cf1.b1', 'old_label': '24.cb1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.cb1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301973
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '24.cc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.p1.a1', '12.r1.a1'], 'contains': ['48.bh1.a1', '48.bn1.b1', '48.bo1.c1', '72.cc1.a1', '72.cd1.a1', '72.ce1.a1'], 'core': '96.e1.b1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [469, 576, 6, 864, 4], 'label': '1728.34767.24.cc1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.e1.a1', 'old_label': '24.cc1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.cc1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301974
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '24.cc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.p1.b1', '12.r1.a1'], 'contains': ['48.bh1.a1', '48.bn1.b1', '48.bo1.d1', '72.cc1.b1', '72.cd1.b1', '72.ce1.b1'], 'core': '96.e1.b1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [1405, 576, 6, 864, 4], 'label': '1728.34767.24.cc1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.e1.a1', 'old_label': '24.cc1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.cc1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301975
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '24.cc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.p1.c1', '12.r1.b1'], 'contains': ['48.bh1.b1', '48.bn1.a1', '48.bo1.a1', '72.cc1.c1', '72.cd1.c1', '72.ce1.c1'], 'core': '96.e1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [937, 576, 474, 864, 48], 'label': '1728.34767.24.cc1.c1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.f1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.e1.b1', 'old_label': '24.cc1.c1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.cc1.c1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301976
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '24.cc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.p1.d1', '12.r1.b1'], 'contains': ['48.bh1.b1', '48.bn1.a1', '48.bo1.b1', '72.cc1.d1', '72.cd1.d1', '72.ce1.d1'], 'core': '96.e1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [1, 576, 474, 864, 48], 'label': '1728.34767.24.cc1.d1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.f1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.e1.b1', 'old_label': '24.cc1.d1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.cc1.d1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301977
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '24.cd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.p1.a1', '12.u1.a1'], 'contains': ['48.bi1.a1', '48.bm1.a1', '48.bo1.a1', '72.cd1.a1', '72.cf1.a1'], 'core': '96.e1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [469, 576, 6, 864, 48], 'label': '1728.34767.24.cd1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.h1.a1', 'old_label': '24.cd1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.cd1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301978
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '4.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.b1.b1', '2.c1.a1', '2.k1.a1'], 'contains': ['8.d1.a1', '8.h1.a1', '8.j1.a1', '12.bk1.a1', '12.bm1.b1', '12.bx1.b1', '12.cg1.a1'], 'core': '4.p1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [433, 48, 4, 42, 576, 72, 864], 'label': '1728.34767.4.p1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.p1.a1', 'normal_contained_in': ['2.b1.b1', '2.c1.a1', '2.k1.a1'], 'normal_contains': ['8.d1.a1', '8.h1.a1', '8.j1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.p1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.p1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301979
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '24.cd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.p1.b1', '12.u1.a1'], 'contains': ['48.bi1.a1', '48.bm1.a1', '48.bo1.b1', '72.cd1.b1', '72.cf1.b1'], 'core': '96.e1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [1405, 576, 6, 864, 48], 'label': '1728.34767.24.cd1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.h1.a1', 'old_label': '24.cd1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.cd1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301980
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '24.cd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.p1.c1', '12.u1.b1'], 'contains': ['48.bi1.b1', '48.bm1.b1', '48.bo1.c1', '72.cd1.c1', '72.cf1.c1'], 'core': '96.e1.b1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [937, 576, 474, 864, 4], 'label': '1728.34767.24.cd1.c1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.f1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.h1.b1', 'old_label': '24.cd1.c1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.cd1.c1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301981
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '24.cd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.p1.d1', '12.u1.b1'], 'contains': ['48.bi1.b1', '48.bm1.b1', '48.bo1.d1', '72.cd1.d1', '72.cf1.d1'], 'core': '96.e1.b1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [1, 576, 474, 864, 4], 'label': '1728.34767.24.cd1.d1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.f1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.h1.b1', 'old_label': '24.cd1.d1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.cd1.d1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301982
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '24.ce1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.p1.a1', '12.x1.a1'], 'contains': ['48.bj1.a1', '48.br1.a1', '48.bs1.a1', '72.ce1.a1', '72.cf1.a1'], 'core': '288.e1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [469, 48, 6, 864, 1156], 'label': '1728.34767.24.ce1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.x1.a1', 'old_label': '24.ce1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.ce1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301983
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '24.ce1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.p1.b1', '12.x1.a1'], 'contains': ['48.bj1.a1', '48.br1.a1', '48.bs1.b1', '72.ce1.b1', '72.cf1.b1'], 'core': '288.e1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [1405, 48, 6, 864, 1156], 'label': '1728.34767.24.ce1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.x1.a1', 'old_label': '24.ce1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.ce1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301984
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '24.ce1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.p1.c1', '12.x1.b1'], 'contains': ['48.bj1.b1', '48.br1.b1', '48.bs1.c1', '72.ce1.c1', '72.cf1.c1'], 'core': '288.e1.b1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [937, 1200, 474, 864, 4], 'label': '1728.34767.24.ce1.c1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.f1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.x1.b1', 'old_label': '24.ce1.c1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.ce1.c1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301985
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '24.ce1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.p1.d1', '12.x1.b1'], 'contains': ['48.bj1.b1', '48.br1.b1', '48.bs1.d1', '72.ce1.d1', '72.cf1.d1'], 'core': '288.e1.b1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [1, 1200, 474, 864, 4], 'label': '1728.34767.24.ce1.d1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.f1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.x1.b1', 'old_label': '24.ce1.d1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.ce1.d1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301986
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '24.cf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.p1.a1', '12.bb1.a1'], 'contains': ['48.bk1.a1', '48.bv1.a1', '48.bw1.a1', '72.cc1.a1', '72.cf1.a1'], 'core': '96.f1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [469, 48, 6, 864, 4], 'label': '1728.34767.24.cf1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.m1.a1', 'old_label': '24.cf1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.cf1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301987
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '24.cf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.p1.b1', '12.bb1.a1'], 'contains': ['48.bk1.a1', '48.bv1.a1', '48.bw1.b1', '72.cc1.b1', '72.cf1.b1'], 'core': '96.f1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [1405, 48, 6, 864, 4], 'label': '1728.34767.24.cf1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.m1.a1', 'old_label': '24.cf1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.cf1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301988
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '24.cf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.p1.c1', '12.bb1.b1'], 'contains': ['48.bk1.b1', '48.bv1.b1', '48.bw1.a1', '72.cc1.c1', '72.cf1.c1'], 'core': '96.f1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [937, 48, 474, 864, 4], 'label': '1728.34767.24.cf1.c1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.f1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.m1.b1', 'old_label': '24.cf1.c1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.cf1.c1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301989
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '4.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '2.c1.b1', '2.k1.a1'], 'contains': ['8.d1.b1', '8.h1.b1', '8.j1.a1', '12.bk1.b1', '12.bm1.a1', '12.bx1.a1', '12.cg1.b1'], 'core': '4.p1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [37, 48, 4, 438, 576, 72, 864], 'label': '1728.34767.4.p1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.p1.b1', 'normal_contained_in': ['2.b1.a1', '2.c1.b1', '2.k1.a1'], 'normal_contains': ['8.d1.b1', '8.h1.b1', '8.j1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.p1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.p1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301990
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '24.cf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.p1.d1', '12.bb1.b1'], 'contains': ['48.bk1.b1', '48.bv1.b1', '48.bw1.b1', '72.cc1.d1', '72.cf1.d1'], 'core': '96.f1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [1, 48, 474, 864, 4], 'label': '1728.34767.24.cf1.d1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.f1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.m1.b1', 'old_label': '24.cf1.d1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.cf1.d1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301991
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '24.cg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.q1.a1', '12.bf1.a1'], 'contains': ['48.bl1.a1', '48.bo1.a1', '48.bp1.a1', '72.cg1.a1', '72.ch1.a1', '72.ci1.a1'], 'core': '96.e1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [979, 576, 432, 864, 48], 'label': '1728.34767.24.cg1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.k1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.t1.a1', 'old_label': '24.cg1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.cg1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301992
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '24.cg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.q1.b1', '12.bf1.a1'], 'contains': ['48.bl1.a1', '48.bo1.b1', '48.bp1.a1', '72.cg1.b1', '72.ch1.b1', '72.ci1.b1'], 'core': '96.e1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [43, 576, 432, 864, 48], 'label': '1728.34767.24.cg1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.k1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.t1.a1', 'old_label': '24.cg1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.cg1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301993
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '24.cg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.q1.a1', '12.bf1.b1'], 'contains': ['48.bl1.b1', '48.bo1.c1', '48.bp1.b1', '72.cg1.c1', '72.ch1.a1', '72.ci1.c1'], 'core': '96.e1.b1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [979, 576, 432, 864, 4], 'label': '1728.34767.24.cg1.c1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.k1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.t1.b1', 'old_label': '24.cg1.c1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.cg1.c1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301994
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '24.cg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.q1.b1', '12.bf1.b1'], 'contains': ['48.bl1.b1', '48.bo1.d1', '48.bp1.b1', '72.cg1.d1', '72.ch1.b1', '72.ci1.d1'], 'core': '96.e1.b1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [43, 576, 432, 864, 4], 'label': '1728.34767.24.cg1.d1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.k1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.t1.b1', 'old_label': '24.cg1.d1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.cg1.d1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301995
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '24.ch1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.q1.a1', '12.bw1.a1'], 'contains': ['48.bq1.a1', '48.bs1.a1', '48.bt1.a1', '72.cg1.a1', '72.ci1.c1', '72.ck1.a1', '72.ck1.b1'], 'core': '288.e1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [979, 48, 432, 864, 1156], 'label': '1728.34767.24.ch1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.k1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bw1.a1', 'old_label': '24.ch1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.ch1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301996
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '24.ch1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.q1.b1', '12.bw1.a1'], 'contains': ['48.bq1.a1', '48.bs1.b1', '48.bt1.a1', '72.cg1.b1', '72.ci1.d1', '72.ck1.c1', '72.ck1.d1'], 'core': '288.e1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [43, 48, 432, 864, 1156], 'label': '1728.34767.24.ch1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.k1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bw1.a1', 'old_label': '24.ch1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.ch1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301997
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '24.ch1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.q1.a1', '12.bw1.b1'], 'contains': ['48.bq1.b1', '48.bs1.c1', '48.bt1.b1', '72.cg1.c1', '72.ci1.a1', '72.ck1.a1', '72.ck1.b1'], 'core': '288.e1.b1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [979, 1200, 432, 864, 4], 'label': '1728.34767.24.ch1.c1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.k1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bw1.b1', 'old_label': '24.ch1.c1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.ch1.c1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301998
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '24.ch1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.q1.b1', '12.bw1.b1'], 'contains': ['48.bq1.b1', '48.bs1.d1', '48.bt1.b1', '72.cg1.d1', '72.ci1.b1', '72.ck1.c1', '72.ck1.d1'], 'core': '288.e1.b1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [43, 1200, 432, 864, 4], 'label': '1728.34767.24.ch1.d1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.k1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bw1.b1', 'old_label': '24.ch1.d1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.ch1.d1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93301999
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '24.ci1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.q1.a1', '12.cb1.a1'], 'contains': ['48.bu1.a1', '48.bw1.a1', '48.bx1.a1', '72.cg1.a1', '72.cg1.c1', '72.cj1.a1', '72.cj1.b1'], 'core': '96.f1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [979, 48, 432, 864, 4], 'label': '1728.34767.24.ci1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.k1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.x1.a1', 'old_label': '24.ci1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.ci1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302000
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '4.q1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.b1.b1', '2.d1.a1', '2.j1.a1'], 'contains': ['8.d1.a1', '8.i1.b1', '8.k1.a1', '12.bl1.a1', '12.bn1.b1', '12.by1.b1', '12.ch1.a1'], 'core': '4.q1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [433, 48, 4, 474, 576, 72, 864], 'label': '1728.34767.4.q1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.q1.a1', 'normal_contained_in': ['2.b1.b1', '2.d1.a1', '2.j1.a1'], 'normal_contains': ['8.d1.a1', '8.i1.b1', '8.k1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.q1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.q1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302001
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '24.ci1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.q1.b1', '12.cb1.a1'], 'contains': ['48.bu1.a1', '48.bw1.b1', '48.bx1.a1', '72.cg1.b1', '72.cg1.d1', '72.cj1.c1', '72.cj1.d1'], 'core': '96.f1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [43, 48, 432, 864, 4], 'label': '1728.34767.24.ci1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.k1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.x1.a1', 'old_label': '24.ci1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.ci1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302002
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '24.cj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.q1.a1', '12.cp1.a1'], 'contains': ['48.by1.a1', '48.bz1.a1', '48.ca1.a1', '72.ch1.a1', '72.cj1.a1', '72.ck1.a1'], 'core': '288.f1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [979, 576, 432, 864, 52], 'label': '1728.34767.24.cj1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.k1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.bb1.a1', 'old_label': '24.cj1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.cj1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302003
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '24.cj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.q1.a1', '12.cp1.a1'], 'contains': ['48.by1.b1', '48.bz1.a1', '48.ca1.a2', '72.ch1.a1', '72.cj1.b1', '72.ck1.b1'], 'core': '288.f1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [979, 576, 432, 864, 100], 'label': '1728.34767.24.cj1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.k1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.bb1.a1', 'old_label': '24.cj1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.cj1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302004
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '24.cj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.q1.b1', '12.cp1.a1'], 'contains': ['48.by1.a1', '48.bz1.b1', '48.ca1.a2', '72.ch1.b1', '72.cj1.c1', '72.ck1.c1'], 'core': '288.f1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [43, 576, 432, 864, 52], 'label': '1728.34767.24.cj1.c1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.k1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.bb1.a1', 'old_label': '24.cj1.c1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.cj1.c1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302005
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '24.cj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.q1.b1', '12.cp1.a1'], 'contains': ['48.by1.b1', '48.bz1.b1', '48.ca1.a1', '72.ch1.b1', '72.cj1.d1', '72.ck1.d1'], 'core': '288.f1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [43, 576, 432, 864, 100], 'label': '1728.34767.24.cj1.d1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.k1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.bb1.a1', 'old_label': '24.cj1.d1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.cj1.d1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302006
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '24.ck1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.q1.a1', '12.cu1.a1'], 'contains': ['48.cb1.a1', '48.cc1.a1', '48.cd1.a1', '72.ci1.a1', '72.ci1.c1', '72.cj1.a1', '72.ck1.b1'], 'core': '864.c1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [979, 624, 432, 864, 1156], 'label': '1728.34767.24.ck1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.k1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.cu1.a1', 'old_label': '24.ck1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.ck1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302007
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '24.ck1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.q1.a1', '12.cu1.a1'], 'contains': ['48.cb1.b1', '48.cc1.a1', '48.cd1.a2', '72.ci1.a1', '72.ci1.c1', '72.cj1.b1', '72.ck1.a1'], 'core': '864.c1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [979, 1200, 432, 864, 1156], 'label': '1728.34767.24.ck1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.k1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.cu1.a1', 'old_label': '24.ck1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.ck1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302008
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '24.ck1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.q1.b1', '12.cu1.a1'], 'contains': ['48.cb1.a1', '48.cc1.b1', '48.cd1.a2', '72.ci1.b1', '72.ci1.d1', '72.cj1.c1', '72.ck1.d1'], 'core': '864.c1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [43, 624, 432, 864, 1156], 'label': '1728.34767.24.ck1.c1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.k1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.cu1.a1', 'old_label': '24.ck1.c1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.ck1.c1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302009
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '24.ck1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.q1.b1', '12.cu1.a1'], 'contains': ['48.cb1.b1', '48.cc1.b1', '48.cd1.a1', '72.ci1.b1', '72.ci1.d1', '72.cj1.d1', '72.ck1.c1'], 'core': '864.c1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [43, 1200, 432, 864, 1156], 'label': '1728.34767.24.ck1.d1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.k1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.cu1.a1', 'old_label': '24.ck1.d1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.ck1.d1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302010
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '27.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['9.a1.a1', '9.b1.a1', '9.b1.b1'], 'contains': ['54.a1.a1', '54.a1.b1', '54.b1.a1', '54.b1.b1', '54.c1.a1', '54.c1.b1', '54.d1.a1', '54.d1.b1', '54.e1.a1', '54.f1.a1', '54.g1.a1', '54.h1.a1', '54.i1.a1', '54.j1.a1', '54.k1.a1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [1, 6, 36, 432], 'label': '1728.34767.27.a1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1.a1', 'old_label': '27.a1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '27.a1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302011
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '4.q1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '2.d1.b1', '2.j1.a1'], 'contains': ['8.d1.b1', '8.i1.a1', '8.k1.a1', '12.bl1.b1', '12.bn1.a1', '12.by1.a1', '12.ch1.b1'], 'core': '4.q1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [469, 48, 4, 438, 576, 72, 864], 'label': '1728.34767.4.q1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.q1.b1', 'normal_contained_in': ['2.b1.a1', '2.d1.b1', '2.j1.a1'], 'normal_contains': ['8.d1.b1', '8.i1.a1', '8.k1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.q1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.q1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302012
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '32.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '16.b1.a1', '16.b1.b1', '16.b1.c1', '16.b1.d1', '16.c1.a1', '16.c1.b1'], 'contains': ['64.a1.a1', '96.a1.a1', '96.a1.b1', '96.b1.a1', '96.g1.a1', '96.g1.b1', '96.h1.a1', '96.i1.a1'], 'core': '32.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [936, 4, 48, 576], 'label': '1728.34767.32.a1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '32.a1.a1', 'normal_contained_in': ['16.a1.a1', '16.b1.c1', '16.b1.a1', '16.b1.d1', '16.b1.b1', '16.c1.b1', '16.c1.a1'], 'normal_contains': ['64.a1.a1', '96.a1.b1', '96.a1.a1', '96.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '32.a1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.a1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302013
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '32.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '16.e1.a1', '16.e1.b1', '16.f1.a1', '16.g1.a1', '16.g1.b1', '16.h1.a1', '16.i1.a1', '16.j1.a1', '16.j1.b1'], 'contains': ['64.a1.a1', '96.c1.a1', '96.c1.b1', '96.d1.a1', '96.j1.a1', '96.j1.b1', '96.k1.a1', '96.l1.a1'], 'core': '32.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [72, 4, 48, 576], 'label': '1728.34767.32.b1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '32.b1.a1', 'normal_contained_in': ['16.a1.a1'], 'normal_contains': ['64.a1.a1', '96.c1.b1', '96.c1.a1', '96.d1.a1'], 'normalizer': '1.a1.a1', 'old_label': '32.b1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.b1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302014
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '32.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '16.d1.a1', '16.d1.b1', '16.k1.a1', '16.k1.b1', '16.l1.a1', '16.m1.a1', '16.m1.b1', '16.n1.a1'], 'contains': ['64.a1.a1', '96.e1.a1', '96.e1.b1', '96.f1.a1', '96.m1.a1', '96.m1.b1', '96.n1.a1', '96.o1.a1'], 'core': '32.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [864, 4, 48, 576], 'label': '1728.34767.32.c1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '32.c1.a1', 'normal_contained_in': ['16.a1.a1', '16.d1.a1', '16.d1.b1'], 'normal_contains': ['64.a1.a1', '96.e1.b1', '96.e1.a1', '96.f1.a1'], 'normalizer': '1.a1.a1', 'old_label': '32.c1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.c1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302015
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '32.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.b1.a1', '16.e1.a1', '16.k1.a1'], 'contains': ['64.a1.a1', '96.p1.a1', '96.q1.a1', '96.r1.a1', '96.s1.a1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [6, 4, 576, 48], 'label': '1728.34767.32.d1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '16.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '32.d1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.d1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302016
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '32.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.b1.b1', '16.e1.a1', '16.k1.a1'], 'contains': ['64.a1.a1', '96.p1.b1', '96.q1.b1', '96.r1.b1', '96.s1.b1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [870, 4, 576, 48], 'label': '1728.34767.32.d1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '16.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '32.d1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.d1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302017
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '32.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.b1.c1', '16.e1.b1', '16.k1.b1'], 'contains': ['64.a1.a1', '96.p1.c1', '96.q1.c1', '96.r1.c1', '96.s1.c1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [1, 48, 576, 4], 'label': '1728.34767.32.d1.c1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '16.b1.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.b1', 'old_label': '32.d1.c1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.d1.c1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302018
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '32.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.b1.d1', '16.e1.b1', '16.k1.b1'], 'contains': ['64.a1.a1', '96.p1.d1', '96.q1.d1', '96.r1.d1', '96.s1.d1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [865, 48, 576, 4], 'label': '1728.34767.32.d1.d1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '16.b1.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.b1', 'old_label': '32.d1.d1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.d1.d1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302019
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '36.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.a1.b1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['12.a1.a1', '12.d1.a1', '12.v1.a1', '18.m1.a1', '18.n1.a1', '18.q1.b1'], 'contains': ['72.a1.a1', '72.b1.a1', '72.c1.a1', '108.a1.a1'], 'core': '36.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [6, 48, 432, 936, 864], 'label': '1728.34767.36.a1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1.a1', 'normal_contained_in': ['12.a1.a1', '12.d1.a1'], 'normal_contains': ['72.a1.a1', '72.b1.a1', '72.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '36.a1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.a1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302020
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '36.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['12.a1.b1', '12.d1.b1', '12.v1.b1', '18.m1.b1', '18.n1.b1', '18.q1.a1'], 'contains': ['72.a1.b1', '72.b1.b1', '72.c1.b1', '108.a1.b1'], 'core': '36.a1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [1, 4, 432, 936, 864], 'label': '1728.34767.36.a1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1.b1', 'normal_contained_in': ['12.a1.b1', '12.d1.b1'], 'normal_contains': ['72.a1.b1', '72.b1.b1', '72.c1.b1'], 'normalizer': '1.a1.a1', 'old_label': '36.a1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.a1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302021
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '36.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.k1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['12.g1.a1', '12.g1.b1', '12.cn1.a1', '18.e1.a1', '18.e1.b1', '18.x1.a1'], 'contains': ['72.d1.a1', '72.e1.a1', '72.f1.a1', '108.h1.a1'], 'core': '36.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [36, 576, 432, 72, 864], 'label': '1728.34767.36.b1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.b1.a1', 'normal_contained_in': ['12.g1.b1', '12.g1.a1'], 'normal_contains': ['72.d1.a1', '72.e1.a1', '72.f1.a1'], 'normalizer': '1.a1.a1', 'old_label': '36.b1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.b1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302022
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '4.r1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.e1.a1', '2.j1.a1', '2.k1.a1'], 'contains': ['8.d1.a1', '8.d1.b1', '8.f1.a1', '12.l1.a1', '12.bo1.a1', '12.bo1.b1'], 'core': '4.r1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [433, 4, 864, 438, 48, 576, 72], 'label': '1728.34767.4.r1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.r1.a1', 'normal_contained_in': ['2.e1.a1', '2.j1.a1', '2.k1.a1'], 'normal_contains': ['8.d1.b1', '8.d1.a1', '8.f1.a1', '12.l1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.r1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.r1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302023
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '36.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.d1.a1', '12.m1.a1', '18.a1.a1', '18.b1.a1', '18.q1.a1'], 'contains': ['72.b1.b1', '72.g1.a1', '72.k1.b1', '108.a1.a1'], 'core': '72.b1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [6, 864, 432, 4, 936], 'label': '1728.34767.36.c1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '36.c1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.c1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302024
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '36.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.d1.b1', '12.m1.b1', '18.a1.b1', '18.b1.b1', '18.q1.b1'], 'contains': ['72.b1.a1', '72.g1.b1', '72.k1.a1', '108.a1.b1'], 'core': '72.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [1, 864, 432, 48, 936], 'label': '1728.34767.36.c1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.d1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.b1', 'old_label': '36.c1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.c1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302025
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '36.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '36.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.n1.a1', '12.y1.a1', '18.a1.a1', '18.c1.a1', '18.r1.a1'], 'contains': ['72.g1.a1', '72.j1.b1', '72.o1.b1', '72.bt1.a1', '108.b1.a1'], 'core': '144.a1.b1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [6, 72, 36, 864, 4], 'label': '1728.34767.36.d1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1.a1', 'old_label': '36.d1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.d1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302026
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '36.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '36.d1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.n1.b1', '12.y1.b1', '18.a1.b1', '18.c1.b1', '18.r1.b1'], 'contains': ['72.g1.b1', '72.j1.a1', '72.o1.a1', '72.bt1.b1', '108.b1.b1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [1, 72, 36, 864, 48], 'label': '1728.34767.36.d1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1.b1', 'old_label': '36.d1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.d1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302027
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '36.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.e1.a1', '12.o1.a1', '18.c1.a1', '18.d1.a1', '18.q1.a1'], 'contains': ['72.c1.b1', '72.g1.a1', '72.n1.b1', '72.bu1.a1', '108.c1.a1'], 'core': '72.c1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [433, 4, 6, 864, 72], 'label': '1728.34767.36.e1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '36.e1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.e1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302028
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '36.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.h1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.e1.b1', '12.o1.b1', '18.c1.b1', '18.d1.b1', '18.q1.b1'], 'contains': ['72.c1.a1', '72.g1.b1', '72.n1.a1', '72.bu1.b1', '108.c1.b1'], 'core': '72.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [1, 48, 438, 864, 72], 'label': '1728.34767.36.e1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.e1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.b1', 'old_label': '36.e1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.e1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302029
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '36.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.p1.a1', '12.z1.a1', '18.a1.a1', '18.d1.a1', '18.s1.a1'], 'contains': ['72.g1.a1', '72.l1.b1', '72.q1.b1', '108.d1.a1'], 'core': '144.a1.b1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [6, 864, 468, 4, 936], 'label': '1728.34767.36.f1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1.a1', 'old_label': '36.f1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.f1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302030
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '36.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.p1.b1', '12.z1.b1', '18.a1.b1', '18.d1.b1', '18.s1.b1'], 'contains': ['72.g1.b1', '72.l1.a1', '72.q1.a1', '108.d1.b1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [1, 864, 468, 48, 936], 'label': '1728.34767.36.f1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.d1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1.b1', 'old_label': '36.f1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.f1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302031
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '36.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.q1.a1', '12.ba1.a1', '18.b1.a1', '18.d1.a1', '18.r1.a1'], 'contains': ['72.g1.a1', '72.p1.b1', '72.t1.b1', '108.e1.a1'], 'core': '144.a1.b1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [37, 4, 6, 72, 864], 'label': '1728.34767.36.g1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1.a1', 'old_label': '36.g1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.g1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302032
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '36.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.q1.b1', '12.ba1.b1', '18.b1.b1', '18.d1.b1', '18.r1.b1'], 'contains': ['72.g1.b1', '72.p1.a1', '72.t1.a1', '108.e1.b1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [1, 48, 42, 936, 864], 'label': '1728.34767.36.g1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1.b1', 'old_label': '36.g1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.g1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302033
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '4.s1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.g1.a1', '2.h1.a1', '2.k1.a1'], 'contains': ['8.e1.a1', '8.f1.a1', '8.j1.a1', '12.bp1.a1', '12.bp1.b1', '12.ci1.a1', '12.cs1.a1'], 'core': '4.s1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [7, 48, 4, 468, 576, 936, 864], 'label': '1728.34767.4.s1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.s1.a1', 'normal_contained_in': ['2.g1.a1', '2.h1.a1', '2.k1.a1'], 'normal_contains': ['8.e1.a1', '8.f1.a1', '8.j1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.s1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.s1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302034
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '36.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.r1.a1', '12.bb1.a1', '18.b1.a1', '18.c1.a1', '18.s1.a1'], 'contains': ['72.g1.a1', '72.r1.b1', '72.s1.b1', '72.cc1.a1', '72.cc1.b1', '108.f1.a1'], 'core': '144.a1.b1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [469, 4, 6, 936, 864], 'label': '1728.34767.36.h1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1.a1', 'old_label': '36.h1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.h1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302035
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '36.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.r1.b1', '12.bb1.b1', '18.b1.b1', '18.c1.b1', '18.s1.b1'], 'contains': ['72.g1.b1', '72.r1.a1', '72.s1.a1', '72.cc1.c1', '72.cc1.d1', '108.f1.b1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [1, 48, 474, 936, 864], 'label': '1728.34767.36.h1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.f1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1.b1', 'old_label': '36.h1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.h1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302036
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '36.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.r1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.a1.a1', '12.m1.a1', '18.e1.a1', '18.f1.a1', '18.j1.a1'], 'contains': ['72.d1.a1', '72.h1.a1', '72.u1.b1', '108.a1.a1'], 'core': '72.d1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [6, 864, 432, 576, 936], 'label': '1728.34767.36.i1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '36.i1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.i1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302037
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '36.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.r1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.a1.b1', '12.m1.b1', '18.e1.b1', '18.f1.b1', '18.j1.a1'], 'contains': ['72.d1.a1', '72.h1.b1', '72.u1.a1', '108.a1.b1'], 'core': '72.d1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [1, 864, 432, 576, 936], 'label': '1728.34767.36.i1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.b1', 'old_label': '36.i1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.i1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302038
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '36.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.b1.a1', '12.n1.a1', '18.e1.a1', '18.g1.a1', '18.k1.a1'], 'contains': ['72.e1.a1', '72.h1.a1', '72.x1.a1', '72.bv1.a1', '108.b1.a1'], 'core': '72.e1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [6, 576, 36, 864, 72], 'label': '1728.34767.36.j1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '36.j1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.j1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302039
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '36.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.g1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.b1.b1', '12.n1.b1', '18.e1.b1', '18.g1.b1', '18.k1.a1'], 'contains': ['72.e1.a1', '72.h1.b1', '72.x1.b1', '72.bv1.b1', '108.b1.b1'], 'core': '72.e1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [1, 576, 36, 864, 72], 'label': '1728.34767.36.j1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.b1', 'old_label': '36.j1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.j1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302040
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '36.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '36.k1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.o1.a1', '12.s1.a1', '18.g1.a1', '18.h1.a1', '18.j1.a1'], 'contains': ['72.h1.a1', '72.u1.a1', '72.w1.a1', '72.bw1.a1', '108.c1.a1'], 'core': '144.b1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [433, 72, 6, 864, 576], 'label': '1728.34767.36.k1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '36.k1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.k1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302041
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '36.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '36.k1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.o1.b1', '12.s1.b1', '18.g1.b1', '18.h1.b1', '18.j1.a1'], 'contains': ['72.h1.b1', '72.u1.b1', '72.w1.a1', '72.bw1.b1', '108.c1.b1'], 'core': '144.b1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [1, 72, 438, 864, 576], 'label': '1728.34767.36.k1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '36.k1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.k1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302042
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '36.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.c1.a1', '12.p1.a1', '18.e1.a1', '18.h1.a1', '18.l1.a1'], 'contains': ['72.f1.a1', '72.h1.a1', '72.y1.b1', '108.d1.a1'], 'core': '72.f1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [6, 576, 468, 936, 864], 'label': '1728.34767.36.l1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '36.l1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.l1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302043
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '36.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.c1.b1', '12.p1.b1', '18.e1.b1', '18.h1.b1', '18.l1.a1'], 'contains': ['72.f1.a1', '72.h1.b1', '72.y1.a1', '108.d1.b1'], 'core': '72.f1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [1, 576, 468, 936, 864], 'label': '1728.34767.36.l1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.c1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.b1', 'old_label': '36.l1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.l1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302044
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '2.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': ['864.d1.a1', '864.d1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.b1', '4.e1.b1', '4.f1.b1', '4.j1.a1', '4.k1.a1', '4.p1.a1', '4.q1.a1', '6.d1.b1', '6.g1.b1', '6.j1.b1', '6.l1.b1'], 'core': '2.b1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [1, 864, 4, 42, 936, 576, 48, 432], 'label': '1728.34767.2.b1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1.b1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.a1.b1', '4.f1.b1', '4.e1.b1', '4.j1.a1', '4.k1.a1', '4.q1.a1', '4.p1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.b1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2.b1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302045
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '4.t1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.d1.a1', '2.d1.b1', '2.h1.a1'], 'contains': ['8.e1.a1', '8.g1.a1', '8.k1.a1', '12.bq1.a1', '12.bq1.b1', '12.cj1.a1', '12.ct1.a1'], 'core': '4.t1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [439, 48, 4, 468, 576, 72, 864], 'label': '1728.34767.4.t1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.t1.a1', 'normal_contained_in': ['2.d1.b1', '2.d1.a1', '2.h1.a1'], 'normal_contains': ['8.e1.a1', '8.g1.a1', '8.k1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.t1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.t1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302046
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '36.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.q1.a1', '12.t1.a1', '18.f1.a1', '18.h1.a1', '18.k1.a1'], 'contains': ['72.h1.a1', '72.x1.b1', '72.ba1.a1', '108.e1.a1'], 'core': '144.b1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [37, 576, 6, 72, 864], 'label': '1728.34767.36.m1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '36.m1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.m1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302047
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '36.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.q1.b1', '12.t1.b1', '18.f1.b1', '18.h1.b1', '18.k1.a1'], 'contains': ['72.h1.b1', '72.x1.a1', '72.ba1.a1', '108.e1.b1'], 'core': '144.b1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [1, 576, 42, 936, 864], 'label': '1728.34767.36.m1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '36.m1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.m1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302048
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '36.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.r1.a1', '12.u1.a1', '18.f1.a1', '18.g1.a1', '18.l1.a1'], 'contains': ['72.h1.a1', '72.y1.a1', '72.z1.a1', '72.cd1.a1', '72.cd1.b1', '108.f1.a1'], 'core': '144.b1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [469, 576, 6, 936, 864], 'label': '1728.34767.36.n1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '36.n1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.n1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302049
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '36.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.r1.b1', '12.u1.b1', '18.f1.b1', '18.g1.b1', '18.l1.a1'], 'contains': ['72.h1.b1', '72.y1.b1', '72.z1.a1', '72.cd1.c1', '72.cd1.d1', '108.f1.b1'], 'core': '144.b1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [1, 576, 474, 936, 864], 'label': '1728.34767.36.n1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.f1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '36.n1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.n1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302050
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '36.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.m1.a1', '12.v1.a1', '18.i1.a1'], 'contains': ['72.i1.a1', '72.bb1.b1', '72.bc1.b1', '108.a1.a1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [6, 864, 432, 1156, 936], 'label': '1728.34767.36.o1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.a1', 'old_label': '36.o1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.o1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302051
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '36.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.m1.b1', '12.v1.b1', '18.i1.b1'], 'contains': ['72.i1.b1', '72.bb1.a1', '72.bc1.a1', '108.a1.b1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [1, 864, 432, 1200, 936], 'label': '1728.34767.36.o1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.b1', 'old_label': '36.o1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.o1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302052
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '36.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.q1.a1', '12.w1.a1', '18.i1.a1'], 'contains': ['72.i1.a1', '72.bd1.b1', '72.bg1.b1', '108.e1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [37, 1156, 6, 72, 864], 'label': '1728.34767.36.p1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.i1.a1', 'old_label': '36.p1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.p1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302053
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '36.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.q1.b1', '12.w1.b1', '18.i1.b1'], 'contains': ['72.i1.b1', '72.bd1.a1', '72.bg1.a1', '108.e1.b1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [1, 1200, 42, 936, 864], 'label': '1728.34767.36.p1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.i1.b1', 'old_label': '36.p1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.p1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302054
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '36.q1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.r1.a1', '12.x1.a1', '18.i1.a1'], 'contains': ['72.i1.a1', '72.be1.b1', '72.bf1.b1', '72.ce1.a1', '72.ce1.b1', '108.f1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [469, 1156, 6, 936, 864], 'label': '1728.34767.36.q1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.i1.a1', 'old_label': '36.q1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.q1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302055
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '36.q1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.r1.b1', '12.x1.b1', '18.i1.b1'], 'contains': ['72.i1.b1', '72.be1.a1', '72.bf1.a1', '72.ce1.c1', '72.ce1.d1', '108.f1.b1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [1, 1200, 474, 936, 864], 'label': '1728.34767.36.q1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.f1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.i1.b1', 'old_label': '36.q1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.q1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302056
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '4.u1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.f1.a1', '2.i1.a1', '2.k1.a1'], 'contains': ['8.f1.a1', '8.h1.a1', '8.h1.b1', '12.br1.a1', '12.br1.b1', '12.ck1.a1'], 'core': '4.u1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [37, 48, 4, 42, 576, 72, 864], 'label': '1728.34767.4.u1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.u1.a1', 'normal_contained_in': ['2.f1.a1', '2.i1.a1', '2.k1.a1'], 'normal_contains': ['8.f1.a1', '8.h1.a1', '8.h1.b1'], 'normalizer': '1.a1.a1', 'old_label': '4.u1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.u1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302057
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '36.r1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.w1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bc1.a1', '12.bc1.b1', '18.j1.a1', '18.k1.a1', '18.l1.a1'], 'contains': ['72.h1.a1', '72.h1.b1', '72.v1.a1', '72.br1.a1', '72.br1.b1', '72.br1.c1', '72.br1.d1', '108.g1.a1'], 'core': '144.b1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [1, 936, 6, 864, 576], 'label': '1728.34767.36.r1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '36.r1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.r1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302058
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '36.s1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.j1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.b1.a1', '12.y1.a1', '18.m1.a1', '18.o1.a1', '18.r1.b1'], 'contains': ['72.a1.a1', '72.j1.a1', '72.p1.a1', '72.bx1.a1', '108.b1.a1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [6, 48, 36, 864, 72], 'label': '1728.34767.36.s1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '36.s1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.s1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302059
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '36.s1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.b1.b1', '12.y1.b1', '18.m1.b1', '18.o1.b1', '18.r1.a1'], 'contains': ['72.a1.b1', '72.j1.b1', '72.p1.b1', '72.bx1.b1', '108.b1.b1'], 'core': '72.a1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [1, 4, 36, 864, 72], 'label': '1728.34767.36.s1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '36.s1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.s1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302060
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '36.t1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.u1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.e1.a1', '12.s1.a1', '18.o1.a1', '18.p1.a1', '18.q1.b1'], 'contains': ['72.a1.a1', '72.k1.a1', '72.n1.a1', '72.by1.a1', '108.c1.a1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [433, 48, 6, 864, 72], 'label': '1728.34767.36.t1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.b1', 'old_label': '36.t1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.t1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302061
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '36.t1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.u1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.e1.b1', '12.s1.b1', '18.o1.b1', '18.p1.b1', '18.q1.a1'], 'contains': ['72.a1.b1', '72.k1.b1', '72.n1.b1', '72.by1.b1', '108.c1.b1'], 'core': '72.a1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [1, 4, 438, 864, 72], 'label': '1728.34767.36.t1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.e1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '36.t1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.t1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302062
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '36.u1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.c1.a1', '12.z1.a1', '18.m1.a1', '18.p1.a1', '18.s1.b1'], 'contains': ['72.a1.a1', '72.l1.a1', '72.r1.a1', '108.d1.a1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [6, 48, 468, 936, 864], 'label': '1728.34767.36.u1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '36.u1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.u1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302063
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '36.u1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.c1.b1', '12.z1.b1', '18.m1.b1', '18.p1.b1', '18.s1.a1'], 'contains': ['72.a1.b1', '72.l1.b1', '72.r1.b1', '108.d1.b1'], 'core': '72.a1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [1, 4, 468, 936, 864], 'label': '1728.34767.36.u1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.c1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '36.u1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.u1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302064
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '36.v1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.t1.a1', '12.w1.a1', '12.ba1.a1', '18.n1.a1', '18.p1.a1', '18.r1.b1'], 'contains': ['72.a1.a1', '72.o1.a1', '72.t1.a1', '108.e1.a1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [37, 48, 6, 72, 864], 'label': '1728.34767.36.v1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1.b1', 'old_label': '36.v1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.v1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302065
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '36.v1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.t1.b1', '12.w1.b1', '12.ba1.b1', '18.n1.b1', '18.p1.b1', '18.r1.a1'], 'contains': ['72.a1.b1', '72.o1.b1', '72.t1.b1', '108.e1.b1'], 'core': '72.a1.b1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [1, 4, 42, 936, 864], 'label': '1728.34767.36.v1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1.a1', 'old_label': '36.v1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.v1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302066
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '36.w1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.u1.a1', '12.x1.a1', '12.bb1.a1', '18.n1.a1', '18.o1.a1', '18.s1.b1'], 'contains': ['72.a1.a1', '72.q1.a1', '72.s1.a1', '72.cf1.a1', '72.cf1.b1', '108.f1.a1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [469, 48, 6, 936, 864], 'label': '1728.34767.36.w1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1.b1', 'old_label': '36.w1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.w1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302067
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '4.v1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.g1.a1', '2.i1.a1', '2.j1.a1'], 'contains': ['8.f1.a1', '8.i1.a1', '8.i1.b1', '12.bs1.a1', '12.bs1.b1', '12.cl1.a1'], 'core': '4.v1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [469, 48, 4, 474, 576, 936, 864], 'label': '1728.34767.4.v1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.v1.a1', 'normal_contained_in': ['2.g1.a1', '2.i1.a1', '2.j1.a1'], 'normal_contains': ['8.f1.a1', '8.i1.b1', '8.i1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.v1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.v1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302186
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '48.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.b1.c1', '24.o1.b1'], 'contains': ['96.g1.b1', '96.r1.c1', '144.c1.c1', '144.i1.c1'], 'core': '144.c1.c1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [1, 936, 1200, 4], 'label': '1728.34767.48.j1.c1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '16.b1.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.b1', 'old_label': '48.j1.c1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.j1.c1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302068
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '36.w1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.i1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.u1.b1', '12.x1.b1', '12.bb1.b1', '18.n1.b1', '18.o1.b1', '18.s1.a1'], 'contains': ['72.a1.b1', '72.q1.b1', '72.s1.b1', '72.cf1.c1', '72.cf1.d1', '108.f1.b1'], 'core': '72.a1.b1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [1, 4, 474, 936, 864], 'label': '1728.34767.36.w1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.f1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1.a1', 'old_label': '36.w1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.w1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302069
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '36.x1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.f1.a1', '12.bc1.a1', '18.q1.a1', '18.r1.a1', '18.s1.a1'], 'contains': ['72.a1.b1', '72.g1.a1', '72.m1.b1', '72.bs1.a1', '72.bs1.b1', '72.bs1.e1', '72.bs1.f1', '108.g1.a1'], 'core': '72.a1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [1, 4, 6, 864, 936], 'label': '1728.34767.36.x1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '36.x1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.x1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302070
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '36.x1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.f1.a1', '12.bc1.b1', '18.q1.b1', '18.r1.b1', '18.s1.b1'], 'contains': ['72.a1.a1', '72.g1.b1', '72.m1.a1', '72.bs1.c1', '72.bs1.d1', '72.bs1.g1', '72.bs1.h1', '108.g1.a1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [1, 48, 6, 864, 936], 'label': '1728.34767.36.x1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.b1', 'old_label': '36.x1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.x1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302071
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '36.y1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.g1.a1', '12.bz1.a1', '18.a1.b1', '18.m1.a1', '18.t1.a1'], 'contains': ['72.b1.a1', '72.j1.a1', '72.l1.a1', '108.h1.a1'], 'core': '72.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [36, 864, 432, 48, 72], 'label': '1728.34767.36.y1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '36.y1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.y1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302072
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '36.y1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.g1.b1', '12.bz1.a1', '18.a1.a1', '18.m1.b1', '18.t1.b1'], 'contains': ['72.b1.b1', '72.j1.b1', '72.l1.b1', '108.h1.a1'], 'core': '72.b1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [36, 864, 432, 4, 72], 'label': '1728.34767.36.y1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.g1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '36.y1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.y1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302073
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '36.z1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.k1.a1', '12.bd1.a1', '18.q1.b1', '18.t1.a1', '18.u1.a1'], 'contains': ['72.b1.a1', '72.m1.a1', '72.n1.a1', '108.i1.a1'], 'core': '72.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [7, 48, 432, 936, 864], 'label': '1728.34767.36.z1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.k1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.b1', 'old_label': '36.z1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.z1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302074
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '36.z1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.k1.a1', '12.bd1.b1', '18.q1.a1', '18.t1.b1', '18.u1.b1'], 'contains': ['72.b1.b1', '72.m1.b1', '72.n1.b1', '108.i1.a1'], 'core': '72.b1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [7, 4, 432, 936, 864], 'label': '1728.34767.36.z1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.k1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '36.z1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.z1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302075
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '36.ba1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.be1.a1', '12.bv1.a1', '12.ca1.b1', '18.a1.b1', '18.n1.a1', '18.u1.a1'], 'contains': ['72.b1.a1', '72.o1.a1', '72.q1.a1', '108.j1.b1'], 'core': '72.b1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [37, 864, 432, 48, 72], 'label': '1728.34767.36.ba1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.j1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1.b1', 'old_label': '36.ba1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.ba1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302076
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '36.ba1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.be1.b1', '12.bv1.b1', '12.ca1.a1', '18.a1.a1', '18.n1.b1', '18.u1.b1'], 'contains': ['72.b1.b1', '72.o1.b1', '72.q1.b1', '108.j1.a1'], 'core': '72.b1.b1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [42, 864, 432, 4, 72], 'label': '1728.34767.36.ba1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.j1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1.a1', 'old_label': '36.ba1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.ba1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302077
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '36.bb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.h1.a1', '12.ca1.a1', '18.b1.b1', '18.m1.a1', '18.u1.a1'], 'contains': ['72.b1.a1', '72.p1.a1', '72.r1.a1', '108.j1.a1'], 'core': '72.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [42, 48, 432, 72, 864], 'label': '1728.34767.36.bb1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.h1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '36.bb1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.bb1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302078
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '4.w1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1', '2.d1.b1', '2.i1.a1'], 'contains': ['8.g1.a1', '8.h1.a1', '8.i1.a1', '12.bt1.b1', '12.bu1.a1', '12.cm1.a1'], 'core': '4.w1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [469, 48, 4, 42, 576, 72, 864], 'label': '1728.34767.4.w1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.w1.a1', 'normal_contained_in': ['2.c1.a1', '2.d1.b1', '2.i1.a1'], 'normal_contains': ['8.g1.a1', '8.i1.a1', '8.h1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.w1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.w1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302079
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '36.bb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.h1.b1', '12.ca1.b1', '18.b1.a1', '18.m1.b1', '18.u1.b1'], 'contains': ['72.b1.b1', '72.p1.b1', '72.r1.b1', '108.j1.b1'], 'core': '72.b1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [37, 4, 432, 72, 864], 'label': '1728.34767.36.bb1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.h1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '36.bb1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.bb1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302080
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '36.bc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bf1.a1', '12.bw1.a1', '12.cb1.a1', '18.b1.b1', '18.n1.a1', '18.t1.a1'], 'contains': ['72.b1.a1', '72.s1.a1', '72.t1.a1', '72.cg1.a1', '72.cg1.b1', '108.k1.a1'], 'core': '72.b1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [43, 48, 432, 936, 864], 'label': '1728.34767.36.bc1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.k1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1.b1', 'old_label': '36.bc1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.bc1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302081
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '36.bc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bf1.b1', '12.bw1.b1', '12.cb1.a1', '18.b1.a1', '18.n1.b1', '18.t1.b1'], 'contains': ['72.b1.b1', '72.s1.b1', '72.t1.b1', '72.cg1.c1', '72.cg1.d1', '108.k1.a1'], 'core': '72.b1.b1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [43, 4, 432, 936, 864], 'label': '1728.34767.36.bc1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.k1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1.a1', 'old_label': '36.bc1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.bc1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302082
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '36.bd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bg1.a1', '12.cc1.a1', '18.a1.b1', '18.o1.a1', '18.v1.a1'], 'contains': ['72.j1.a1', '72.k1.a1', '72.q1.a1', '108.l1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [433, 864, 36, 48, 72], 'label': '1728.34767.36.bd1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.l1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1.b1', 'old_label': '36.bd1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.bd1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302083
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '36.bd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bg1.b1', '12.cc1.b1', '18.a1.a1', '18.o1.b1', '18.v1.b1'], 'contains': ['72.j1.b1', '72.k1.b1', '72.q1.b1', '108.l1.b1'], 'core': '144.a1.b1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [438, 864, 36, 4, 72], 'label': '1728.34767.36.bd1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.l1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1.a1', 'old_label': '36.bd1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.bd1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302084
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '36.be1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.i1.a1', '12.cc1.b1', '18.c1.b1', '18.m1.a1', '18.v1.a1'], 'contains': ['72.c1.a1', '72.j1.a1', '72.r1.a1', '108.l1.b1'], 'core': '72.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [438, 48, 36, 72, 864], 'label': '1728.34767.36.be1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.i1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '36.be1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.be1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302085
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '36.be1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.i1.b1', '12.cc1.a1', '18.c1.a1', '18.m1.b1', '18.v1.b1'], 'contains': ['72.c1.b1', '72.j1.b1', '72.r1.b1', '108.l1.a1'], 'core': '72.c1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [433, 4, 36, 72, 864], 'label': '1728.34767.36.be1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.i1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '36.be1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.be1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302086
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '36.bf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bh1.a1', '12.cd1.a1', '18.r1.b1', '18.t1.a1', '18.v1.a1'], 'contains': ['72.j1.a1', '72.m1.a1', '72.t1.a1', '108.m1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [7, 48, 36, 936, 864], 'label': '1728.34767.36.bf1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.m1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1.b1', 'old_label': '36.bf1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.bf1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302087
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '36.bf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bh1.b1', '12.cd1.a1', '18.r1.a1', '18.t1.b1', '18.v1.b1'], 'contains': ['72.j1.b1', '72.m1.b1', '72.t1.b1', '108.m1.a1'], 'core': '144.a1.b1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [7, 4, 36, 936, 864], 'label': '1728.34767.36.bf1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.m1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1.a1', 'old_label': '36.bf1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.bf1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302187
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '48.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.b1.d1', '24.o1.b1'], 'contains': ['96.g1.b1', '96.r1.d1', '144.c1.d1', '144.i1.d1'], 'core': '144.c1.d1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [865, 936, 1200, 4], 'label': '1728.34767.48.j1.d1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '16.b1.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.b1', 'old_label': '48.j1.d1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.j1.d1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302088
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '36.bg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bi1.a1', '12.ce1.a1', '18.c1.b1', '18.o1.a1', '18.t1.a1'], 'contains': ['72.j1.a1', '72.n1.a1', '72.s1.a1', '108.n1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [439, 48, 36, 72, 864], 'label': '1728.34767.36.bg1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.n1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1.b1', 'old_label': '36.bg1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.bg1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302089
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '4.w1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.c1.b1', '2.d1.a1', '2.i1.a1'], 'contains': ['8.g1.a1', '8.h1.b1', '8.i1.b1', '12.bt1.a1', '12.bu1.b1', '12.cm1.b1'], 'core': '4.w1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [37, 48, 4, 474, 576, 72, 864], 'label': '1728.34767.4.w1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.w1.b1', 'normal_contained_in': ['2.c1.b1', '2.d1.a1', '2.i1.a1'], 'normal_contains': ['8.g1.a1', '8.i1.b1', '8.h1.b1'], 'normalizer': '1.a1.a1', 'old_label': '4.w1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.w1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302090
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '36.bg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bi1.b1', '12.ce1.a1', '18.c1.a1', '18.o1.b1', '18.t1.b1'], 'contains': ['72.j1.b1', '72.n1.b1', '72.s1.b1', '108.n1.a1'], 'core': '144.a1.b1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [439, 4, 36, 72, 864], 'label': '1728.34767.36.bg1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.n1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1.a1', 'old_label': '36.bg1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.bg1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302091
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '36.bh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bj1.a1', '12.cf1.a1', '18.a1.b1', '18.p1.a1', '18.w1.a1'], 'contains': ['72.k1.a1', '72.l1.a1', '72.o1.a1', '72.bz1.a1', '108.o1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [433, 72, 468, 864, 48], 'label': '1728.34767.36.bh1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.o1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1.b1', 'old_label': '36.bh1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.bh1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302092
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '36.bh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bj1.b1', '12.cf1.b1', '18.a1.a1', '18.p1.b1', '18.w1.b1'], 'contains': ['72.k1.b1', '72.l1.b1', '72.o1.b1', '72.bz1.b1', '108.o1.b1'], 'core': '144.a1.b1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [438, 72, 468, 864, 4], 'label': '1728.34767.36.bh1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.o1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1.a1', 'old_label': '36.bh1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.bh1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302093
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '36.bi1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bk1.a1', '12.cg1.a1', '18.b1.b1', '18.o1.a1', '18.w1.a1'], 'contains': ['72.k1.a1', '72.p1.a1', '72.s1.a1', '108.p1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [433, 48, 42, 72, 864], 'label': '1728.34767.36.bi1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.p1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1.b1', 'old_label': '36.bi1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.bi1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302094
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '36.bi1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bk1.b1', '12.cg1.b1', '18.b1.a1', '18.o1.b1', '18.w1.b1'], 'contains': ['72.k1.b1', '72.p1.b1', '72.s1.b1', '108.p1.b1'], 'core': '144.a1.b1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [37, 4, 438, 72, 864], 'label': '1728.34767.36.bi1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.p1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1.a1', 'old_label': '36.bi1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.bi1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302095
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '36.bj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bl1.a1', '12.ch1.a1', '18.b1.b1', '18.p1.a1', '18.v1.a1'], 'contains': ['72.k1.a1', '72.r1.a1', '72.t1.a1', '108.q1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [433, 48, 474, 72, 864], 'label': '1728.34767.36.bj1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.q1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1.b1', 'old_label': '36.bj1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.bj1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302096
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '36.bj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bl1.b1', '12.ch1.b1', '18.b1.a1', '18.p1.b1', '18.v1.b1'], 'contains': ['72.k1.b1', '72.r1.b1', '72.t1.b1', '108.q1.b1'], 'core': '144.a1.b1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [469, 4, 438, 72, 864], 'label': '1728.34767.36.bj1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.q1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1.a1', 'old_label': '36.bj1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.bj1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302097
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '36.bk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.j1.a1', '12.cf1.b1', '18.d1.b1', '18.m1.a1', '18.w1.a1'], 'contains': ['72.c1.a1', '72.l1.a1', '72.p1.a1', '72.ca1.a1', '108.o1.b1'], 'core': '72.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [438, 48, 468, 864, 72], 'label': '1728.34767.36.bk1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.j1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '36.bk1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.bk1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302098
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '36.bk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.j1.b1', '12.cf1.a1', '18.d1.a1', '18.m1.b1', '18.w1.b1'], 'contains': ['72.c1.b1', '72.l1.b1', '72.p1.b1', '72.ca1.b1', '108.o1.a1'], 'core': '72.c1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [433, 4, 468, 864, 72], 'label': '1728.34767.36.bk1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.j1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '36.bk1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.bk1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302099
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '36.bl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bm1.a1', '12.bx1.a1', '12.cg1.b1', '18.c1.b1', '18.n1.a1', '18.w1.a1'], 'contains': ['72.c1.a1', '72.o1.a1', '72.s1.a1', '108.p1.b1'], 'core': '72.c1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [37, 48, 438, 72, 864], 'label': '1728.34767.36.bl1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.p1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1.b1', 'old_label': '36.bl1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.bl1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302100
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '6.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.a1.b1', 'complements': ['288.s1.c1', '288.s1.d1'], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '3.a1.b1'], 'contains': ['12.a1.a1', '12.b1.a1', '12.c1.a1', '12.g1.a1', '12.h1.a1', '12.i1.a1', '12.j1.a1', '18.e1.a1', '18.m1.a1'], 'core': '6.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [6, 48, 864, 36, 576, 432, 72], 'label': '1728.34767.6.a1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1.a1', 'normal_contained_in': ['2.a1.a1'], 'normal_contains': ['12.a1.a1', '12.b1.a1', '12.c1.a1', '12.g1.a1', '12.h1.a1', '12.i1.a1', '12.j1.a1'], 'normalizer': '1.a1.a1', 'old_label': '6.a1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.a1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302101
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '36.bl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bm1.b1', '12.bx1.b1', '12.cg1.a1', '18.c1.a1', '18.n1.b1', '18.w1.b1'], 'contains': ['72.c1.b1', '72.o1.b1', '72.s1.b1', '108.p1.a1'], 'core': '72.c1.b1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [433, 4, 42, 72, 864], 'label': '1728.34767.36.bl1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.p1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1.a1', 'old_label': '36.bl1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.bl1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302102
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '36.bm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bn1.a1', '12.by1.a1', '12.ch1.b1', '18.d1.b1', '18.n1.a1', '18.v1.a1'], 'contains': ['72.c1.a1', '72.q1.a1', '72.t1.a1', '108.q1.b1'], 'core': '72.c1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [469, 48, 438, 72, 864], 'label': '1728.34767.36.bm1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.q1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1.b1', 'old_label': '36.bm1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.bm1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302103
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '36.bm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bn1.b1', '12.by1.b1', '12.ch1.a1', '18.d1.a1', '18.n1.b1', '18.v1.b1'], 'contains': ['72.c1.b1', '72.q1.b1', '72.t1.b1', '108.q1.a1'], 'core': '72.c1.b1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [433, 4, 474, 72, 864], 'label': '1728.34767.36.bm1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.q1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1.a1', 'old_label': '36.bm1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.bm1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302104
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '36.bn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.l1.a1', '12.bo1.a1', '18.q1.b1', '18.v1.a1', '18.w1.a1'], 'contains': ['72.c1.a1', '72.k1.a1', '72.m1.a1', '108.r1.a1'], 'core': '72.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [433, 48, 438, 72, 864], 'label': '1728.34767.36.bn1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.l1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.b1', 'old_label': '36.bn1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.bn1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302105
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '36.bn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.l1.a1', '12.bo1.b1', '18.q1.a1', '18.v1.b1', '18.w1.b1'], 'contains': ['72.c1.b1', '72.k1.b1', '72.m1.b1', '108.r1.a1'], 'core': '72.c1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [433, 4, 438, 72, 864], 'label': '1728.34767.36.bn1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.l1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '36.bn1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.bn1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302106
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '36.bo1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bp1.a1', '12.ci1.a1', '18.s1.b1', '18.t1.a1', '18.w1.a1'], 'contains': ['72.l1.a1', '72.m1.a1', '72.s1.a1', '108.s1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [7, 48, 468, 936, 864], 'label': '1728.34767.36.bo1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.s1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1.b1', 'old_label': '36.bo1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.bo1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302107
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '36.bo1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bp1.b1', '12.ci1.a1', '18.s1.a1', '18.t1.b1', '18.w1.b1'], 'contains': ['72.l1.b1', '72.m1.b1', '72.s1.b1', '108.s1.a1'], 'core': '144.a1.b1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [7, 4, 468, 936, 864], 'label': '1728.34767.36.bo1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.s1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1.a1', 'old_label': '36.bo1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.bo1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302108
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '36.bp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bq1.a1', '12.cj1.a1', '18.d1.b1', '18.p1.a1', '18.t1.a1'], 'contains': ['72.l1.a1', '72.n1.a1', '72.t1.a1', '108.t1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [439, 48, 468, 72, 864], 'label': '1728.34767.36.bp1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.t1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1.b1', 'old_label': '36.bp1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.bp1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302109
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '36.bp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bq1.b1', '12.cj1.a1', '18.d1.a1', '18.p1.b1', '18.t1.b1'], 'contains': ['72.l1.b1', '72.n1.b1', '72.t1.b1', '108.t1.a1'], 'core': '144.a1.b1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [439, 4, 468, 72, 864], 'label': '1728.34767.36.bp1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.t1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1.a1', 'old_label': '36.bp1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.bp1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302110
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '36.bq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.br1.a1', '12.ck1.a1', '18.r1.b1', '18.u1.a1', '18.w1.a1'], 'contains': ['72.m1.a1', '72.o1.a1', '72.p1.a1', '108.u1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [37, 48, 42, 72, 864], 'label': '1728.34767.36.bq1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.u1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1.b1', 'old_label': '36.bq1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.bq1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302111
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '6.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.a1.a1', 'complements': ['288.s1.a1', '288.s1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.b1', '3.a1.a1'], 'contains': ['12.a1.b1', '12.b1.b1', '12.c1.b1', '12.g1.b1', '12.h1.b1', '12.i1.b1', '12.j1.b1', '18.e1.b1', '18.m1.b1'], 'core': '6.a1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [1, 4, 864, 36, 576, 432, 72], 'label': '1728.34767.6.a1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1.b1', 'normal_contained_in': ['2.a1.b1'], 'normal_contains': ['12.a1.b1', '12.b1.b1', '12.c1.b1', '12.g1.b1', '12.h1.b1', '12.i1.b1', '12.j1.b1'], 'normalizer': '1.a1.a1', 'old_label': '6.a1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.a1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302112
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '36.bq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.br1.b1', '12.ck1.a1', '18.r1.a1', '18.u1.b1', '18.w1.b1'], 'contains': ['72.m1.b1', '72.o1.b1', '72.p1.b1', '108.u1.a1'], 'core': '144.a1.b1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [37, 4, 42, 72, 864], 'label': '1728.34767.36.bq1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.u1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1.a1', 'old_label': '36.bq1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.bq1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302113
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '36.br1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bs1.a1', '12.cl1.a1', '18.s1.b1', '18.u1.a1', '18.v1.a1'], 'contains': ['72.m1.a1', '72.q1.a1', '72.r1.a1', '108.v1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [469, 48, 474, 936, 864], 'label': '1728.34767.36.br1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.v1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1.b1', 'old_label': '36.br1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.br1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302114
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '36.br1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bs1.b1', '12.cl1.a1', '18.s1.a1', '18.u1.b1', '18.v1.b1'], 'contains': ['72.m1.b1', '72.q1.b1', '72.r1.b1', '108.v1.a1'], 'core': '144.a1.b1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [469, 4, 474, 936, 864], 'label': '1728.34767.36.br1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.v1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1.a1', 'old_label': '36.br1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.br1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302115
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '36.bs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bt1.a1', '12.cm1.b1', '18.c1.b1', '18.p1.a1', '18.u1.a1'], 'contains': ['72.n1.a1', '72.o1.a1', '72.r1.a1', '108.w1.b1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [37, 48, 474, 72, 864], 'label': '1728.34767.36.bs1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.w1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1.b1', 'old_label': '36.bs1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.bs1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302116
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '36.bs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bt1.b1', '12.cm1.a1', '18.c1.a1', '18.p1.b1', '18.u1.b1'], 'contains': ['72.n1.b1', '72.o1.b1', '72.r1.b1', '108.w1.a1'], 'core': '144.a1.b1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [469, 4, 42, 72, 864], 'label': '1728.34767.36.bs1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.w1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1.a1', 'old_label': '36.bs1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.bs1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302117
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '36.bt1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bu1.a1', '12.cm1.a1', '18.d1.b1', '18.o1.a1', '18.u1.a1'], 'contains': ['72.n1.a1', '72.p1.a1', '72.q1.a1', '108.w1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [469, 48, 42, 72, 864], 'label': '1728.34767.36.bt1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.w1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1.b1', 'old_label': '36.bt1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.bt1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302118
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '36.bt1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bu1.b1', '12.cm1.b1', '18.d1.a1', '18.o1.b1', '18.u1.b1'], 'contains': ['72.n1.b1', '72.p1.b1', '72.q1.b1', '108.w1.b1'], 'core': '144.a1.b1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [37, 4, 474, 72, 864], 'label': '1728.34767.36.bt1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.w1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1.a1', 'old_label': '36.bt1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.bt1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302119
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '36.bu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '36.bu1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bd1.a1', '12.bd1.b1', '12.co1.a1', '18.j1.a1', '18.x1.a1', '18.y1.a1'], 'contains': ['72.d1.a1', '72.v1.a1', '72.w1.a1', '108.i1.a1'], 'core': '72.d1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [7, 864, 432, 576, 936], 'label': '1728.34767.36.bu1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.i1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '36.bu1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.bu1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302120
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '36.bv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.h1.a1', '12.be1.b1', '18.e1.a1', '18.f1.b1', '18.y1.a1'], 'contains': ['72.d1.a1', '72.x1.a1', '72.y1.b1', '108.j1.a1'], 'core': '72.d1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [42, 576, 432, 72, 864], 'label': '1728.34767.36.bv1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.h1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '36.bv1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.bv1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302121
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '36.bv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.h1.b1', '12.be1.a1', '18.e1.b1', '18.f1.a1', '18.y1.a1'], 'contains': ['72.d1.a1', '72.x1.b1', '72.y1.a1', '108.j1.b1'], 'core': '72.d1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [37, 576, 432, 72, 864], 'label': '1728.34767.36.bv1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.h1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.b1', 'old_label': '36.bv1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.bv1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302122
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '6.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.e1.a1', '3.b1.a1'], 'contains': ['12.d1.a1', '12.d1.b1', '12.e1.a1', '12.e1.b1', '12.f1.a1', '12.k1.a1', '12.l1.a1', '18.q1.a1', '18.q1.b1'], 'core': '6.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [1, 4, 864, 6, 48, 432, 936], 'label': '1728.34767.6.b1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1.a1', 'normal_contained_in': ['2.e1.a1'], 'normal_contains': ['12.d1.b1', '12.d1.a1', '12.e1.b1', '12.e1.a1', '12.f1.a1', '12.k1.a1', '12.l1.a1'], 'normalizer': '1.a1.a1', 'old_label': '6.b1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.b1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302123
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '36.bw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bf1.a1', '12.bf1.b1', '12.cp1.a1', '18.f1.a1', '18.f1.b1', '18.x1.a1'], 'contains': ['72.d1.a1', '72.z1.a1', '72.ba1.a1', '72.ch1.a1', '72.ch1.b1', '108.k1.a1'], 'core': '72.d1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [43, 576, 432, 936, 864], 'label': '1728.34767.36.bw1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.k1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '36.bw1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.bw1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302124
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '36.bx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.i1.b1', '12.bg1.a1', '18.e1.b1', '18.g1.a1', '18.z1.a1'], 'contains': ['72.e1.a1', '72.u1.a1', '72.y1.a1', '108.l1.a1'], 'core': '72.e1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [433, 576, 36, 72, 864], 'label': '1728.34767.36.bx1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.i1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.b1', 'old_label': '36.bx1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.bx1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302125
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '36.bx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.i1.a1', '12.bg1.b1', '18.e1.a1', '18.g1.b1', '18.z1.a1'], 'contains': ['72.e1.a1', '72.u1.b1', '72.y1.b1', '108.l1.b1'], 'core': '72.e1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [438, 576, 36, 72, 864], 'label': '1728.34767.36.bx1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.i1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '36.bx1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.bx1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302126
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '36.by1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bh1.a1', '12.bh1.b1', '12.cq1.a1', '18.k1.a1', '18.x1.a1', '18.z1.a1'], 'contains': ['72.e1.a1', '72.v1.a1', '72.ba1.a1', '108.m1.a1'], 'core': '72.e1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [7, 576, 36, 936, 864], 'label': '1728.34767.36.by1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.m1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '36.by1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.by1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302127
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '36.bz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '108.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bi1.a1', '12.bi1.b1', '12.cr1.a1', '18.g1.a1', '18.g1.b1', '18.x1.a1'], 'contains': ['72.e1.a1', '72.w1.a1', '72.z1.a1', '108.n1.a1'], 'core': '72.e1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [439, 576, 36, 72, 864], 'label': '1728.34767.36.bz1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.n1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '36.bz1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.bz1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302128
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '36.ca1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.j1.b1', '12.bj1.a1', '18.e1.b1', '18.h1.a1', '18.ba1.a1'], 'contains': ['72.f1.a1', '72.u1.a1', '72.x1.b1', '72.cb1.a1', '108.o1.a1'], 'core': '72.f1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [433, 576, 468, 864, 72], 'label': '1728.34767.36.ca1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.j1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.b1', 'old_label': '36.ca1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.ca1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302129
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '36.ca1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.j1.a1', '12.bj1.b1', '18.e1.a1', '18.h1.b1', '18.ba1.a1'], 'contains': ['72.f1.a1', '72.u1.b1', '72.x1.a1', '72.cb1.b1', '108.o1.b1'], 'core': '72.f1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [438, 576, 468, 864, 72], 'label': '1728.34767.36.ca1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.j1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '36.ca1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.ca1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302130
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '36.cb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bk1.a1', '12.bm1.b1', '18.f1.b1', '18.g1.a1', '18.ba1.a1'], 'contains': ['72.u1.a1', '72.x1.a1', '72.z1.a1', '108.p1.a1'], 'core': '144.b1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [433, 576, 42, 72, 864], 'label': '1728.34767.36.cb1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.p1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '36.cb1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.cb1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302131
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '36.cb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bk1.b1', '12.bm1.a1', '18.f1.a1', '18.g1.b1', '18.ba1.a1'], 'contains': ['72.u1.b1', '72.x1.b1', '72.z1.a1', '108.p1.b1'], 'core': '144.b1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [37, 576, 438, 72, 864], 'label': '1728.34767.36.cb1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.p1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '36.cb1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.cb1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302132
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '36.cc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bl1.a1', '12.bn1.b1', '18.f1.b1', '18.h1.a1', '18.z1.a1'], 'contains': ['72.u1.a1', '72.y1.b1', '72.ba1.a1', '108.q1.a1'], 'core': '144.b1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [433, 576, 474, 72, 864], 'label': '1728.34767.36.cc1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.q1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '36.cc1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.cc1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302133
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '6.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '3.a1.a1'], 'contains': ['12.g1.b1', '12.m1.a1', '12.n1.a1', '12.p1.a1', '12.be1.b1', '12.bg1.b1', '12.bj1.b1', '18.a1.a1', '18.e1.a1'], 'core': '12.g1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [6, 864, 72, 36, 576, 432, 4], 'label': '1728.34767.6.c1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '6.c1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.c1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302134
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '36.cc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bl1.b1', '12.bn1.a1', '18.f1.a1', '18.h1.b1', '18.z1.a1'], 'contains': ['72.u1.b1', '72.y1.a1', '72.ba1.a1', '108.q1.b1'], 'core': '144.b1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [469, 576, 438, 72, 864], 'label': '1728.34767.36.cc1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.q1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '36.cc1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.cc1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302135
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '36.cd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.w1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bo1.a1', '12.bo1.b1', '18.j1.a1', '18.z1.a1', '18.ba1.a1'], 'contains': ['72.u1.a1', '72.u1.b1', '72.v1.a1', '108.r1.a1'], 'core': '144.b1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [433, 864, 438, 576, 72], 'label': '1728.34767.36.cd1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.r1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '36.cd1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.cd1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302136
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '36.ce1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bp1.a1', '12.bp1.b1', '12.cs1.a1', '18.l1.a1', '18.x1.a1', '18.ba1.a1'], 'contains': ['72.f1.a1', '72.v1.a1', '72.z1.a1', '108.s1.a1'], 'core': '72.f1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [7, 576, 468, 936, 864], 'label': '1728.34767.36.ce1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.s1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '36.ce1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.ce1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302137
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '36.cf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bq1.a1', '12.bq1.b1', '12.ct1.a1', '18.h1.a1', '18.h1.b1', '18.x1.a1'], 'contains': ['72.f1.a1', '72.w1.a1', '72.ba1.a1', '108.t1.a1'], 'core': '72.f1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [439, 576, 468, 72, 864], 'label': '1728.34767.36.cf1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.t1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '36.cf1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.cf1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302138
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '36.cg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.br1.a1', '12.br1.b1', '18.k1.a1', '18.y1.a1', '18.ba1.a1'], 'contains': ['72.v1.a1', '72.x1.a1', '72.x1.b1', '108.u1.a1'], 'core': '144.b1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [37, 576, 42, 72, 864], 'label': '1728.34767.36.cg1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.u1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '36.cg1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.cg1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302139
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '36.ch1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bs1.a1', '12.bs1.b1', '18.l1.a1', '18.y1.a1', '18.z1.a1'], 'contains': ['72.v1.a1', '72.y1.a1', '72.y1.b1', '108.v1.a1'], 'core': '144.b1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [469, 576, 474, 936, 864], 'label': '1728.34767.36.ch1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.v1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '36.ch1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.ch1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302140
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '36.ci1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bt1.b1', '12.bu1.a1', '18.g1.a1', '18.h1.b1', '18.y1.a1'], 'contains': ['72.w1.a1', '72.x1.a1', '72.y1.a1', '108.w1.a1'], 'core': '144.b1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [469, 576, 42, 72, 864], 'label': '1728.34767.36.ci1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.w1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '36.ci1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.ci1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302141
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '36.ci1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bt1.a1', '12.bu1.b1', '18.g1.b1', '18.h1.a1', '18.y1.a1'], 'contains': ['72.w1.a1', '72.x1.b1', '72.y1.b1', '108.w1.b1'], 'core': '144.b1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [37, 576, 474, 72, 864], 'label': '1728.34767.36.ci1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.w1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '36.ci1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.ci1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302142
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '36.cj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.h1.a1', '12.bv1.b1', '18.i1.b1'], 'contains': ['72.bb1.a1', '72.bd1.a1', '72.be1.a1', '108.j1.a1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [42, 1200, 432, 72, 864], 'label': '1728.34767.36.cj1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.h1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.j1.b1', 'old_label': '36.cj1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.cj1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302143
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '36.cj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.h1.b1', '12.bv1.a1', '18.i1.a1'], 'contains': ['72.bb1.b1', '72.bd1.b1', '72.be1.b1', '108.j1.b1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [37, 1156, 432, 72, 864], 'label': '1728.34767.36.cj1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.h1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.j1.a1', 'old_label': '36.cj1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.cj1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302144
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '6.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.b1', '3.a1.b1'], 'contains': ['12.g1.a1', '12.m1.b1', '12.n1.b1', '12.p1.b1', '12.be1.a1', '12.bg1.a1', '12.bj1.a1', '18.a1.b1', '18.e1.b1'], 'core': '12.g1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [1, 864, 72, 36, 576, 432, 48], 'label': '1728.34767.6.c1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.b1', 'old_label': '6.c1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.c1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302145
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '36.ck1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bf1.a1', '12.bw1.b1', '12.cu1.a1', '18.i1.b1'], 'contains': ['72.bb1.a1', '72.bf1.a1', '72.bg1.a1', '72.ci1.a1', '72.ci1.b1', '108.k1.a1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [43, 1200, 432, 936, 864], 'label': '1728.34767.36.ck1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.k1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.i1.b1', 'old_label': '36.ck1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.ck1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302146
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '36.ck1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bf1.b1', '12.bw1.a1', '12.cu1.a1', '18.i1.a1'], 'contains': ['72.bb1.b1', '72.bf1.b1', '72.bg1.b1', '72.ci1.c1', '72.ci1.d1', '108.k1.a1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [43, 1156, 432, 936, 864], 'label': '1728.34767.36.ck1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.k1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.i1.a1', 'old_label': '36.ck1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.ck1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302147
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '36.cl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bk1.a1', '12.bx1.b1', '18.i1.b1'], 'contains': ['72.bc1.a1', '72.bd1.a1', '72.bf1.a1', '108.p1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [433, 1200, 42, 72, 864], 'label': '1728.34767.36.cl1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.p1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.i1.b1', 'old_label': '36.cl1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.cl1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302148
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '36.cl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bk1.b1', '12.bx1.a1', '18.i1.a1'], 'contains': ['72.bc1.b1', '72.bd1.b1', '72.bf1.b1', '108.p1.b1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [37, 1156, 438, 72, 864], 'label': '1728.34767.36.cl1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.p1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.i1.a1', 'old_label': '36.cl1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.cl1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302149
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '36.cm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bl1.a1', '12.by1.b1', '18.i1.b1'], 'contains': ['72.bc1.a1', '72.be1.a1', '72.bg1.a1', '108.q1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [433, 1200, 474, 72, 864], 'label': '1728.34767.36.cm1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.q1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.i1.b1', 'old_label': '36.cm1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.cm1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302150
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '36.cm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bl1.b1', '12.by1.a1', '18.i1.a1'], 'contains': ['72.bc1.b1', '72.be1.b1', '72.bg1.b1', '108.q1.b1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [469, 1156, 438, 72, 864], 'label': '1728.34767.36.cm1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.q1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.i1.a1', 'old_label': '36.cm1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.cm1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302151
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '36.cn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bz1.a1', '12.cn1.a1', '18.bb1.a1'], 'contains': ['72.bh1.a1', '72.bi1.a1', '72.bj1.a1', '108.h1.a1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [36, 864, 432, 100, 72], 'label': '1728.34767.36.cn1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.h1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.x1.a1', 'old_label': '36.cn1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.cn1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302152
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '36.co1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.k1.a1', '12.co1.a1', '18.bb1.a1'], 'contains': ['72.bh1.a1', '72.bk1.a1', '72.bl1.a1', '108.i1.a1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [7, 100, 432, 936, 864], 'label': '1728.34767.36.co1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.k1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.bb1.a1', 'old_label': '36.co1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.co1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302153
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '36.cp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.cb1.a1', '12.cp1.a1', '12.cu1.a1', '18.bb1.a1'], 'contains': ['72.bh1.a1', '72.bm1.a1', '72.bn1.a1', '72.cj1.a1', '72.cj1.b1', '72.cj1.c1', '72.cj1.d1', '108.k1.a1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [43, 100, 432, 936, 864], 'label': '1728.34767.36.cp1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.k1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bb1.a1', 'old_label': '36.cp1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.cp1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302154
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '36.cq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.cd1.a1', '12.cq1.a1', '18.bb1.a1'], 'contains': ['72.bi1.a1', '72.bk1.a1', '72.bn1.a1', '108.m1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [7, 100, 36, 936, 864], 'label': '1728.34767.36.cq1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.m1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bb1.a1', 'old_label': '36.cq1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.cq1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302155
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '2.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': ['864.d1.c1', '864.d1.d1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.b1.a1', '4.c1.a1', '4.f1.a1', '4.l1.a1', '4.n1.a1', '4.p1.a1', '4.w1.a1', '6.e1.a1', '6.h1.a1', '6.m1.a1'], 'core': '2.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [433, 864, 4, 6, 72, 576, 48, 36], 'label': '1728.34767.2.c1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.b1.a1', '4.c1.a1', '4.f1.a1', '4.l1.a1', '4.n1.a1', '4.p1.a1', '4.w1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.c1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2.c1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302156
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '6.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '3.a1.a1'], 'contains': ['12.h1.b1', '12.m1.a1', '12.q1.a1', '12.r1.a1', '12.bf1.b1', '12.bk1.b1', '12.bl1.b1', '18.b1.a1', '18.f1.a1', '18.i1.a1'], 'core': '12.h1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [37, 4, 864, 6, 576, 432, 72], 'label': '1728.34767.6.d1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '6.d1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.d1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302157
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '36.cr1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.ce1.a1', '12.cr1.a1', '18.bb1.a1'], 'contains': ['72.bi1.a1', '72.bl1.a1', '72.bm1.a1', '108.n1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [439, 100, 36, 72, 864], 'label': '1728.34767.36.cr1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.n1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bb1.a1', 'old_label': '36.cr1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.cr1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302158
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '36.cs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.ci1.a1', '12.cs1.a1', '18.bb1.a1'], 'contains': ['72.bj1.a1', '72.bk1.a1', '72.bm1.a1', '108.s1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [7, 100, 468, 936, 864], 'label': '1728.34767.36.cs1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.s1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bb1.a1', 'old_label': '36.cs1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.cs1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302159
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '36.ct1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.cj1.a1', '12.ct1.a1', '18.bb1.a1'], 'contains': ['72.bj1.a1', '72.bl1.a1', '72.bn1.a1', '108.t1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [439, 100, 468, 72, 864], 'label': '1728.34767.36.ct1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.t1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bb1.a1', 'old_label': '36.ct1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.ct1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302160
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '36.cu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.bw1.a1', '12.bw1.b1', '12.cp1.a1', '12.cu1.a1'], 'contains': ['72.bo1.a1', '72.bp1.a1', '72.bq1.a1', '72.ck1.a1', '72.ck1.b1', '72.ck1.c1', '72.ck1.d1', '108.k1.a1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [43, 1204, 432, 936, 864], 'label': '1728.34767.36.cu1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.k1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.cu1.a1', 'old_label': '36.cu1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.cu1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302161
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '48.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.a1.b1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '24.a1.a1', '24.c1.a1', '24.d1.a1', '24.e1.a1', '24.f1.a1', '24.g1.a1', '24.h1.a1', '24.n1.b1', '24.p1.a1', '24.q1.a1', '24.r1.a1', '24.s1.a1', '24.t1.a1', '24.u1.a1', '24.v1.a1'], 'contains': ['96.a1.a1', '96.c1.a1', '96.e1.a1', '144.a1.a1', '144.b1.a1', '144.d1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [936, 864, 48, 576], 'label': '1728.34767.48.a1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '48.a1.a1', 'normal_contained_in': ['16.a1.a1', '24.a1.a1', '24.c1.a1', '24.d1.a1', '24.e1.a1', '24.f1.a1', '24.h1.a1', '24.g1.a1'], 'normal_contains': ['96.a1.a1', '96.c1.a1', '96.e1.a1', '144.a1.a1', '144.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '48.a1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.a1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302162
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '48.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '24.a1.b1', '24.c1.b1', '24.d1.b1', '24.e1.b1', '24.f1.b1', '24.g1.b1', '24.h1.b1', '24.n1.a1', '24.p1.b1', '24.q1.b1', '24.r1.b1', '24.s1.b1', '24.t1.b1', '24.u1.b1', '24.v1.b1'], 'contains': ['96.a1.b1', '96.c1.b1', '96.e1.b1', '144.a1.b1', '144.b1.a1', '144.d1.b1'], 'core': '48.a1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [936, 864, 4, 576], 'label': '1728.34767.48.a1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '48.a1.b1', 'normal_contained_in': ['16.a1.a1', '24.a1.b1', '24.c1.b1', '24.d1.b1', '24.e1.b1', '24.f1.b1', '24.h1.b1', '24.g1.b1'], 'normal_contains': ['96.a1.b1', '96.c1.b1', '96.e1.b1', '144.a1.b1', '144.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '48.a1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.a1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302163
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '48.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.h1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '24.b1.a1', '24.b1.b1', '24.i1.a1', '24.j1.a1', '24.j1.b1', '24.k1.a1', '24.l1.a1', '24.bc1.a1', '24.bd1.a1', '24.be1.a1', '24.be1.b1', '24.bf1.a1', '24.bf1.b1', '24.bg1.a1', '24.bh1.a1'], 'contains': ['96.b1.a1', '96.d1.a1', '96.f1.a1', '144.a1.a1', '144.a1.b1', '144.e1.a1'], 'core': '48.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [936, 864, 4, 48], 'label': '1728.34767.48.b1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '48.b1.a1', 'normal_contained_in': ['16.a1.a1', '24.b1.b1', '24.b1.a1', '24.i1.a1', '24.j1.b1', '24.j1.a1', '24.k1.a1', '24.l1.a1'], 'normal_contains': ['96.b1.a1', '96.d1.a1', '96.f1.a1', '144.a1.b1', '144.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '48.b1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.b1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302164
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '48.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.e1.b1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.b1.a1', '24.a1.a1', '24.bs1.c1', '24.bs1.d1'], 'contains': ['96.a1.a1', '96.q1.a1', '144.c1.a1', '144.h1.a1'], 'core': '48.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [6, 936, 576, 48], 'label': '1728.34767.48.c1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '48.c1.a1', 'normal_contained_in': ['16.b1.a1', '24.a1.a1'], 'normal_contains': ['96.a1.a1', '144.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '48.c1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.c1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302165
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '48.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.e1.b1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.b1.b1', '24.a1.a1', '24.bs1.g1', '24.bs1.h1'], 'contains': ['96.a1.a1', '96.q1.b1', '144.c1.b1', '144.h1.b1'], 'core': '48.c1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [870, 936, 576, 48], 'label': '1728.34767.48.c1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '48.c1.b1', 'normal_contained_in': ['16.b1.b1', '24.a1.a1'], 'normal_contains': ['96.a1.a1', '144.c1.b1'], 'normalizer': '1.a1.a1', 'old_label': '48.c1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.c1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302166
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '48.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.e1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.b1.c1', '24.a1.b1', '24.bs1.a1', '24.bs1.e1'], 'contains': ['96.a1.b1', '96.q1.c1', '144.c1.c1', '144.h1.c1'], 'core': '48.c1.c1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [1, 936, 576, 4], 'label': '1728.34767.48.c1.c1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '48.c1.c1', 'normal_contained_in': ['16.b1.c1', '24.a1.b1'], 'normal_contains': ['96.a1.b1', '144.c1.c1'], 'normalizer': '1.a1.a1', 'old_label': '48.c1.c1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.c1.c1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302167
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '6.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1.b1', '3.a1.b1'], 'contains': ['12.h1.a1', '12.m1.b1', '12.q1.b1', '12.r1.b1', '12.bf1.a1', '12.bk1.a1', '12.bl1.a1', '18.b1.b1', '18.f1.b1', '18.i1.b1'], 'core': '12.h1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [1, 48, 864, 42, 576, 432, 936], 'label': '1728.34767.6.d1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.b1', 'old_label': '6.d1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.d1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302168
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '48.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.e1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.b1.d1', '24.a1.b1', '24.bs1.b1', '24.bs1.f1'], 'contains': ['96.a1.b1', '96.q1.d1', '144.c1.d1', '144.h1.d1'], 'core': '48.c1.d1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [865, 936, 576, 4], 'label': '1728.34767.48.c1.d1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '48.c1.d1', 'normal_contained_in': ['16.b1.d1', '24.a1.b1'], 'normal_contains': ['96.a1.b1', '144.c1.d1'], 'normalizer': '1.a1.a1', 'old_label': '48.c1.d1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.c1.d1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302169
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '48.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.d1.b1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.b1.a1', '24.b1.a1', '24.m1.a1', '24.m1.b1'], 'contains': ['96.b1.a1', '96.s1.a1', '144.c1.a1', '144.g1.a1'], 'core': '48.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [6, 936, 4, 48], 'label': '1728.34767.48.d1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '48.d1.a1', 'normal_contained_in': ['16.b1.a1', '24.b1.a1', '24.m1.a1', '24.m1.b1'], 'normal_contains': ['96.b1.a1', '144.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '48.d1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.d1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302170
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '48.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.d1.b1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.b1.b1', '24.b1.a1', '24.m1.c1', '24.m1.d1'], 'contains': ['96.b1.a1', '96.s1.b1', '144.c1.b1', '144.g1.b1'], 'core': '48.d1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [870, 936, 4, 48], 'label': '1728.34767.48.d1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '48.d1.b1', 'normal_contained_in': ['16.b1.b1', '24.b1.a1', '24.m1.c1', '24.m1.d1'], 'normal_contains': ['96.b1.a1', '144.c1.b1'], 'normalizer': '1.a1.a1', 'old_label': '48.d1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.d1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302171
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '48.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.d1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.b1.c1', '24.b1.b1', '24.m1.a1', '24.m1.c1'], 'contains': ['96.b1.a1', '96.s1.c1', '144.c1.c1', '144.g1.c1'], 'core': '48.d1.c1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [1, 936, 48, 4], 'label': '1728.34767.48.d1.c1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '48.d1.c1', 'normal_contained_in': ['16.b1.c1', '24.b1.b1', '24.m1.a1', '24.m1.c1'], 'normal_contains': ['96.b1.a1', '144.c1.c1'], 'normalizer': '1.a1.a1', 'old_label': '48.d1.c1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.d1.c1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302172
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '48.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.d1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.b1.d1', '24.b1.b1', '24.m1.b1', '24.m1.d1'], 'contains': ['96.b1.a1', '96.s1.d1', '144.c1.d1', '144.g1.d1'], 'core': '48.d1.d1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [865, 936, 48, 4], 'label': '1728.34767.48.d1.d1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '48.d1.d1', 'normal_contained_in': ['16.b1.d1', '24.b1.b1', '24.m1.b1', '24.m1.d1'], 'normal_contains': ['96.b1.a1', '144.c1.d1'], 'normalizer': '1.a1.a1', 'old_label': '48.d1.d1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.d1.d1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302173
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '48.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '36.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.c1.a1', '24.k1.a1', '24.m1.a1', '24.m1.d1'], 'contains': ['96.b1.a1', '144.j1.a1', '144.j1.c1', '144.l1.a1'], 'core': '48.e1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [7, 936, 4, 48], 'label': '1728.34767.48.e1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '48.e1.a1', 'normal_contained_in': ['16.c1.a1', '24.k1.a1', '24.m1.a1', '24.m1.d1'], 'normal_contains': ['96.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '48.e1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.e1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302174
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '48.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '36.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.c1.b1', '24.k1.a1', '24.m1.b1', '24.m1.c1'], 'contains': ['96.b1.a1', '144.j1.b1', '144.j1.d1', '144.l1.b1'], 'core': '48.e1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [871, 936, 4, 48], 'label': '1728.34767.48.e1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '48.e1.b1', 'normal_contained_in': ['16.c1.b1', '24.k1.a1', '24.m1.c1', '24.m1.b1'], 'normal_contains': ['96.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '48.e1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.e1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302175
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '48.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '24.o1.a1', '24.w1.a1', '24.x1.a1', '24.y1.a1', '24.z1.a1', '24.ba1.a1', '24.bb1.a1'], 'contains': ['96.g1.a1', '96.j1.a1', '96.m1.a1', '144.a1.a1', '144.d1.b1', '144.f1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [936, 864, 1156, 48], 'label': '1728.34767.48.f1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '16.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '48.f1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.f1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302176
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '48.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '24.o1.b1', '24.w1.b1', '24.x1.b1', '24.y1.b1', '24.z1.b1', '24.ba1.b1', '24.bb1.b1'], 'contains': ['96.g1.b1', '96.j1.b1', '96.m1.b1', '144.a1.b1', '144.d1.a1', '144.f1.a1'], 'core': '144.a1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [936, 864, 4, 1200], 'label': '1728.34767.48.f1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '16.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.b1', 'old_label': '48.f1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.f1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302177
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '48.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '24.bi1.a1', '24.bj1.a1', '24.bk1.a1', '24.bl1.a1', '24.bm1.a1', '24.bn1.a1', '24.bo1.a1'], 'contains': ['96.h1.a1', '96.k1.a1', '96.n1.a1', '144.b1.a1', '144.e1.a1', '144.f1.a1'], 'core': '144.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [936, 864, 100, 576], 'label': '1728.34767.48.g1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '16.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.h1.a1', 'old_label': '48.g1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.g1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302178
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '6.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1', '3.a1.a1'], 'contains': ['12.i1.b1', '12.n1.a1', '12.o1.a1', '12.r1.a1', '12.bi1.b1', '12.bm1.b1', '12.bt1.b1', '18.c1.a1', '18.g1.a1'], 'core': '12.i1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [433, 4, 864, 6, 576, 36, 72], 'label': '1728.34767.6.e1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '6.e1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.e1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302179
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '48.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '24.bp1.a1', '24.bq1.a1', '24.br1.a1'], 'contains': ['96.i1.a1', '96.l1.a1', '96.o1.a1', '144.d1.a1', '144.d1.b1', '144.e1.a1', '144.f1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [936, 864, 1156, 1200], 'label': '1728.34767.48.h1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '16.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.k1.a1', 'old_label': '48.h1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.h1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302180
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '48.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.n1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.b1.a1', '24.n1.a1', '24.bs1.a1', '24.bs1.b1'], 'contains': ['96.a1.b1', '96.p1.a1', '144.g1.a1', '144.h1.a1', '144.i1.a1'], 'core': '96.a1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [6, 936, 4, 576], 'label': '1728.34767.48.i1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '16.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '48.i1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.i1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302181
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '48.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.n1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.b1.b1', '24.n1.a1', '24.bs1.e1', '24.bs1.f1'], 'contains': ['96.a1.b1', '96.p1.b1', '144.g1.b1', '144.h1.b1', '144.i1.b1'], 'core': '96.a1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [870, 936, 4, 576], 'label': '1728.34767.48.i1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '16.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '48.i1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.i1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302182
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '48.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.n1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.b1.c1', '24.n1.b1', '24.bs1.c1', '24.bs1.g1'], 'contains': ['96.a1.a1', '96.p1.c1', '144.g1.c1', '144.h1.c1', '144.i1.c1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [1, 936, 48, 576], 'label': '1728.34767.48.i1.c1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '16.b1.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.b1', 'old_label': '48.i1.c1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.i1.c1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302183
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '48.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.n1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.b1.d1', '24.n1.b1', '24.bs1.d1', '24.bs1.h1'], 'contains': ['96.a1.a1', '96.p1.d1', '144.g1.d1', '144.h1.d1', '144.i1.d1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [865, 936, 48, 576], 'label': '1728.34767.48.i1.d1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '16.b1.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.b1', 'old_label': '48.i1.d1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.i1.d1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302184
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '48.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.b1.a1', '24.o1.a1'], 'contains': ['96.g1.a1', '96.r1.a1', '144.c1.a1', '144.i1.a1'], 'core': '144.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [6, 936, 1156, 48], 'label': '1728.34767.48.j1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '16.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '48.j1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.j1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302188
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '48.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.c1.a1', '24.q1.a1', '24.bs1.c1', '24.bs1.h1'], 'contains': ['96.a1.a1', '144.j1.a1', '144.k1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [7, 576, 936, 48], 'label': '1728.34767.48.k1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '16.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.b1', 'old_label': '48.k1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.k1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302189
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '6.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.c1.b1', '3.a1.b1'], 'contains': ['12.i1.a1', '12.n1.b1', '12.o1.b1', '12.r1.b1', '12.bi1.a1', '12.bm1.a1', '12.bt1.a1', '18.c1.b1', '18.g1.b1'], 'core': '12.i1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [1, 48, 864, 438, 576, 36, 72], 'label': '1728.34767.6.e1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.b1', 'old_label': '6.e1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.e1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302190
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '48.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.c1.b1', '24.q1.a1', '24.bs1.d1', '24.bs1.g1'], 'contains': ['96.a1.a1', '144.j1.b1', '144.k1.b1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [871, 576, 936, 48], 'label': '1728.34767.48.k1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '16.c1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.b1', 'old_label': '48.k1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.k1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302191
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '48.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.c1.a1', '24.q1.b1', '24.bs1.a1', '24.bs1.f1'], 'contains': ['96.a1.b1', '144.j1.c1', '144.k1.a1'], 'core': '96.a1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [7, 576, 936, 4], 'label': '1728.34767.48.k1.c1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '16.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '48.k1.c1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.k1.c1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302192
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '48.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.c1.b1', '24.q1.b1', '24.bs1.b1', '24.bs1.e1'], 'contains': ['96.a1.b1', '144.j1.d1', '144.k1.b1'], 'core': '96.a1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [871, 576, 936, 4], 'label': '1728.34767.48.k1.d1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '16.c1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '48.k1.d1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.k1.d1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302193
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '48.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.c1.a1', '24.bl1.a1'], 'contains': ['96.h1.a1', '144.k1.a1', '144.l1.a1'], 'core': '288.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [7, 576, 936, 100], 'label': '1728.34767.48.l1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '16.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.bb1.a1', 'old_label': '48.l1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.l1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302194
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '48.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.c1.b1', '24.bl1.a1'], 'contains': ['96.h1.a1', '144.k1.b1', '144.l1.b1'], 'core': '288.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [871, 576, 936, 100], 'label': '1728.34767.48.l1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '16.c1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.bb1.a1', 'old_label': '48.l1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.l1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302195
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '48.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.n1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.e1.a1', '24.n1.a1', '24.bt1.a1', '24.bu1.a1'], 'contains': ['96.c1.b1', '96.p1.a1', '96.p1.b1', '144.m1.a1', '144.n1.a1', '144.o1.a1'], 'core': '96.c1.b1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [6, 72, 4, 576], 'label': '1728.34767.48.m1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.e1.a1', 'old_label': '48.m1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.m1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302196
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '48.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.n1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.e1.b1', '24.n1.b1', '24.bt1.b1', '24.bu1.b1'], 'contains': ['96.c1.a1', '96.p1.c1', '96.p1.d1', '144.m1.b1', '144.n1.b1', '144.o1.b1'], 'core': '96.c1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [1, 72, 48, 576], 'label': '1728.34767.48.m1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.e1.b1', 'old_label': '48.m1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.m1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302197
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '48.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.e1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.e1.a1', '24.a1.a1', '24.bv1.a1', '24.bw1.a1'], 'contains': ['96.c1.a1', '96.q1.a1', '96.q1.b1', '144.n1.a1', '144.p1.a1'], 'core': '96.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [6, 72, 576, 48], 'label': '1728.34767.48.n1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '48.n1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.n1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302198
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '48.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.e1.b1', '24.a1.b1', '24.bv1.b1', '24.bw1.b1'], 'contains': ['96.c1.b1', '96.q1.c1', '96.q1.d1', '144.n1.b1', '144.p1.b1'], 'core': '96.c1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [1, 72, 576, 4], 'label': '1728.34767.48.n1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.b1', 'old_label': '48.n1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.n1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302199
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '48.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.e1.a1', '24.o1.a1'], 'contains': ['96.j1.a1', '96.r1.a1', '96.r1.b1', '144.o1.a1', '144.p1.a1'], 'core': '288.c1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [6, 72, 1156, 48], 'label': '1728.34767.48.o1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.f1.a1', 'old_label': '48.o1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.o1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302200
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '6.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.d1.a1', '3.a1.a1'], 'contains': ['12.j1.b1', '12.o1.a1', '12.p1.a1', '12.q1.a1', '12.bn1.b1', '12.bq1.b1', '12.bu1.b1', '18.d1.a1', '18.h1.a1'], 'core': '12.j1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [433, 4, 864, 6, 576, 468, 72], 'label': '1728.34767.6.f1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '6.f1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.f1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302201
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '48.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.e1.b1', '24.o1.b1'], 'contains': ['96.j1.b1', '96.r1.c1', '96.r1.d1', '144.o1.b1', '144.p1.b1'], 'core': '288.c1.b1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [1, 72, 1200, 4], 'label': '1728.34767.48.o1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.f1.b1', 'old_label': '48.o1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.o1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302202
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '48.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.d1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.e1.a1', '24.b1.a1', '24.bx1.a1', '24.by1.a1'], 'contains': ['96.d1.a1', '96.s1.a1', '96.s1.b1', '144.m1.a1', '144.p1.a1'], 'core': '96.d1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [6, 72, 4, 48], 'label': '1728.34767.48.p1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '48.p1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.p1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302203
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '48.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.e1.b1', '24.b1.b1', '24.bx1.b1', '24.by1.b1'], 'contains': ['96.d1.a1', '96.s1.c1', '96.s1.d1', '144.m1.b1', '144.p1.b1'], 'core': '96.d1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [1, 72, 48, 4], 'label': '1728.34767.48.p1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.b1', 'old_label': '48.p1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.p1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302204
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '48.q1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.f1.a1', '24.d1.a1', '24.bt1.b1', '24.bv1.a1'], 'contains': ['96.c1.a1', '144.q1.a1', '144.x1.a1'], 'core': '96.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [36, 48, 72, 576], 'label': '1728.34767.48.q1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.f1.a1', 'old_label': '48.q1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.q1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302205
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '48.q1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.f1.a1', '24.d1.b1', '24.bt1.a1', '24.bv1.b1'], 'contains': ['96.c1.b1', '144.q1.b1', '144.x1.a1'], 'core': '96.c1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [36, 4, 72, 576], 'label': '1728.34767.48.q1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.d1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.f1.a1', 'old_label': '48.q1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.q1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302206
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '48.r1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.p1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.g1.a1', '24.p1.a1', '24.bw1.a1', '24.bz1.a1'], 'contains': ['96.c1.a1', '144.r1.a1', '144.y1.a1', '144.bc1.a1'], 'core': '96.c1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [433, 48, 576, 72], 'label': '1728.34767.48.r1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.i1.a1', 'old_label': '48.r1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.r1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302207
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '48.r1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.p1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.g1.b1', '24.p1.b1', '24.bw1.b1', '24.bz1.b1'], 'contains': ['96.c1.b1', '144.r1.b1', '144.y1.b1', '144.bc1.b1'], 'core': '96.c1.b1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [438, 4, 576, 72], 'label': '1728.34767.48.r1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.d1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.i1.b1', 'old_label': '48.r1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.r1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302208
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '48.s1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.g1.b1', '24.e1.a1', '24.bu1.b1', '24.ca1.a1'], 'contains': ['96.c1.a1', '144.s1.a1', '144.y1.b1'], 'core': '96.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [438, 576, 72, 48], 'label': '1728.34767.48.s1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.b1', 'old_label': '48.s1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.s1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302209
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '48.s1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.g1.a1', '24.e1.b1', '24.bu1.a1', '24.ca1.b1'], 'contains': ['96.c1.b1', '144.s1.b1', '144.y1.a1'], 'core': '96.c1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [433, 576, 72, 4], 'label': '1728.34767.48.s1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.e1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.a1', 'old_label': '48.s1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.s1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302210
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '48.t1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.h1.a1', '24.f1.a1', '24.bz1.a1', '24.ca1.a1'], 'contains': ['96.c1.a1', '144.t1.a1', '144.z1.a1'], 'core': '96.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [468, 48, 72, 576], 'label': '1728.34767.48.t1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.k1.a1', 'old_label': '48.t1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.t1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302211
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '6.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.d1.b1', '3.a1.b1'], 'contains': ['12.j1.a1', '12.o1.b1', '12.p1.b1', '12.q1.b1', '12.bn1.a1', '12.bq1.a1', '12.bu1.a1', '18.d1.b1', '18.h1.b1'], 'core': '12.j1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [1, 48, 864, 438, 576, 468, 72], 'label': '1728.34767.6.f1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.b1', 'old_label': '6.f1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.f1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302212
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '48.t1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.h1.a1', '24.f1.b1', '24.bz1.b1', '24.ca1.b1'], 'contains': ['96.c1.b1', '144.t1.b1', '144.z1.a1'], 'core': '96.c1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [468, 4, 72, 576], 'label': '1728.34767.48.t1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.f1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.k1.a1', 'old_label': '48.t1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.t1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302213
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '48.u1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '36.i1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.i1.a1', '24.r1.a1', '24.bu1.b1', '24.bw1.a1'], 'contains': ['96.c1.a1', '144.u1.a1', '144.ba1.a1'], 'core': '96.c1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [439, 576, 72, 48], 'label': '1728.34767.48.u1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.o1.b1', 'old_label': '48.u1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.u1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302214
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '48.u1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '36.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.i1.a1', '24.r1.b1', '24.bu1.a1', '24.bw1.b1'], 'contains': ['96.c1.b1', '144.u1.b1', '144.ba1.a1'], 'core': '96.c1.b1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [439, 576, 72, 4], 'label': '1728.34767.48.u1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.o1.a1', 'old_label': '48.u1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.u1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302215
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '48.v1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.g1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.j1.b1', '24.s1.a1', '24.bt1.b1', '24.bz1.a1'], 'contains': ['96.c1.a1', '144.v1.a1', '144.bb1.b1'], 'core': '96.c1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [37, 48, 72, 576], 'label': '1728.34767.48.v1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.h1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.c1.b1', 'old_label': '48.v1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.v1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302216
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '48.v1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.j1.a1', '24.s1.b1', '24.bt1.a1', '24.bz1.b1'], 'contains': ['96.c1.b1', '144.v1.b1', '144.bb1.a1'], 'core': '96.c1.b1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [42, 4, 72, 576], 'label': '1728.34767.48.v1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.h1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.c1.a1', 'old_label': '48.v1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.v1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302217
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '48.w1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.j1.a1', '24.g1.a1', '24.bv1.a1', '24.ca1.a1'], 'contains': ['96.c1.a1', '144.w1.a1', '144.bb1.a1', '144.bd1.a1'], 'core': '96.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [42, 72, 48, 576], 'label': '1728.34767.48.w1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '48.w1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.w1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302218
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '48.w1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.j1.b1', '24.g1.b1', '24.bv1.b1', '24.ca1.b1'], 'contains': ['96.c1.b1', '144.w1.b1', '144.bb1.b1', '144.bd1.b1'], 'core': '96.c1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [37, 72, 4, 576], 'label': '1728.34767.48.w1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.g1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.b1', 'old_label': '48.w1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.w1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302219
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '48.x1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.g1.b1', '24.x1.a1'], 'contains': ['96.j1.a1', '144.s1.a1', '144.bc1.b1'], 'core': '288.c1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [438, 1156, 72, 48], 'label': '1728.34767.48.x1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.d1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.q1.b1', 'old_label': '48.x1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.x1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302220
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '48.x1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.g1.a1', '24.x1.b1'], 'contains': ['96.j1.b1', '144.s1.b1', '144.bc1.a1'], 'core': '288.c1.b1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [433, 1200, 72, 4], 'label': '1728.34767.48.x1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.q1.a1', 'old_label': '48.x1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.x1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302221
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '48.y1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.j1.b1', '24.y1.a1'], 'contains': ['96.j1.a1', '144.v1.a1', '144.bd1.b1'], 'core': '288.c1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [37, 48, 72, 1156], 'label': '1728.34767.48.y1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.h1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bv1.a1', 'old_label': '48.y1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.y1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302222
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '6.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '3.a1.b1'], 'contains': ['12.a1.a1', '12.t1.a1', '12.u1.a1', '12.be1.a1', '12.bf1.a1', '12.bm1.a1', '12.bn1.a1', '18.f1.a1', '18.n1.a1'], 'core': '12.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [37, 48, 864, 6, 576, 432, 72], 'label': '1728.34767.6.g1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.b1', 'old_label': '6.g1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.g1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302223
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '48.y1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.j1.a1', '24.y1.b1'], 'contains': ['96.j1.b1', '144.v1.b1', '144.bd1.a1'], 'core': '288.c1.b1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [42, 4, 72, 1200], 'label': '1728.34767.48.y1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.h1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bv1.b1', 'old_label': '48.y1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.y1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302224
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '48.z1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.bc1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.f1.a1', '24.bc1.a1', '24.bx1.a1', '24.bx1.b1'], 'contains': ['96.d1.a1', '144.q1.a1', '144.q1.b1', '144.be1.a1'], 'core': '96.d1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [36, 4, 48, 72], 'label': '1728.34767.48.z1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.r1.a1', 'old_label': '48.z1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.z1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302225
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '48.ba1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.g1.a1', '24.j1.a1', '24.by1.a1', '24.cb1.a1'], 'contains': ['96.d1.a1', '144.r1.a1', '144.s1.b1'], 'core': '96.d1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [433, 48, 72, 4], 'label': '1728.34767.48.ba1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.j1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.a1', 'old_label': '48.ba1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.ba1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302226
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '48.ba1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.g1.b1', '24.j1.b1', '24.by1.b1', '24.cb1.b1'], 'contains': ['96.d1.a1', '144.r1.b1', '144.s1.a1'], 'core': '96.d1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [438, 4, 72, 48], 'label': '1728.34767.48.ba1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.j1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.b1', 'old_label': '48.ba1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.ba1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302227
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '48.bb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.bd1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.h1.a1', '24.bd1.a1', '24.cb1.a1', '24.cb1.b1'], 'contains': ['96.d1.a1', '144.t1.a1', '144.t1.b1', '144.bf1.a1'], 'core': '96.d1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [468, 4, 48, 72], 'label': '1728.34767.48.bb1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.ba1.a1', 'old_label': '48.bb1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bb1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302228
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '48.bc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.i1.a1', '24.l1.a1', '24.by1.a1', '24.by1.b1'], 'contains': ['96.d1.a1', '144.u1.a1', '144.u1.b1', '144.bg1.a1'], 'core': '96.d1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [439, 72, 4, 48], 'label': '1728.34767.48.bc1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.l1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.e1.a1', 'old_label': '48.bc1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bc1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302229
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '48.bd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.j1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.j1.a1', '24.be1.a1', '24.bx1.a1', '24.cb1.b1'], 'contains': ['96.d1.a1', '144.v1.b1', '144.w1.a1'], 'core': '96.d1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [42, 4, 72, 48], 'label': '1728.34767.48.bd1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.h1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.k1.a1', 'old_label': '48.bd1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bd1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302230
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '48.bd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.j1.b1', '24.be1.b1', '24.bx1.b1', '24.cb1.a1'], 'contains': ['96.d1.a1', '144.v1.a1', '144.w1.b1'], 'core': '96.d1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [37, 48, 72, 4], 'label': '1728.34767.48.bd1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.h1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.k1.b1', 'old_label': '48.bd1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bd1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302231
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '48.be1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.f1.a1', '24.bj1.a1'], 'contains': ['96.k1.a1', '144.x1.a1', '144.be1.a1'], 'core': '288.d1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [36, 100, 72, 576], 'label': '1728.34767.48.be1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.m1.a1', 'old_label': '48.be1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.be1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302232
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '48.bf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.h1.a1', '24.bk1.a1'], 'contains': ['96.k1.a1', '144.z1.a1', '144.bf1.a1'], 'core': '288.d1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [468, 100, 72, 576], 'label': '1728.34767.48.bf1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.s1.a1', 'old_label': '48.bf1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bf1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302233
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '6.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1.b1', '3.a1.a1'], 'contains': ['12.a1.b1', '12.t1.b1', '12.u1.b1', '12.be1.b1', '12.bf1.b1', '12.bm1.b1', '12.bn1.b1', '18.f1.b1', '18.n1.b1'], 'core': '12.a1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [1, 4, 864, 42, 576, 432, 936], 'label': '1728.34767.6.g1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '6.g1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.g1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302235
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '48.bh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.n1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.k1.a1', '24.n1.a1', '24.cc1.a1', '24.cc1.b1'], 'contains': ['96.e1.b1', '96.p1.a1', '96.p1.b1', '144.bh1.a1', '144.bi1.a1', '144.bj1.a1'], 'core': '96.e1.b1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [6, 864, 4, 576], 'label': '1728.34767.48.bh1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.e1.a1', 'old_label': '48.bh1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bh1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302236
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '48.bh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.n1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.k1.b1', '24.n1.b1', '24.cc1.c1', '24.cc1.d1'], 'contains': ['96.e1.a1', '96.p1.c1', '96.p1.d1', '144.bh1.b1', '144.bi1.b1', '144.bj1.b1'], 'core': '96.e1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [1, 864, 48, 576], 'label': '1728.34767.48.bh1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.e1.b1', 'old_label': '48.bh1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bh1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302237
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '48.bi1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.e1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.k1.a1', '24.a1.a1', '24.cd1.a1', '24.cd1.b1'], 'contains': ['96.e1.a1', '96.q1.a1', '96.q1.b1', '144.bi1.a1', '144.bk1.a1'], 'core': '96.e1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [6, 864, 576, 48], 'label': '1728.34767.48.bi1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '48.bi1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bi1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302238
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '48.bi1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.k1.b1', '24.a1.b1', '24.cd1.c1', '24.cd1.d1'], 'contains': ['96.e1.b1', '96.q1.c1', '96.q1.d1', '144.bi1.b1', '144.bk1.b1'], 'core': '96.e1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [1, 864, 576, 4], 'label': '1728.34767.48.bi1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.b1', 'old_label': '48.bi1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bi1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302239
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '48.bj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.k1.a1', '24.o1.a1', '24.ce1.a1', '24.ce1.b1'], 'contains': ['96.m1.a1', '96.r1.a1', '96.r1.b1', '144.bj1.a1', '144.bk1.a1'], 'core': '288.e1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [6, 864, 1156, 48], 'label': '1728.34767.48.bj1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.f1.a1', 'old_label': '48.bj1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bj1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302240
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '48.bj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.k1.b1', '24.o1.b1', '24.ce1.c1', '24.ce1.d1'], 'contains': ['96.m1.b1', '96.r1.c1', '96.r1.d1', '144.bj1.b1', '144.bk1.b1'], 'core': '288.e1.b1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [1, 864, 1200, 4], 'label': '1728.34767.48.bj1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.f1.b1', 'old_label': '48.bj1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bj1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302241
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '48.bk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.d1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.k1.a1', '24.b1.a1', '24.cf1.a1', '24.cf1.b1'], 'contains': ['96.f1.a1', '96.s1.a1', '96.s1.b1', '144.bh1.a1', '144.bk1.a1'], 'core': '96.f1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [6, 864, 4, 48], 'label': '1728.34767.48.bk1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '48.bk1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bk1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302242
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '48.bk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.k1.b1', '24.b1.b1', '24.cf1.c1', '24.cf1.d1'], 'contains': ['96.f1.a1', '96.s1.c1', '96.s1.d1', '144.bh1.b1', '144.bk1.b1'], 'core': '96.f1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [1, 864, 48, 4], 'label': '1728.34767.48.bk1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.b1', 'old_label': '48.bk1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bk1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302243
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '48.bl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.l1.a1', '24.c1.a1', '24.cg1.a1', '24.cg1.b1'], 'contains': ['96.e1.a1', '144.bl1.a1', '144.bq1.a1', '144.bu1.a1'], 'core': '96.e1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [432, 48, 576, 864], 'label': '1728.34767.48.bl1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.h1.a1', 'old_label': '48.bl1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bl1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302244
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '6.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1', '3.a1.b1'], 'contains': ['12.b1.a1', '12.s1.a1', '12.u1.a1', '12.bg1.a1', '12.bi1.a1', '12.bk1.a1', '12.bu1.a1', '18.g1.a1', '18.o1.a1'], 'core': '12.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [433, 48, 864, 6, 576, 36, 72], 'label': '1728.34767.6.h1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.b1', 'old_label': '6.h1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.h1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302245
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '48.bl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.l1.a1', '24.c1.b1', '24.cg1.c1', '24.cg1.d1'], 'contains': ['96.e1.b1', '144.bl1.b1', '144.bq1.a1', '144.bu1.b1'], 'core': '96.e1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [432, 4, 576, 864], 'label': '1728.34767.48.bl1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.c1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.h1.a1', 'old_label': '48.bl1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bl1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302246
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '48.bm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.m1.a1', '24.t1.a1', '24.cd1.a1', '24.cd1.b1'], 'contains': ['96.e1.a1', '144.bm1.a1', '144.br1.a1'], 'core': '96.e1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [469, 48, 864, 576], 'label': '1728.34767.48.bm1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.i1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.h1.a1', 'old_label': '48.bm1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bm1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302247
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '48.bm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.m1.b1', '24.t1.b1', '24.cd1.c1', '24.cd1.d1'], 'contains': ['96.e1.b1', '144.bm1.b1', '144.br1.b1'], 'core': '96.e1.b1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [474, 4, 864, 576], 'label': '1728.34767.48.bm1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.i1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.h1.b1', 'old_label': '48.bm1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bm1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302248
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '48.bn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.m1.b1', '24.h1.a1', '24.cc1.c1', '24.cc1.d1'], 'contains': ['96.e1.a1', '144.bn1.a1', '144.br1.b1', '144.bv1.a1'], 'core': '96.e1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [474, 864, 48, 576], 'label': '1728.34767.48.bn1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.h1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.b1', 'old_label': '48.bn1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bn1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302249
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '48.bn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.m1.a1', '24.h1.b1', '24.cc1.a1', '24.cc1.b1'], 'contains': ['96.e1.b1', '144.bn1.b1', '144.br1.a1', '144.bv1.b1'], 'core': '96.e1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [469, 864, 4, 576], 'label': '1728.34767.48.bn1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.h1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '48.bn1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bn1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302250
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '48.bo1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.d1.a1', '24.u1.a1', '24.cc1.c1', '24.cd1.a1', '24.cg1.a1'], 'contains': ['96.e1.a1', '144.bo1.a1', '144.bs1.a1', '144.bw1.a1'], 'core': '96.e1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [1411, 864, 48, 576], 'label': '1728.34767.48.bo1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '16.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.b1', 'old_label': '48.bo1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bo1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302251
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '48.bo1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.d1.b1', '24.u1.a1', '24.cc1.d1', '24.cd1.b1', '24.cg1.b1'], 'contains': ['96.e1.a1', '144.bo1.b1', '144.bs1.b1', '144.bw1.b1'], 'core': '96.e1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [475, 864, 48, 576], 'label': '1728.34767.48.bo1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '16.d1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.b1', 'old_label': '48.bo1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bo1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302252
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '48.bo1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.d1.a1', '24.u1.b1', '24.cc1.a1', '24.cd1.c1', '24.cg1.c1'], 'contains': ['96.e1.b1', '144.bo1.c1', '144.bs1.a1', '144.bw1.c1'], 'core': '96.e1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [1411, 864, 4, 576], 'label': '1728.34767.48.bo1.c1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '16.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '48.bo1.c1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bo1.c1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302253
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '48.bo1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.d1.b1', '24.u1.b1', '24.cc1.b1', '24.cd1.d1', '24.cg1.d1'], 'contains': ['96.e1.b1', '144.bo1.d1', '144.bs1.b1', '144.bw1.d1'], 'core': '96.e1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [475, 864, 4, 576], 'label': '1728.34767.48.bo1.d1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '16.d1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '48.bo1.d1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bo1.d1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302254
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '48.bp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.n1.a1', '24.v1.a1', '24.cg1.a1', '24.cg1.b1'], 'contains': ['96.e1.a1', '144.bp1.a1', '144.bt1.a1', '144.bx1.a1'], 'core': '96.e1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [43, 864, 48, 576], 'label': '1728.34767.48.bp1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.k1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.t1.a1', 'old_label': '48.bp1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bp1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302255
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '6.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.c1.b1', '3.a1.a1'], 'contains': ['12.b1.b1', '12.s1.b1', '12.u1.b1', '12.bg1.b1', '12.bi1.b1', '12.bk1.b1', '12.bu1.b1', '18.g1.b1', '18.o1.b1'], 'core': '12.b1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [1, 4, 864, 438, 576, 36, 72], 'label': '1728.34767.6.h1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '6.h1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.h1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302256
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '48.bp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.n1.a1', '24.v1.b1', '24.cg1.c1', '24.cg1.d1'], 'contains': ['96.e1.b1', '144.bp1.b1', '144.bt1.a1', '144.bx1.b1'], 'core': '96.e1.b1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [43, 864, 4, 576], 'label': '1728.34767.48.bp1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.k1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.t1.b1', 'old_label': '48.bp1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bp1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302257
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '48.bq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.l1.a1', '24.w1.a1', '24.ch1.a1', '24.ch1.b1'], 'contains': ['96.m1.a1', '144.bl1.a1', '144.bu1.b1', '144.cb1.a1', '144.cb1.b1'], 'core': '288.e1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [432, 1156, 48, 864], 'label': '1728.34767.48.bq1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.k1.a1', 'old_label': '48.bq1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bq1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302258
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '48.bq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.l1.a1', '24.w1.b1', '24.ch1.c1', '24.ch1.d1'], 'contains': ['96.m1.b1', '144.bl1.b1', '144.bu1.a1', '144.cb1.a1', '144.cb1.b1'], 'core': '288.e1.b1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [432, 4, 1200, 864], 'label': '1728.34767.48.bq1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.k1.a1', 'old_label': '48.bq1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bq1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302259
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '48.br1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.m1.a1', '24.z1.a1', '24.ce1.a1', '24.ce1.b1'], 'contains': ['96.m1.a1', '144.bm1.a1', '144.bv1.b1'], 'core': '288.e1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [469, 48, 864, 1156], 'label': '1728.34767.48.br1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.i1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.x1.a1', 'old_label': '48.br1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.br1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302260
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '48.br1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.m1.b1', '24.z1.b1', '24.ce1.c1', '24.ce1.d1'], 'contains': ['96.m1.b1', '144.bm1.b1', '144.bv1.a1'], 'core': '288.e1.b1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [474, 4, 864, 1200], 'label': '1728.34767.48.br1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.i1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.x1.b1', 'old_label': '48.br1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.br1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302261
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '48.bs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.d1.a1', '24.ba1.a1', '24.ce1.a1', '24.ch1.a1'], 'contains': ['96.m1.a1', '144.bo1.a1', '144.bw1.c1', '144.cc1.a1'], 'core': '288.e1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [1411, 864, 1156, 48], 'label': '1728.34767.48.bs1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '16.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.j1.a1', 'old_label': '48.bs1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bs1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302262
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '48.bs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.d1.b1', '24.ba1.a1', '24.ce1.b1', '24.ch1.b1'], 'contains': ['96.m1.a1', '144.bo1.b1', '144.bw1.d1', '144.cc1.b1'], 'core': '288.e1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [475, 864, 1156, 48], 'label': '1728.34767.48.bs1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '16.d1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.j1.a1', 'old_label': '48.bs1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bs1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302263
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '48.bs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.d1.a1', '24.ba1.b1', '24.ce1.c1', '24.ch1.c1'], 'contains': ['96.m1.b1', '144.bo1.c1', '144.bw1.a1', '144.cc1.a1'], 'core': '288.e1.b1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [1411, 864, 4, 1200], 'label': '1728.34767.48.bs1.c1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '16.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.j1.b1', 'old_label': '48.bs1.c1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bs1.c1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302264
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '48.bs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.d1.b1', '24.ba1.b1', '24.ce1.d1', '24.ch1.d1'], 'contains': ['96.m1.b1', '144.bo1.d1', '144.bw1.b1', '144.cc1.b1'], 'core': '288.e1.b1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [475, 864, 4, 1200], 'label': '1728.34767.48.bs1.d1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '16.d1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.j1.b1', 'old_label': '48.bs1.d1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bs1.d1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302265
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '48.bt1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.n1.a1', '24.bb1.a1', '24.ch1.a1', '24.ch1.b1'], 'contains': ['96.m1.a1', '144.bp1.a1', '144.bx1.b1', '144.cd1.a1', '144.cd1.a2'], 'core': '288.e1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [43, 864, 1156, 48], 'label': '1728.34767.48.bt1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.k1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bw1.a1', 'old_label': '48.bt1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bt1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302266
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '2.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': ['864.d1.a1', '864.d1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.b1.b1', '4.c1.b1', '4.f1.b1', '4.l1.b1', '4.n1.a1', '4.p1.b1', '4.w1.b1', '6.e1.b1', '6.h1.b1', '6.m1.b1'], 'core': '2.c1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [1, 864, 4, 438, 72, 576, 48, 36], 'label': '1728.34767.2.c1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1.b1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.b1.b1', '4.c1.b1', '4.f1.b1', '4.l1.b1', '4.n1.a1', '4.p1.b1', '4.w1.b1'], 'normalizer': '1.a1.a1', 'old_label': '2.c1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2.c1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302267
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '6.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.d1.a1', '3.a1.b1'], 'contains': ['12.c1.a1', '12.s1.a1', '12.t1.a1', '12.bj1.a1', '12.bl1.a1', '12.bq1.a1', '12.bt1.a1', '18.h1.a1', '18.p1.a1'], 'core': '12.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [433, 48, 864, 6, 576, 468, 72], 'label': '1728.34767.6.i1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.b1', 'old_label': '6.i1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.i1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302268
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '48.bt1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.n1.a1', '24.bb1.b1', '24.ch1.c1', '24.ch1.d1'], 'contains': ['96.m1.b1', '144.bp1.b1', '144.bx1.a1', '144.cd1.a1', '144.cd1.a2'], 'core': '288.e1.b1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [43, 864, 4, 1200], 'label': '1728.34767.48.bt1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.k1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bw1.b1', 'old_label': '48.bt1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bt1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302269
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '48.bu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.l1.a1', '24.i1.a1', '24.ci1.a1', '24.ci1.b1'], 'contains': ['96.f1.a1', '144.bl1.a1', '144.bl1.b1', '144.by1.a1', '144.by1.b1'], 'core': '96.f1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [432, 4, 48, 864], 'label': '1728.34767.48.bu1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.i1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.h1.a1', 'old_label': '48.bu1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bu1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302270
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '48.bv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.m1.a1', '24.bf1.a1', '24.cf1.a1', '24.cf1.b1'], 'contains': ['96.f1.a1', '144.bm1.a1', '144.bn1.b1'], 'core': '96.f1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [469, 48, 864, 4], 'label': '1728.34767.48.bv1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.i1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.m1.a1', 'old_label': '48.bv1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bv1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302271
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '48.bv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.m1.b1', '24.bf1.b1', '24.cf1.c1', '24.cf1.d1'], 'contains': ['96.f1.a1', '144.bm1.b1', '144.bn1.a1'], 'core': '96.f1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [474, 4, 864, 48], 'label': '1728.34767.48.bv1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.i1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.m1.b1', 'old_label': '48.bv1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bv1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302272
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '48.bw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.d1.a1', '24.bg1.a1', '24.cf1.a1', '24.cf1.c1', '24.ci1.a1'], 'contains': ['96.f1.a1', '144.bo1.a1', '144.bo1.c1', '144.bz1.a1'], 'core': '96.f1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [1411, 864, 4, 48], 'label': '1728.34767.48.bw1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '16.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '48.bw1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bw1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302273
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '48.bw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.d1.b1', '24.bg1.a1', '24.cf1.b1', '24.cf1.d1', '24.ci1.b1'], 'contains': ['96.f1.a1', '144.bo1.b1', '144.bo1.d1', '144.bz1.b1'], 'core': '96.f1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [475, 864, 4, 48], 'label': '1728.34767.48.bw1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '16.d1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '48.bw1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bw1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302274
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '48.bx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.n1.a1', '24.bh1.a1', '24.ci1.a1', '24.ci1.b1'], 'contains': ['96.f1.a1', '144.bp1.a1', '144.bp1.b1', '144.ca1.a1', '144.ca1.a2'], 'core': '96.f1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [43, 864, 4, 48], 'label': '1728.34767.48.bx1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.k1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.x1.a1', 'old_label': '48.bx1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bx1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302275
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '48.by1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.l1.a1', '24.bi1.a1', '24.cj1.a1', '24.cj1.c1'], 'contains': ['96.n1.a1', '144.bq1.a1', '144.by1.a1', '144.cb1.a1'], 'core': '288.f1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [432, 52, 576, 864], 'label': '1728.34767.48.by1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.h1.a1', 'old_label': '48.by1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.by1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302276
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '48.by1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.l1.a1', '24.bi1.a1', '24.cj1.b1', '24.cj1.d1'], 'contains': ['96.n1.a1', '144.bq1.a1', '144.by1.b1', '144.cb1.b1'], 'core': '288.f1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [432, 100, 576, 864], 'label': '1728.34767.48.by1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.h1.a1', 'old_label': '48.by1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.by1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302277
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '48.bz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.d1.a1', '24.bn1.a1', '24.cj1.a1', '24.cj1.b1'], 'contains': ['96.n1.a1', '144.bs1.a1', '144.bz1.a1', '144.cc1.a1'], 'core': '288.f1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [1411, 864, 100, 576], 'label': '1728.34767.48.bz1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '16.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.bb1.a1', 'old_label': '48.bz1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bz1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302278
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '6.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.d1.b1', '3.a1.a1'], 'contains': ['12.c1.b1', '12.s1.b1', '12.t1.b1', '12.bj1.b1', '12.bl1.b1', '12.bq1.b1', '12.bt1.b1', '18.h1.b1', '18.p1.b1'], 'core': '12.c1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [1, 4, 864, 438, 576, 468, 72], 'label': '1728.34767.6.i1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '6.i1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.i1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302279
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '48.bz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.d1.b1', '24.bn1.a1', '24.cj1.c1', '24.cj1.d1'], 'contains': ['96.n1.a1', '144.bs1.b1', '144.bz1.b1', '144.cc1.b1'], 'core': '288.f1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [475, 864, 100, 576], 'label': '1728.34767.48.bz1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '16.d1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.bb1.a1', 'old_label': '48.bz1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bz1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302280
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '48.ca1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.n1.a1', '24.bo1.a1', '24.cj1.a1', '24.cj1.d1'], 'contains': ['96.n1.a1', '144.bt1.a1', '144.ca1.a1', '144.cd1.a1'], 'core': '288.f1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [43, 864, 100, 576], 'label': '1728.34767.48.ca1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.k1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.bb1.a1', 'old_label': '48.ca1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.ca1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302281
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '48.ca1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.n1.a1', '24.bo1.a1', '24.cj1.b1', '24.cj1.c1'], 'contains': ['96.n1.a1', '144.bt1.a1', '144.ca1.a2', '144.cd1.a2'], 'core': '288.f1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [43, 864, 52, 576], 'label': '1728.34767.48.ca1.a2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.k1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.bb1.a1', 'old_label': '48.ca1.a2', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.ca1.a2', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302282
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '48.cb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.l1.a1', '24.bp1.a1', '24.ck1.a1', '24.ck1.c1'], 'contains': ['96.o1.a1', '144.bu1.a1', '144.bu1.b1', '144.by1.a1', '144.cb1.b1'], 'core': '864.c1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [432, 1156, 624, 864], 'label': '1728.34767.48.cb1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.k1.a1', 'old_label': '48.cb1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.cb1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302283
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '48.cb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.l1.a1', '24.bp1.a1', '24.ck1.b1', '24.ck1.d1'], 'contains': ['96.o1.a1', '144.bu1.a1', '144.bu1.b1', '144.by1.b1', '144.cb1.a1'], 'core': '864.c1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [432, 1156, 1200, 864], 'label': '1728.34767.48.cb1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.k1.a1', 'old_label': '48.cb1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.cb1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302284
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '48.cc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.d1.a1', '24.bq1.a1', '24.ck1.a1', '24.ck1.b1'], 'contains': ['96.o1.a1', '144.bw1.a1', '144.bw1.c1', '144.bz1.a1', '144.cc1.a1'], 'core': '864.c1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [1411, 864, 1156, 1200], 'label': '1728.34767.48.cc1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '16.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.cu1.a1', 'old_label': '48.cc1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.cc1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302285
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '48.cc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.d1.b1', '24.bq1.a1', '24.ck1.c1', '24.ck1.d1'], 'contains': ['96.o1.a1', '144.bw1.b1', '144.bw1.d1', '144.bz1.b1', '144.cc1.b1'], 'core': '864.c1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [475, 864, 1156, 1200], 'label': '1728.34767.48.cc1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '16.d1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.cu1.a1', 'old_label': '48.cc1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.cc1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302286
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '48.cd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.n1.a1', '24.br1.a1', '24.ck1.a1', '24.ck1.d1'], 'contains': ['96.o1.a1', '144.bx1.a1', '144.bx1.b1', '144.ca1.a1', '144.cd1.a2'], 'core': '864.c1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [43, 864, 1156, 1200], 'label': '1728.34767.48.cd1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.k1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.cu1.a1', 'old_label': '48.cd1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.cd1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302287
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '48.cd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.n1.a1', '24.br1.a1', '24.ck1.b1', '24.ck1.c1'], 'contains': ['96.o1.a1', '144.bx1.a1', '144.bx1.b1', '144.ca1.a2', '144.cd1.a1'], 'core': '864.c1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [43, 864, 1156, 624], 'label': '1728.34767.48.cd1.a2', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.k1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.cu1.a1', 'old_label': '48.cd1.a2', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.cd1.a2', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302288
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '54.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.a1.a1', '18.e1.a1', '18.m1.a1', '27.a1.a1'], 'contains': ['108.a1.a1', '108.b1.a1', '108.d1.a1', '108.h1.a1', '108.j1.a1', '108.l1.b1', '108.o1.b1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [6, 36, 432], 'label': '1728.34767.54.a1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1.a1', 'old_label': '54.a1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.a1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302289
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '6.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1'], 'contains': ['12.v1.a1', '12.w1.a1', '12.x1.a1', '12.bv1.a1', '12.bw1.a1', '12.bx1.a1', '12.by1.a1', '18.i1.a1', '18.n1.a1'], 'core': '36.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [37, 1156, 864, 6, 48, 432, 72], 'label': '1728.34767.6.j1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.j1.a1', 'old_label': '6.j1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.j1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302290
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '54.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.a1.b1', '18.e1.b1', '18.m1.b1', '27.a1.a1'], 'contains': ['108.a1.b1', '108.b1.b1', '108.d1.b1', '108.h1.a1', '108.j1.b1', '108.l1.a1', '108.o1.a1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [1, 36, 432], 'label': '1728.34767.54.a1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1.b1', 'old_label': '54.a1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.a1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302291
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '54.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.b1.a1', '18.f1.a1', '18.i1.a1', '18.n1.a1', '27.a1.a1'], 'contains': ['108.a1.a1', '108.e1.a1', '108.f1.a1', '108.j1.b1', '108.k1.a1', '108.p1.b1', '108.q1.b1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [37, 6, 432], 'label': '1728.34767.54.b1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1.a1', 'old_label': '54.b1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.b1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302292
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '54.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.b1.b1', '18.f1.b1', '18.i1.b1', '18.n1.b1', '27.a1.a1'], 'contains': ['108.a1.b1', '108.e1.b1', '108.f1.b1', '108.j1.a1', '108.k1.a1', '108.p1.a1', '108.q1.a1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [1, 42, 432], 'label': '1728.34767.54.b1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1.a1', 'old_label': '54.b1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.b1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302293
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '54.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.c1.a1', '18.g1.a1', '18.o1.a1', '27.a1.a1'], 'contains': ['108.b1.a1', '108.c1.a1', '108.f1.a1', '108.l1.a1', '108.n1.a1', '108.p1.a1', '108.w1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [433, 6, 36], 'label': '1728.34767.54.c1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1.a1', 'old_label': '54.c1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.c1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302294
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '54.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.c1.b1', '18.g1.b1', '18.o1.b1', '27.a1.a1'], 'contains': ['108.b1.b1', '108.c1.b1', '108.f1.b1', '108.l1.b1', '108.n1.a1', '108.p1.b1', '108.w1.b1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [1, 438, 36], 'label': '1728.34767.54.c1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1.a1', 'old_label': '54.c1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.c1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302295
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '54.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.d1.a1', '18.h1.a1', '18.p1.a1', '27.a1.a1'], 'contains': ['108.c1.a1', '108.d1.a1', '108.e1.a1', '108.o1.a1', '108.q1.a1', '108.t1.a1', '108.w1.b1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [433, 6, 468], 'label': '1728.34767.54.d1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1.a1', 'old_label': '54.d1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.d1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302296
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '54.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.d1.b1', '18.h1.b1', '18.p1.b1', '27.a1.a1'], 'contains': ['108.c1.b1', '108.d1.b1', '108.e1.b1', '108.o1.b1', '108.q1.b1', '108.t1.a1', '108.w1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [1, 438, 468], 'label': '1728.34767.54.d1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1.a1', 'old_label': '54.d1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.d1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302297
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '54.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.w1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.j1.a1', '18.q1.a1', '18.q1.b1', '27.a1.a1'], 'contains': ['108.a1.a1', '108.a1.b1', '108.c1.a1', '108.c1.b1', '108.g1.a1', '108.i1.a1', '108.r1.a1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [1, 6, 432], 'label': '1728.34767.54.e1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '6.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '54.e1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.e1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302298
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '54.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.k1.a1', '18.r1.a1', '18.r1.b1', '27.a1.a1'], 'contains': ['108.b1.a1', '108.b1.b1', '108.e1.a1', '108.e1.b1', '108.g1.a1', '108.m1.a1', '108.u1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [1, 6, 36], 'label': '1728.34767.54.f1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1.a1', 'old_label': '54.f1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.f1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302299
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '54.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.l1.a1', '18.s1.a1', '18.s1.b1', '27.a1.a1'], 'contains': ['108.d1.a1', '108.d1.b1', '108.f1.a1', '108.f1.b1', '108.g1.a1', '108.s1.a1', '108.v1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [1, 6, 468], 'label': '1728.34767.54.g1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1.a1', 'old_label': '54.g1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.g1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302300
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '6.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1.b1'], 'contains': ['12.v1.b1', '12.w1.b1', '12.x1.b1', '12.bv1.b1', '12.bw1.b1', '12.bx1.b1', '12.by1.b1', '18.i1.b1', '18.n1.b1'], 'core': '36.a1.b1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [1, 4, 864, 42, 1200, 432, 936], 'label': '1728.34767.6.j1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.j1.b1', 'old_label': '6.j1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.j1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302301
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '54.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.t1.a1', '18.t1.b1', '18.x1.a1', '18.bb1.a1', '27.a1.a1'], 'contains': ['108.h1.a1', '108.i1.a1', '108.k1.a1', '108.m1.a1', '108.n1.a1', '108.s1.a1', '108.t1.a1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [7, 36, 432], 'label': '1728.34767.54.h1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.h1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1.a1', 'old_label': '54.h1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.h1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302302
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '54.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.u1.a1', '18.u1.b1', '18.y1.a1', '27.a1.a1'], 'contains': ['108.i1.a1', '108.j1.a1', '108.j1.b1', '108.u1.a1', '108.v1.a1', '108.w1.a1', '108.w1.b1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [37, 42, 432], 'label': '1728.34767.54.i1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.i1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1.a1', 'old_label': '54.i1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.i1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302303
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '54.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.v1.a1', '18.v1.b1', '18.z1.a1', '27.a1.a1'], 'contains': ['108.l1.a1', '108.l1.b1', '108.m1.a1', '108.q1.a1', '108.q1.b1', '108.r1.a1', '108.v1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [433, 438, 36], 'label': '1728.34767.54.j1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.j1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1.a1', 'old_label': '54.j1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.j1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302304
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '54.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.w1.a1', '18.w1.b1', '18.ba1.a1', '27.a1.a1'], 'contains': ['108.o1.a1', '108.o1.b1', '108.p1.a1', '108.p1.b1', '108.r1.a1', '108.s1.a1', '108.u1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [433, 438, 468], 'label': '1728.34767.54.k1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.k1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1.a1', 'old_label': '54.k1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.k1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302305
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '64.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8.b1.a1', 'complements': ['27.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['32.a1.a1', '32.b1.a1', '32.c1.a1', '32.d1.a1', '32.d1.b1', '32.d1.c1', '32.d1.d1'], 'contains': ['192.a1.a1', '192.a1.b1', '192.b1.a1', '192.c1.a1', '192.c1.b1', '192.d1.a1', '192.e1.a1'], 'core': '64.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [4, 48, 576], 'label': '1728.34767.64.a1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '64.a1.a1', 'normal_contained_in': ['32.a1.a1', '32.b1.a1', '32.c1.a1'], 'normal_contains': ['192.a1.b1', '192.a1.a1', '192.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '64.a1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.a1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302306
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '72.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12.i1.b1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['24.a1.a1', '24.b1.a1', '24.o1.a1', '36.a1.a1', '36.s1.a1', '36.t1.a1', '36.u1.a1', '36.v1.a1', '36.w1.a1', '36.x1.b1'], 'contains': ['144.a1.a1', '144.c1.a1', '144.c1.b1', '144.p1.a1', '144.bk1.a1', '216.b1.a1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [6, 936, 864, 48], 'label': '1728.34767.72.a1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '72.a1.a1', 'normal_contained_in': ['24.a1.a1', '24.b1.a1', '36.a1.a1'], 'normal_contains': ['144.a1.a1', '144.c1.a1', '144.c1.b1'], 'normalizer': '1.a1.a1', 'old_label': '72.a1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.a1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302307
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '72.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12.i1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['24.a1.b1', '24.b1.b1', '24.o1.b1', '36.a1.b1', '36.s1.b1', '36.t1.b1', '36.u1.b1', '36.v1.b1', '36.w1.b1', '36.x1.a1'], 'contains': ['144.a1.b1', '144.c1.c1', '144.c1.d1', '144.p1.b1', '144.bk1.b1', '216.b1.b1'], 'core': '72.a1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [1, 936, 864, 4], 'label': '1728.34767.72.a1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '72.a1.b1', 'normal_contained_in': ['24.a1.b1', '24.b1.b1', '36.a1.b1'], 'normal_contains': ['144.a1.b1', '144.c1.c1', '144.c1.d1'], 'normalizer': '1.a1.a1', 'old_label': '72.a1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.a1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302308
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '72.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['24.c1.a1', '24.i1.a1', '24.w1.a1', '36.a1.a1', '36.c1.b1', '36.y1.a1', '36.z1.a1', '36.ba1.a1', '36.bb1.a1', '36.bc1.a1'], 'contains': ['144.a1.a1', '144.bl1.a1', '216.a1.a1'], 'core': '72.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [432, 936, 48, 864], 'label': '1728.34767.72.b1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '72.b1.a1', 'normal_contained_in': ['24.c1.a1', '24.i1.a1', '36.a1.a1'], 'normal_contains': ['144.a1.a1', '216.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '72.b1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.b1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302309
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '72.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['24.c1.b1', '24.i1.a1', '24.w1.b1', '36.a1.b1', '36.c1.a1', '36.y1.b1', '36.z1.b1', '36.ba1.b1', '36.bb1.b1', '36.bc1.b1'], 'contains': ['144.a1.b1', '144.bl1.b1', '216.a1.a1'], 'core': '72.b1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [432, 936, 4, 864], 'label': '1728.34767.72.b1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '72.b1.b1', 'normal_contained_in': ['24.c1.b1', '24.i1.a1', '36.a1.b1'], 'normal_contains': ['144.a1.b1', '216.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '72.b1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.b1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302310
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '72.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.a1.b1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['24.e1.a1', '24.j1.b1', '24.x1.a1', '36.a1.a1', '36.e1.b1', '36.be1.a1', '36.bk1.a1', '36.bl1.a1', '36.bm1.a1', '36.bn1.a1'], 'contains': ['144.a1.a1', '144.s1.a1', '216.d1.b1'], 'core': '72.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [438, 864, 72, 48], 'label': '1728.34767.72.c1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '72.c1.a1', 'normal_contained_in': ['24.e1.a1', '24.j1.b1', '36.a1.a1'], 'normal_contains': ['144.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '72.c1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.c1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302311
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '6.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '3.b1.a1'], 'contains': ['12.d1.a1', '12.y1.a1', '12.z1.a1', '12.bz1.a1', '12.ca1.a1', '12.cc1.b1', '12.cf1.b1', '18.a1.a1', '18.m1.a1'], 'core': '12.d1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [6, 864, 72, 36, 48, 432, 4], 'label': '1728.34767.6.k1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '6.k1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.k1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302312
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '72.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['24.e1.b1', '24.j1.a1', '24.x1.b1', '36.a1.b1', '36.e1.a1', '36.be1.b1', '36.bk1.b1', '36.bl1.b1', '36.bm1.b1', '36.bn1.b1'], 'contains': ['144.a1.b1', '144.s1.b1', '216.d1.a1'], 'core': '72.c1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [433, 864, 72, 4], 'label': '1728.34767.72.c1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '72.c1.b1', 'normal_contained_in': ['24.e1.b1', '24.j1.a1', '36.a1.b1'], 'normal_contains': ['144.a1.b1'], 'normalizer': '1.a1.a1', 'old_label': '72.c1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.c1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302313
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '72.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.i1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['24.c1.a1', '24.c1.b1', '24.bi1.a1', '36.b1.a1', '36.i1.a1', '36.i1.b1', '36.bu1.a1', '36.bv1.a1', '36.bv1.b1', '36.bw1.a1'], 'contains': ['144.b1.a1', '144.bq1.a1', '216.a1.a1'], 'core': '72.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [432, 936, 576, 864], 'label': '1728.34767.72.d1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '72.d1.a1', 'normal_contained_in': ['24.c1.b1', '24.c1.a1', '36.b1.a1'], 'normal_contains': ['144.b1.a1', '216.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '72.d1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.d1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302314
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '72.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12.f1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['24.d1.a1', '24.d1.b1', '24.bj1.a1', '36.b1.a1', '36.j1.a1', '36.j1.b1', '36.bx1.a1', '36.bx1.b1', '36.by1.a1', '36.bz1.a1'], 'contains': ['144.b1.a1', '144.x1.a1', '216.c1.a1'], 'core': '72.e1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [36, 864, 72, 576], 'label': '1728.34767.72.e1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '72.e1.a1', 'normal_contained_in': ['24.d1.b1', '24.d1.a1', '36.b1.a1'], 'normal_contains': ['144.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '72.e1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.e1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302315
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '72.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.k1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['24.f1.a1', '24.f1.b1', '24.bk1.a1', '36.b1.a1', '36.l1.a1', '36.l1.b1', '36.ca1.a1', '36.ca1.b1', '36.ce1.a1', '36.cf1.a1'], 'contains': ['144.b1.a1', '144.z1.a1', '216.e1.a1'], 'core': '72.f1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [468, 864, 72, 576], 'label': '1728.34767.72.f1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '72.f1.a1', 'normal_contained_in': ['24.f1.b1', '24.f1.a1', '36.b1.a1'], 'normal_contains': ['144.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '72.f1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.f1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302316
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '72.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12.n1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.b1.a1', '24.n1.a1', '36.c1.a1', '36.d1.a1', '36.e1.a1', '36.f1.a1', '36.g1.a1', '36.h1.a1', '36.x1.a1'], 'contains': ['144.a1.b1', '144.g1.a1', '144.g1.b1', '144.m1.a1', '144.bh1.a1', '216.b1.a1'], 'core': '144.a1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [6, 936, 864, 4], 'label': '1728.34767.72.g1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '72.g1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.g1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302317
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '72.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12.n1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.b1.b1', '24.n1.b1', '36.c1.b1', '36.d1.b1', '36.e1.b1', '36.f1.b1', '36.g1.b1', '36.h1.b1', '36.x1.b1'], 'contains': ['144.a1.a1', '144.g1.c1', '144.g1.d1', '144.m1.b1', '144.bh1.b1', '216.b1.b1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [1, 936, 864, 48], 'label': '1728.34767.72.g1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.b1', 'old_label': '72.g1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.g1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302318
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '72.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12.o1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.a1.a1', '24.n1.a1', '36.i1.a1', '36.j1.a1', '36.k1.a1', '36.l1.a1', '36.m1.a1', '36.n1.a1', '36.r1.a1'], 'contains': ['144.b1.a1', '144.h1.a1', '144.h1.b1', '144.n1.a1', '144.bi1.a1', '216.b1.a1'], 'core': '144.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [6, 936, 864, 576], 'label': '1728.34767.72.h1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '72.h1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.h1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302319
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '72.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12.o1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.a1.b1', '24.n1.b1', '36.i1.b1', '36.j1.b1', '36.k1.b1', '36.l1.b1', '36.m1.b1', '36.n1.b1', '36.r1.a1'], 'contains': ['144.b1.a1', '144.h1.c1', '144.h1.d1', '144.n1.b1', '144.bi1.b1', '216.b1.b1'], 'core': '144.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [1, 936, 864, 576], 'label': '1728.34767.72.h1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.b1', 'old_label': '72.h1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.h1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302320
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '72.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.n1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.n1.a1', '24.o1.a1', '36.o1.a1', '36.p1.a1', '36.q1.a1'], 'contains': ['144.d1.b1', '144.i1.a1', '144.i1.b1', '144.o1.a1', '144.bj1.a1', '216.b1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [6, 936, 864, 1156], 'label': '1728.34767.72.i1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.a1', 'old_label': '72.i1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.i1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302321
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '72.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.n1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.n1.b1', '24.o1.b1', '36.o1.b1', '36.p1.b1', '36.q1.b1'], 'contains': ['144.d1.a1', '144.i1.c1', '144.i1.d1', '144.o1.b1', '144.bj1.b1', '216.b1.b1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [1, 936, 864, 1200], 'label': '1728.34767.72.i1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.b1', 'old_label': '72.i1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.i1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302322
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '6.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.b1', '3.b1.a1'], 'contains': ['12.d1.b1', '12.y1.b1', '12.z1.b1', '12.bz1.a1', '12.ca1.b1', '12.cc1.a1', '12.cf1.a1', '18.a1.b1', '18.m1.b1'], 'core': '12.d1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [1, 864, 72, 36, 4, 432, 48], 'label': '1728.34767.6.k1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '6.k1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.k1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302323
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '72.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12.y1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.d1.a1', '24.bc1.a1', '36.d1.b1', '36.s1.a1', '36.y1.a1', '36.bd1.a1', '36.be1.a1', '36.bf1.a1', '36.bg1.a1'], 'contains': ['144.a1.a1', '144.q1.a1', '216.c1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [36, 864, 48, 72], 'label': '1728.34767.72.j1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '72.j1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.j1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302324
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '72.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12.y1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.d1.b1', '24.bc1.a1', '36.d1.a1', '36.s1.b1', '36.y1.b1', '36.bd1.b1', '36.be1.b1', '36.bf1.b1', '36.bg1.b1'], 'contains': ['144.a1.b1', '144.q1.b1', '216.c1.a1'], 'core': '144.a1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [36, 864, 4, 72], 'label': '1728.34767.72.j1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.d1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '72.j1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.j1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302325
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '72.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.p1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.j1.a1', '24.p1.a1', '36.c1.b1', '36.t1.a1', '36.bd1.a1', '36.bh1.a1', '36.bi1.a1', '36.bj1.a1', '36.bn1.a1'], 'contains': ['144.a1.a1', '144.r1.a1', '216.d1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [433, 864, 48, 72], 'label': '1728.34767.72.k1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.j1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.b1', 'old_label': '72.k1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.k1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302326
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '72.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.p1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.j1.b1', '24.p1.b1', '36.c1.a1', '36.t1.b1', '36.bd1.b1', '36.bh1.b1', '36.bi1.b1', '36.bj1.b1', '36.bn1.b1'], 'contains': ['144.a1.b1', '144.r1.b1', '216.d1.b1'], 'core': '144.a1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [438, 864, 4, 72], 'label': '1728.34767.72.k1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.j1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '72.k1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.k1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302327
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '72.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.bd1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.f1.a1', '24.bd1.a1', '36.f1.b1', '36.u1.a1', '36.y1.a1', '36.bh1.a1', '36.bk1.a1', '36.bo1.a1', '36.bp1.a1'], 'contains': ['144.a1.a1', '144.t1.a1', '216.e1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [468, 864, 48, 72], 'label': '1728.34767.72.l1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '72.l1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.l1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302328
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '72.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.bd1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.f1.b1', '24.bd1.a1', '36.f1.a1', '36.u1.b1', '36.y1.b1', '36.bh1.b1', '36.bk1.b1', '36.bo1.b1', '36.bp1.b1'], 'contains': ['144.a1.b1', '144.t1.b1', '216.e1.a1'], 'core': '144.a1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [468, 864, 4, 72], 'label': '1728.34767.72.l1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.f1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '72.l1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.l1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302329
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '72.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '36.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.k1.a1', '24.q1.a1', '36.x1.b1', '36.z1.a1', '36.bf1.a1', '36.bn1.a1', '36.bo1.a1', '36.bq1.a1', '36.br1.a1'], 'contains': ['144.a1.a1', '144.j1.a1', '144.j1.b1', '216.f1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [7, 864, 936, 48], 'label': '1728.34767.72.m1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.k1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.b1', 'old_label': '72.m1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.m1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302330
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '72.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '36.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.k1.a1', '24.q1.b1', '36.x1.a1', '36.z1.b1', '36.bf1.b1', '36.bn1.b1', '36.bo1.b1', '36.bq1.b1', '36.br1.b1'], 'contains': ['144.a1.b1', '144.j1.c1', '144.j1.d1', '216.f1.a1'], 'core': '144.a1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [7, 864, 936, 4], 'label': '1728.34767.72.m1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.k1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '72.m1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.m1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302331
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '72.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '36.i1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.l1.a1', '24.r1.a1', '36.e1.b1', '36.t1.a1', '36.z1.a1', '36.bg1.a1', '36.bp1.a1', '36.bs1.a1', '36.bt1.a1'], 'contains': ['144.a1.a1', '144.u1.a1', '216.g1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [439, 864, 72, 48], 'label': '1728.34767.72.n1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.l1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.b1', 'old_label': '72.n1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.n1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302332
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '72.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '36.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.l1.a1', '24.r1.b1', '36.e1.a1', '36.t1.b1', '36.z1.b1', '36.bg1.b1', '36.bp1.b1', '36.bs1.b1', '36.bt1.b1'], 'contains': ['144.a1.b1', '144.u1.b1', '216.g1.a1'], 'core': '144.a1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [439, 864, 72, 4], 'label': '1728.34767.72.n1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.l1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '72.n1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.n1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302333
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '6.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '3.b1.a1'], 'contains': ['12.d1.a1', '12.ba1.a1', '12.bb1.a1', '12.ca1.b1', '12.cb1.a1', '12.cg1.b1', '12.ch1.b1', '18.b1.a1', '18.n1.a1'], 'core': '12.d1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [37, 4, 864, 6, 48, 432, 72], 'label': '1728.34767.6.l1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '6.l1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.l1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302334
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '72.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '36.d1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.s1.a1', '24.y1.a1', '24.be1.b1', '36.d1.b1', '36.v1.a1', '36.ba1.a1', '36.bh1.a1', '36.bl1.a1', '36.bq1.a1', '36.bs1.a1'], 'contains': ['144.a1.a1', '144.v1.a1', '216.h1.b1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [37, 864, 48, 72], 'label': '1728.34767.72.o1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.h1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1.b1', 'old_label': '72.o1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.o1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302335
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '72.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '36.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.s1.b1', '24.y1.b1', '24.be1.a1', '36.d1.a1', '36.v1.b1', '36.ba1.b1', '36.bh1.b1', '36.bl1.b1', '36.bq1.b1', '36.bs1.b1'], 'contains': ['144.a1.b1', '144.v1.b1', '216.h1.a1'], 'core': '144.a1.b1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [42, 864, 4, 72], 'label': '1728.34767.72.o1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.h1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1.a1', 'old_label': '72.o1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.o1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302336
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '72.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.j1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.g1.a1', '24.be1.a1', '36.g1.b1', '36.s1.a1', '36.bb1.a1', '36.bi1.a1', '36.bk1.a1', '36.bq1.a1', '36.bt1.a1'], 'contains': ['144.a1.a1', '144.w1.a1', '216.h1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [42, 864, 72, 48], 'label': '1728.34767.72.p1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '72.p1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.p1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302337
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '72.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.g1.b1', '24.be1.b1', '36.g1.a1', '36.s1.b1', '36.bb1.b1', '36.bi1.b1', '36.bk1.b1', '36.bq1.b1', '36.bt1.b1'], 'contains': ['144.a1.b1', '144.w1.b1', '216.h1.b1'], 'core': '144.a1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [37, 864, 72, 4], 'label': '1728.34767.72.p1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.g1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '72.p1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.p1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302338
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '72.q1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.q1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.t1.a1', '24.z1.a1', '24.bf1.a1', '36.f1.b1', '36.w1.a1', '36.ba1.a1', '36.bd1.a1', '36.bm1.a1', '36.br1.a1', '36.bt1.a1'], 'contains': ['144.a1.a1', '144.bm1.a1', '216.i1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [469, 936, 48, 864], 'label': '1728.34767.72.q1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.i1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1.b1', 'old_label': '72.q1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.q1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302339
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '72.q1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.q1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.t1.b1', '24.z1.b1', '24.bf1.b1', '36.f1.a1', '36.w1.b1', '36.ba1.b1', '36.bd1.b1', '36.bm1.b1', '36.br1.b1', '36.bt1.b1'], 'contains': ['144.a1.b1', '144.bm1.b1', '216.i1.b1'], 'core': '144.a1.b1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [474, 936, 4, 864], 'label': '1728.34767.72.q1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.i1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1.a1', 'old_label': '72.q1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.q1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302340
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '72.r1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.h1.a1', '24.bf1.b1', '36.h1.b1', '36.u1.a1', '36.bb1.a1', '36.be1.a1', '36.bj1.a1', '36.br1.a1', '36.bs1.a1'], 'contains': ['144.a1.a1', '144.bn1.a1', '216.i1.b1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [474, 936, 864, 48], 'label': '1728.34767.72.r1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.h1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '72.r1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.r1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302341
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '72.r1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.h1.b1', '24.bf1.a1', '36.h1.a1', '36.u1.b1', '36.bb1.b1', '36.be1.b1', '36.bj1.b1', '36.br1.b1', '36.bs1.b1'], 'contains': ['144.a1.b1', '144.bn1.b1', '216.i1.a1'], 'core': '144.a1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [469, 936, 864, 4], 'label': '1728.34767.72.r1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.h1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '72.r1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.r1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302342
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '72.s1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '108.d1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.u1.a1', '24.ba1.a1', '24.bg1.a1', '36.h1.b1', '36.w1.a1', '36.bc1.a1', '36.bg1.a1', '36.bi1.a1', '36.bl1.a1', '36.bo1.a1'], 'contains': ['144.a1.a1', '144.bo1.a1', '144.bo1.b1', '216.j1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [475, 936, 864, 48], 'label': '1728.34767.72.s1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.j1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1.b1', 'old_label': '72.s1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.s1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302343
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '72.s1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '108.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.u1.b1', '24.ba1.b1', '24.bg1.a1', '36.h1.a1', '36.w1.b1', '36.bc1.b1', '36.bg1.b1', '36.bi1.b1', '36.bl1.b1', '36.bo1.b1'], 'contains': ['144.a1.b1', '144.bo1.c1', '144.bo1.d1', '216.j1.a1'], 'core': '144.a1.b1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [475, 936, 864, 4], 'label': '1728.34767.72.s1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.j1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1.a1', 'old_label': '72.s1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.s1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302344
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '6.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1.b1', '3.b1.a1'], 'contains': ['12.d1.b1', '12.ba1.b1', '12.bb1.b1', '12.ca1.a1', '12.cb1.a1', '12.cg1.a1', '12.ch1.a1', '18.b1.b1', '18.n1.b1'], 'core': '12.d1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [1, 4, 864, 42, 48, 432, 936], 'label': '1728.34767.6.l1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '6.l1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.l1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302345
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '72.t1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.v1.a1', '24.bb1.a1', '24.bh1.a1', '36.g1.b1', '36.v1.a1', '36.bc1.a1', '36.bf1.a1', '36.bj1.a1', '36.bm1.a1', '36.bp1.a1'], 'contains': ['144.a1.a1', '144.bp1.a1', '216.k1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [43, 936, 864, 48], 'label': '1728.34767.72.t1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.k1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1.b1', 'old_label': '72.t1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.t1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302346
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '72.t1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.v1.b1', '24.bb1.b1', '24.bh1.a1', '36.g1.a1', '36.v1.b1', '36.bc1.b1', '36.bf1.b1', '36.bj1.b1', '36.bm1.b1', '36.bp1.b1'], 'contains': ['144.a1.b1', '144.bp1.b1', '216.k1.a1'], 'core': '144.a1.b1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [43, 936, 864, 4], 'label': '1728.34767.72.t1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.k1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1.a1', 'old_label': '72.t1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.t1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302347
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '72.u1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12.s1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.e1.b1', '24.p1.a1', '36.i1.b1', '36.k1.a1', '36.bx1.a1', '36.ca1.a1', '36.cb1.a1', '36.cc1.a1', '36.cd1.a1'], 'contains': ['144.b1.a1', '144.y1.a1', '216.d1.a1'], 'core': '144.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [433, 864, 576, 72], 'label': '1728.34767.72.u1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.e1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.b1', 'old_label': '72.u1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.u1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302348
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '72.u1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12.s1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.e1.a1', '24.p1.b1', '36.i1.a1', '36.k1.b1', '36.bx1.b1', '36.ca1.b1', '36.cb1.b1', '36.cc1.b1', '36.cd1.a1'], 'contains': ['144.b1.a1', '144.y1.b1', '216.d1.b1'], 'core': '144.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [438, 864, 576, 72], 'label': '1728.34767.72.u1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '72.u1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.u1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302349
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '72.v1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '36.bu1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.q1.a1', '24.q1.b1', '24.bl1.a1', '36.r1.a1', '36.bu1.a1', '36.by1.a1', '36.cd1.a1', '36.ce1.a1', '36.cg1.a1', '36.ch1.a1'], 'contains': ['144.b1.a1', '144.k1.a1', '144.k1.b1', '216.f1.a1'], 'core': '144.b1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [7, 864, 576, 936], 'label': '1728.34767.72.v1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '72.v1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.v1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302350
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '72.w1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '18.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.r1.a1', '24.r1.b1', '24.bm1.a1', '36.k1.a1', '36.k1.b1', '36.bu1.a1', '36.bz1.a1', '36.cf1.a1', '36.ci1.a1', '36.ci1.b1'], 'contains': ['144.b1.a1', '144.ba1.a1', '216.g1.a1'], 'core': '144.b1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [439, 864, 576, 72], 'label': '1728.34767.72.w1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '72.w1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.w1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302351
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '72.x1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.g1.a1', '24.s1.b1', '36.j1.a1', '36.m1.b1', '36.bv1.a1', '36.ca1.b1', '36.cb1.a1', '36.cg1.a1', '36.ci1.a1'], 'contains': ['144.b1.a1', '144.bb1.a1', '216.h1.a1'], 'core': '144.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [42, 864, 72, 576], 'label': '1728.34767.72.x1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '72.x1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.x1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302352
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '72.x1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.g1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.g1.b1', '24.s1.a1', '36.j1.b1', '36.m1.a1', '36.bv1.b1', '36.ca1.a1', '36.cb1.b1', '36.cg1.a1', '36.ci1.b1'], 'contains': ['144.b1.a1', '144.bb1.b1', '216.h1.b1'], 'core': '144.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [37, 864, 72, 576], 'label': '1728.34767.72.x1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.g1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.b1', 'old_label': '72.x1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.x1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302353
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '72.y1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.h1.b1', '24.t1.a1', '36.l1.b1', '36.n1.a1', '36.bv1.b1', '36.bx1.a1', '36.cc1.b1', '36.ch1.a1', '36.ci1.a1'], 'contains': ['144.b1.a1', '144.br1.a1', '216.i1.a1'], 'core': '144.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [469, 936, 864, 576], 'label': '1728.34767.72.y1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.h1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.b1', 'old_label': '72.y1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.y1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302354
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '72.y1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.h1.a1', '24.t1.b1', '36.l1.a1', '36.n1.b1', '36.bv1.a1', '36.bx1.b1', '36.cc1.a1', '36.ch1.a1', '36.ci1.b1'], 'contains': ['144.b1.a1', '144.br1.b1', '216.i1.b1'], 'core': '144.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [474, 936, 864, 576], 'label': '1728.34767.72.y1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.h1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '72.y1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.y1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302355
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '6.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1', '3.b1.a1'], 'contains': ['12.e1.a1', '12.y1.a1', '12.bb1.a1', '12.cc1.a1', '12.ce1.a1', '12.cg1.a1', '12.cm1.a1', '18.c1.a1', '18.o1.a1'], 'core': '12.e1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [433, 4, 864, 6, 48, 36, 72], 'label': '1728.34767.6.m1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '6.m1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.m1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302356
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '72.z1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '108.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.u1.a1', '24.u1.b1', '24.bn1.a1', '36.n1.a1', '36.n1.b1', '36.bw1.a1', '36.bz1.a1', '36.cb1.a1', '36.cb1.b1', '36.ce1.a1'], 'contains': ['144.b1.a1', '144.bs1.a1', '144.bs1.b1', '216.j1.a1'], 'core': '144.b1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [475, 936, 864, 576], 'label': '1728.34767.72.z1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.j1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '72.z1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.z1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302357
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '72.ba1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.v1.a1', '24.v1.b1', '24.bo1.a1', '36.m1.a1', '36.m1.b1', '36.bw1.a1', '36.by1.a1', '36.cc1.a1', '36.cc1.b1', '36.cf1.a1'], 'contains': ['144.b1.a1', '144.bt1.a1', '216.k1.a1'], 'core': '144.b1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [43, 936, 864, 576], 'label': '1728.34767.72.ba1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.k1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '72.ba1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ba1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302358
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '72.bb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.c1.a1', '24.w1.b1', '24.bp1.a1', '36.o1.b1', '36.cj1.a1', '36.ck1.a1'], 'contains': ['144.d1.a1', '144.bu1.a1', '216.a1.a1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [432, 936, 1200, 864], 'label': '1728.34767.72.bb1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.b1', 'old_label': '72.bb1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bb1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302359
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '72.bb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.c1.b1', '24.w1.a1', '24.bp1.a1', '36.o1.a1', '36.cj1.b1', '36.ck1.b1'], 'contains': ['144.d1.b1', '144.bu1.b1', '216.a1.a1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [432, 936, 1156, 864], 'label': '1728.34767.72.bb1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.c1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '72.bb1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bb1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302360
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '72.bc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.p1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.p1.a1', '24.x1.b1', '36.o1.b1', '36.cl1.a1', '36.cm1.a1'], 'contains': ['144.d1.a1', '144.bc1.a1', '216.d1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [433, 864, 1200, 72], 'label': '1728.34767.72.bc1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.b1', 'old_label': '72.bc1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bc1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302361
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '72.bc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.p1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.p1.b1', '24.x1.a1', '36.o1.a1', '36.cl1.b1', '36.cm1.b1'], 'contains': ['144.d1.b1', '144.bc1.b1', '216.d1.b1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [438, 864, 1156, 72], 'label': '1728.34767.72.bc1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.d1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.a1', 'old_label': '72.bc1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bc1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302362
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '72.bd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.g1.a1', '24.y1.b1', '36.p1.b1', '36.cj1.a1', '36.cl1.a1'], 'contains': ['144.d1.a1', '144.bd1.a1', '216.h1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [42, 864, 72, 1200], 'label': '1728.34767.72.bd1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.j1.b1', 'old_label': '72.bd1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bd1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302363
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '72.bd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.g1.b1', '24.y1.a1', '36.p1.a1', '36.cj1.b1', '36.cl1.b1'], 'contains': ['144.d1.b1', '144.bd1.b1', '216.h1.b1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [37, 864, 72, 1156], 'label': '1728.34767.72.bd1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.g1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.j1.a1', 'old_label': '72.bd1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bd1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302364
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '72.be1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.h1.a1', '24.z1.b1', '36.q1.b1', '36.cj1.a1', '36.cm1.a1'], 'contains': ['144.d1.a1', '144.bv1.a1', '216.i1.b1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [474, 936, 864, 1200], 'label': '1728.34767.72.be1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.h1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.j1.b1', 'old_label': '72.be1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.be1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302365
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '72.be1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.h1.b1', '24.z1.a1', '36.q1.a1', '36.cj1.b1', '36.cm1.b1'], 'contains': ['144.d1.b1', '144.bv1.b1', '216.i1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [469, 936, 864, 1156], 'label': '1728.34767.72.be1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.h1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.j1.a1', 'old_label': '72.be1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.be1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302366
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '6.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.c1.b1', '3.b1.a1'], 'contains': ['12.e1.b1', '12.y1.b1', '12.bb1.b1', '12.cc1.b1', '12.ce1.a1', '12.cg1.b1', '12.cm1.b1', '18.c1.b1', '18.o1.b1'], 'core': '12.e1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [1, 4, 864, 438, 48, 36, 72], 'label': '1728.34767.6.m1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.c1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '6.m1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.m1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302367
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '72.bf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.u1.a1', '24.ba1.b1', '24.bq1.a1', '36.q1.b1', '36.ck1.a1', '36.cl1.a1'], 'contains': ['144.d1.a1', '144.bw1.a1', '144.bw1.b1', '216.j1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [475, 936, 864, 1200], 'label': '1728.34767.72.bf1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.j1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.i1.b1', 'old_label': '72.bf1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bf1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302368
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '72.bf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.u1.b1', '24.ba1.a1', '24.bq1.a1', '36.q1.a1', '36.ck1.b1', '36.cl1.b1'], 'contains': ['144.d1.b1', '144.bw1.c1', '144.bw1.d1', '216.j1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [475, 936, 864, 1156], 'label': '1728.34767.72.bf1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.j1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.i1.a1', 'old_label': '72.bf1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bf1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302369
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '72.bg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.v1.a1', '24.bb1.b1', '24.br1.a1', '36.p1.b1', '36.ck1.a1', '36.cm1.a1'], 'contains': ['144.d1.a1', '144.bx1.a1', '216.k1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [43, 936, 864, 1200], 'label': '1728.34767.72.bg1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.k1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.i1.b1', 'old_label': '72.bg1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bg1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302370
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '72.bg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.v1.b1', '24.bb1.a1', '24.br1.a1', '36.p1.a1', '36.ck1.b1', '36.cm1.b1'], 'contains': ['144.d1.b1', '144.bx1.b1', '216.k1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [43, 936, 864, 1156], 'label': '1728.34767.72.bg1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.k1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.i1.a1', 'old_label': '72.bg1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bg1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302371
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '72.bh1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.i1.a1', '24.bi1.a1', '24.bp1.a1', '36.cn1.a1', '36.co1.a1', '36.cp1.a1'], 'contains': ['144.e1.a1', '144.by1.a1', '144.by1.b1', '216.a1.a1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [432, 936, 100, 864], 'label': '1728.34767.72.bh1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.i1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.h1.a1', 'old_label': '72.bh1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bh1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302372
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '72.bi1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.bc1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bc1.a1', '24.bj1.a1', '36.cn1.a1', '36.cq1.a1', '36.cr1.a1'], 'contains': ['144.e1.a1', '144.be1.a1', '216.c1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [36, 864, 100, 72], 'label': '1728.34767.72.bi1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.x1.a1', 'old_label': '72.bi1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bi1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302373
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '72.bj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.bd1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bd1.a1', '24.bk1.a1', '36.cn1.a1', '36.cs1.a1', '36.ct1.a1'], 'contains': ['144.e1.a1', '144.bf1.a1', '216.e1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [468, 864, 100, 72], 'label': '1728.34767.72.bj1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.x1.a1', 'old_label': '72.bj1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bj1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302374
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '72.bk1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '36.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.k1.a1', '24.bl1.a1', '36.co1.a1', '36.cq1.a1', '36.cs1.a1'], 'contains': ['144.e1.a1', '144.l1.a1', '144.l1.b1', '216.f1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [7, 864, 936, 100], 'label': '1728.34767.72.bk1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.k1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.bb1.a1', 'old_label': '72.bk1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bk1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302375
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '72.bl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.l1.a1', '24.bm1.a1', '36.co1.a1', '36.cr1.a1', '36.ct1.a1'], 'contains': ['144.e1.a1', '144.bg1.a1', '216.g1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [439, 864, 72, 100], 'label': '1728.34767.72.bl1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.l1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.bb1.a1', 'old_label': '72.bl1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bl1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302376
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '72.bm1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bg1.a1', '24.bn1.a1', '24.bq1.a1', '36.cp1.a1', '36.cr1.a1', '36.cs1.a1'], 'contains': ['144.e1.a1', '144.bz1.a1', '144.bz1.b1', '216.j1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [475, 936, 864, 100], 'label': '1728.34767.72.bm1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.j1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bb1.a1', 'old_label': '72.bm1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bm1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302377
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '2.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': ['864.d1.c1', '864.d1.d1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.c1.a1', '4.d1.a1', '4.e1.a1', '4.o1.a1', '4.q1.a1', '4.t1.a1', '4.w1.b1', '6.f1.a1', '6.i1.a1', '6.n1.a1'], 'core': '2.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [433, 864, 4, 6, 72, 576, 48, 468], 'label': '1728.34767.2.d1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.c1.a1', '4.d1.a1', '4.e1.a1', '4.o1.a1', '4.q1.a1', '4.t1.a1', '4.w1.b1'], 'normalizer': '1.a1.a1', 'old_label': '2.d1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2.d1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302378
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '6.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.d1.a1', '3.b1.a1'], 'contains': ['12.e1.a1', '12.z1.a1', '12.ba1.a1', '12.cf1.a1', '12.ch1.a1', '12.cj1.a1', '12.cm1.b1', '18.d1.a1', '18.p1.a1'], 'core': '12.e1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [433, 4, 864, 6, 48, 468, 72], 'label': '1728.34767.6.n1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '6.n1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.n1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302379
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '72.bn1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bh1.a1', '24.bo1.a1', '24.br1.a1', '36.cp1.a1', '36.cq1.a1', '36.ct1.a1'], 'contains': ['144.e1.a1', '144.ca1.a1', '144.ca1.a2', '216.k1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [43, 936, 864, 100], 'label': '1728.34767.72.bn1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.k1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bb1.a1', 'old_label': '72.bn1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bn1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302380
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '72.bo1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.w1.a1', '24.w1.b1', '24.bi1.a1', '24.bp1.a1', '36.cu1.a1'], 'contains': ['144.f1.a1', '144.cb1.a1', '144.cb1.b1', '216.a1.a1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [432, 936, 1204, 864], 'label': '1728.34767.72.bo1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.k1.a1', 'old_label': '72.bo1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bo1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302381
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '72.bp1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.ba1.a1', '24.ba1.b1', '24.bn1.a1', '24.bq1.a1', '36.cu1.a1'], 'contains': ['144.f1.a1', '144.cc1.a1', '144.cc1.b1', '216.j1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [475, 936, 864, 1204], 'label': '1728.34767.72.bp1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.j1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.cu1.a1', 'old_label': '72.bp1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bp1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302382
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '72.bq1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bb1.a1', '24.bb1.b1', '24.bo1.a1', '24.br1.a1', '36.cu1.a1'], 'contains': ['144.f1.a1', '144.cd1.a1', '144.cd1.a2', '216.k1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [43, 936, 864, 1204], 'label': '1728.34767.72.bq1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.k1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.cu1.a1', 'old_label': '72.bq1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bq1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302383
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '72.br1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.w1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bs1.a1', '24.bs1.c1', '36.r1.a1'], 'contains': ['144.h1.a1', '144.h1.c1', '144.k1.a1', '216.l1.a1'], 'core': '288.b1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [1, 6, 576, 936], 'label': '1728.34767.72.br1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.l1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '72.br1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.br1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302384
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '72.br1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.w1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bs1.b1', '24.bs1.d1', '36.r1.a1'], 'contains': ['144.h1.a1', '144.h1.d1', '144.k1.b1', '216.l1.b1'], 'core': '288.b1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [865, 6, 576, 936], 'label': '1728.34767.72.br1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.l1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '72.br1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.br1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302385
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '72.br1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.w1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bs1.e1', '24.bs1.g1', '36.r1.a1'], 'contains': ['144.h1.b1', '144.h1.c1', '144.k1.b1', '216.l1.c1'], 'core': '288.b1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [1, 870, 576, 936], 'label': '1728.34767.72.br1.c1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.l1.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '72.br1.c1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.br1.c1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302386
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '72.br1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.w1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bs1.f1', '24.bs1.h1', '36.r1.a1'], 'contains': ['144.h1.b1', '144.h1.d1', '144.k1.a1', '216.l1.d1'], 'core': '288.b1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [865, 870, 576, 936], 'label': '1728.34767.72.br1.d1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.l1.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '72.br1.d1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.br1.d1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302387
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '72.bs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.m1.a1', '24.bs1.a1', '36.x1.a1'], 'contains': ['144.c1.c1', '144.g1.a1', '144.j1.c1', '216.l1.a1'], 'core': '144.c1.c1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [1, 6, 936, 4], 'label': '1728.34767.72.bs1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.m1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '72.bs1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bs1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302388
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '72.bs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.m1.b1', '24.bs1.b1', '36.x1.a1'], 'contains': ['144.c1.d1', '144.g1.a1', '144.j1.d1', '216.l1.b1'], 'core': '144.c1.d1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [865, 6, 936, 4], 'label': '1728.34767.72.bs1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.m1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '72.bs1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bs1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302389
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '6.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.d1.b1', '3.b1.a1'], 'contains': ['12.e1.b1', '12.z1.b1', '12.ba1.b1', '12.cf1.b1', '12.ch1.b1', '12.cj1.a1', '12.cm1.a1', '18.d1.b1', '18.p1.b1'], 'core': '12.e1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [1, 4, 864, 438, 48, 468, 72], 'label': '1728.34767.6.n1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '6.n1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.n1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302390
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '72.bs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.m1.a1', '24.bs1.c1', '36.x1.b1'], 'contains': ['144.c1.a1', '144.g1.c1', '144.j1.a1', '216.l1.a1'], 'core': '144.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [1, 6, 936, 48], 'label': '1728.34767.72.bs1.c1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.m1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.b1', 'old_label': '72.bs1.c1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bs1.c1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302391
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '72.bs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.m1.b1', '24.bs1.d1', '36.x1.b1'], 'contains': ['144.c1.a1', '144.g1.d1', '144.j1.b1', '216.l1.b1'], 'core': '144.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [865, 6, 936, 48], 'label': '1728.34767.72.bs1.d1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.m1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.b1', 'old_label': '72.bs1.d1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bs1.d1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302392
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '72.bs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.m1.c1', '24.bs1.e1', '36.x1.a1'], 'contains': ['144.c1.c1', '144.g1.b1', '144.j1.d1', '216.l1.c1'], 'core': '144.c1.c1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [1, 870, 936, 4], 'label': '1728.34767.72.bs1.e1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.m1.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '72.bs1.e1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bs1.e1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302393
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '72.bs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.m1.d1', '24.bs1.f1', '36.x1.a1'], 'contains': ['144.c1.d1', '144.g1.b1', '144.j1.c1', '216.l1.d1'], 'core': '144.c1.d1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [865, 870, 936, 4], 'label': '1728.34767.72.bs1.f1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.m1.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '72.bs1.f1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bs1.f1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302394
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '72.bs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.m1.c1', '24.bs1.g1', '36.x1.b1'], 'contains': ['144.c1.b1', '144.g1.c1', '144.j1.b1', '216.l1.c1'], 'core': '144.c1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [1, 870, 936, 48], 'label': '1728.34767.72.bs1.g1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.m1.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.b1', 'old_label': '72.bs1.g1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bs1.g1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302395
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '72.bs1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.m1.d1', '24.bs1.h1', '36.x1.b1'], 'contains': ['144.c1.b1', '144.g1.d1', '144.j1.a1', '216.l1.d1'], 'core': '144.c1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [865, 870, 936, 48], 'label': '1728.34767.72.bs1.h1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.m1.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.b1', 'old_label': '72.bs1.h1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bs1.h1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302396
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '72.bt1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '36.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bt1.a1', '24.bx1.a1', '36.d1.a1'], 'contains': ['144.m1.a1', '144.q1.b1', '144.v1.b1', '216.m1.a1'], 'core': '288.c1.b1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [6, 36, 4, 72], 'label': '1728.34767.72.bt1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.d1.a1', 'old_label': '72.bt1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bt1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302397
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '72.bt1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '36.d1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bt1.b1', '24.bx1.b1', '36.d1.b1'], 'contains': ['144.m1.b1', '144.q1.a1', '144.v1.a1', '216.m1.b1'], 'core': '288.c1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [1, 36, 48, 72], 'label': '1728.34767.72.bt1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.d1.b1', 'old_label': '72.bt1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bt1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302398
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '72.bu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bu1.a1', '24.by1.a1', '36.e1.a1'], 'contains': ['144.m1.a1', '144.s1.b1', '144.u1.b1', '216.n1.a1'], 'core': '288.c1.b1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [433, 6, 72, 4], 'label': '1728.34767.72.bu1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.o1.a1', 'old_label': '72.bu1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bu1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302399
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '72.bu1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.h1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bu1.b1', '24.by1.b1', '36.e1.b1'], 'contains': ['144.m1.b1', '144.s1.a1', '144.u1.a1', '216.n1.b1'], 'core': '288.c1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [1, 438, 72, 48], 'label': '1728.34767.72.bu1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.e1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.o1.b1', 'old_label': '72.bu1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bu1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302400
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '6.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.e1.a1', '3.a1.a1'], 'contains': ['12.a1.b1', '12.m1.a1', '12.o1.a1', '12.s1.b1', '12.bc1.a1', '12.bd1.b1', '12.bo1.b1', '18.j1.a1', '18.q1.a1'], 'core': '12.a1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [1, 864, 936, 6, 4, 432, 576], 'label': '1728.34767.6.o1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '6.o1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.o1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302401
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '72.bv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bt1.a1', '24.bv1.a1', '36.j1.a1'], 'contains': ['144.n1.a1', '144.x1.a1', '144.bb1.a1', '216.m1.a1'], 'core': '288.d1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [6, 36, 72, 576], 'label': '1728.34767.72.bv1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.n1.a1', 'old_label': '72.bv1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bv1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302402
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '72.bv1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.g1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bt1.b1', '24.bv1.b1', '36.j1.b1'], 'contains': ['144.n1.b1', '144.x1.a1', '144.bb1.b1', '216.m1.b1'], 'core': '288.d1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [1, 36, 72, 576], 'label': '1728.34767.72.bv1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.n1.b1', 'old_label': '72.bv1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bv1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302403
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '72.bw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '36.k1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bu1.a1', '24.bw1.a1', '36.k1.a1'], 'contains': ['144.n1.a1', '144.y1.a1', '144.ba1.a1', '216.n1.a1'], 'core': '288.d1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [433, 6, 576, 72], 'label': '1728.34767.72.bw1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.k1.a1', 'old_label': '72.bw1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bw1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302404
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '72.bw1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '36.k1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bu1.b1', '24.bw1.b1', '36.k1.b1'], 'contains': ['144.n1.b1', '144.y1.b1', '144.ba1.a1', '216.n1.b1'], 'core': '288.d1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [1, 438, 576, 72], 'label': '1728.34767.72.bw1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.c1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.k1.b1', 'old_label': '72.bw1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bw1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302405
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '72.bx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.j1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bv1.a1', '24.bx1.a1', '36.s1.a1'], 'contains': ['144.p1.a1', '144.q1.a1', '144.w1.a1', '216.m1.a1'], 'core': '288.c1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [6, 36, 72, 48], 'label': '1728.34767.72.bx1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.y1.a1', 'old_label': '72.bx1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bx1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302406
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '72.bx1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bv1.b1', '24.bx1.b1', '36.s1.b1'], 'contains': ['144.p1.b1', '144.q1.b1', '144.w1.b1', '216.m1.b1'], 'core': '288.c1.b1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [1, 36, 72, 4], 'label': '1728.34767.72.bx1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.y1.b1', 'old_label': '72.bx1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bx1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302407
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '72.by1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.u1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bw1.a1', '24.by1.a1', '36.t1.a1'], 'contains': ['144.p1.a1', '144.r1.a1', '144.u1.a1', '216.n1.a1'], 'core': '288.c1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [433, 6, 72, 48], 'label': '1728.34767.72.by1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.s1.a1', 'old_label': '72.by1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.by1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302408
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '72.by1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.u1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bw1.b1', '24.by1.b1', '36.t1.b1'], 'contains': ['144.p1.b1', '144.r1.b1', '144.u1.b1', '216.n1.b1'], 'core': '288.c1.b1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [1, 438, 72, 4], 'label': '1728.34767.72.by1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.e1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.s1.b1', 'old_label': '72.by1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.by1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302409
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '72.bz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bz1.a1', '24.cb1.a1', '36.bh1.a1'], 'contains': ['144.r1.a1', '144.t1.a1', '144.v1.a1', '216.o1.a1'], 'core': '288.c1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [433, 468, 48, 72], 'label': '1728.34767.72.bz1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.o1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.bh1.a1', 'old_label': '72.bz1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bz1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302410
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '72.bz1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bz1.b1', '24.cb1.b1', '36.bh1.b1'], 'contains': ['144.r1.b1', '144.t1.b1', '144.v1.b1', '216.o1.b1'], 'core': '288.c1.b1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [438, 468, 4, 72], 'label': '1728.34767.72.bz1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.o1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.bh1.b1', 'old_label': '72.bz1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.bz1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302411
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '6.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.e1.a1', '3.a1.b1'], 'contains': ['12.a1.a1', '12.m1.b1', '12.o1.b1', '12.s1.a1', '12.bc1.b1', '12.bd1.a1', '12.bo1.a1', '18.j1.a1', '18.q1.b1'], 'core': '12.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [1, 864, 936, 6, 48, 432, 576], 'label': '1728.34767.6.o1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.b1', 'old_label': '6.o1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.o1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302412
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '72.ca1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.ca1.a1', '24.cb1.b1', '36.bk1.a1'], 'contains': ['144.s1.a1', '144.t1.a1', '144.w1.a1', '216.o1.b1'], 'core': '288.c1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [438, 468, 72, 48], 'label': '1728.34767.72.ca1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.j1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.cf1.b1', 'old_label': '72.ca1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ca1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302413
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '72.ca1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.ca1.b1', '24.cb1.a1', '36.bk1.b1'], 'contains': ['144.s1.b1', '144.t1.b1', '144.w1.b1', '216.o1.a1'], 'core': '288.c1.b1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [433, 468, 72, 4], 'label': '1728.34767.72.ca1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.j1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.cf1.a1', 'old_label': '72.ca1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ca1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302414
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '72.cb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bz1.a1', '24.ca1.b1', '36.ca1.a1'], 'contains': ['144.y1.a1', '144.z1.a1', '144.bb1.b1', '216.o1.a1'], 'core': '288.d1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [433, 468, 72, 576], 'label': '1728.34767.72.cb1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.j1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bj1.a1', 'old_label': '72.cb1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.cb1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302415
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '72.cb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.bz1.b1', '24.ca1.a1', '36.ca1.b1'], 'contains': ['144.y1.b1', '144.z1.a1', '144.bb1.a1', '216.o1.b1'], 'core': '288.d1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [438, 468, 72, 576], 'label': '1728.34767.72.cb1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.j1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.bj1.b1', 'old_label': '72.cb1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.cb1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302416
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '72.cc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cc1.a1', '24.cf1.a1', '36.h1.a1'], 'contains': ['144.bh1.a1', '144.bn1.b1', '144.bo1.c1', '216.p1.a1'], 'core': '288.e1.b1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [469, 6, 864, 4], 'label': '1728.34767.72.cc1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.c1.a1', 'old_label': '72.cc1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.cc1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302417
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '72.cc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cc1.b1', '24.cf1.b1', '36.h1.a1'], 'contains': ['144.bh1.a1', '144.bn1.b1', '144.bo1.d1', '216.p1.b1'], 'core': '288.e1.b1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [1405, 6, 864, 4], 'label': '1728.34767.72.cc1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.c1.a1', 'old_label': '72.cc1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.cc1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302418
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '72.cc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cc1.c1', '24.cf1.c1', '36.h1.b1'], 'contains': ['144.bh1.b1', '144.bn1.a1', '144.bo1.a1', '216.p1.c1'], 'core': '288.e1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [937, 474, 864, 48], 'label': '1728.34767.72.cc1.c1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.f1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.c1.b1', 'old_label': '72.cc1.c1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.cc1.c1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302419
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '72.cc1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cc1.d1', '24.cf1.d1', '36.h1.b1'], 'contains': ['144.bh1.b1', '144.bn1.a1', '144.bo1.b1', '216.p1.d1'], 'core': '288.e1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [1, 474, 864, 48], 'label': '1728.34767.72.cc1.d1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.f1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.c1.b1', 'old_label': '72.cc1.d1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.cc1.d1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302420
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '72.cd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cc1.a1', '24.cd1.a1', '36.n1.a1'], 'contains': ['144.bi1.a1', '144.br1.a1', '144.bs1.a1', '216.p1.a1'], 'core': '288.f1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [469, 6, 864, 576], 'label': '1728.34767.72.cd1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.g1.a1', 'old_label': '72.cd1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.cd1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302421
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '72.cd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cc1.b1', '24.cd1.b1', '36.n1.a1'], 'contains': ['144.bi1.a1', '144.br1.a1', '144.bs1.b1', '216.p1.b1'], 'core': '288.f1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [1405, 6, 864, 576], 'label': '1728.34767.72.cd1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.g1.a1', 'old_label': '72.cd1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.cd1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302422
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '6.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.f1.a1', '3.a1.a1'], 'contains': ['12.b1.b1', '12.n1.a1', '12.q1.a1', '12.t1.b1', '12.bc1.a1', '12.bh1.b1', '12.br1.b1', '18.k1.a1', '18.r1.a1'], 'core': '12.b1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [1, 4, 864, 6, 576, 36, 936], 'label': '1728.34767.6.p1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '6.p1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.p1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302423
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '72.cd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cc1.c1', '24.cd1.c1', '36.n1.b1'], 'contains': ['144.bi1.b1', '144.br1.b1', '144.bs1.a1', '216.p1.c1'], 'core': '288.f1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [937, 474, 864, 576], 'label': '1728.34767.72.cd1.c1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.f1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.g1.b1', 'old_label': '72.cd1.c1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.cd1.c1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302424
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '72.cd1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cc1.d1', '24.cd1.d1', '36.n1.b1'], 'contains': ['144.bi1.b1', '144.br1.b1', '144.bs1.b1', '216.p1.d1'], 'core': '288.f1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [1, 474, 864, 576], 'label': '1728.34767.72.cd1.d1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.f1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.g1.b1', 'old_label': '72.cd1.d1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.cd1.d1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302425
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '72.ce1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cc1.a1', '24.ce1.a1', '36.q1.a1'], 'contains': ['144.bj1.a1', '144.bv1.b1', '144.bw1.c1', '216.p1.a1'], 'core': '864.c1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [469, 6, 864, 1156], 'label': '1728.34767.72.ce1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.q1.a1', 'old_label': '72.ce1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ce1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302426
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '72.ce1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cc1.b1', '24.ce1.b1', '36.q1.a1'], 'contains': ['144.bj1.a1', '144.bv1.b1', '144.bw1.d1', '216.p1.b1'], 'core': '864.c1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [1405, 6, 864, 1156], 'label': '1728.34767.72.ce1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.q1.a1', 'old_label': '72.ce1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ce1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302427
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '72.ce1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cc1.c1', '24.ce1.c1', '36.q1.b1'], 'contains': ['144.bj1.b1', '144.bv1.a1', '144.bw1.a1', '216.p1.c1'], 'core': '864.c1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [937, 474, 864, 1200], 'label': '1728.34767.72.ce1.c1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.f1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.q1.b1', 'old_label': '72.ce1.c1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ce1.c1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302428
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '72.ce1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cc1.d1', '24.ce1.d1', '36.q1.b1'], 'contains': ['144.bj1.b1', '144.bv1.a1', '144.bw1.b1', '216.p1.d1'], 'core': '864.c1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [1, 474, 864, 1200], 'label': '1728.34767.72.ce1.d1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.f1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.q1.b1', 'old_label': '72.ce1.d1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ce1.d1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302429
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '72.cf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cd1.a1', '24.ce1.a1', '24.cf1.a1', '36.w1.a1'], 'contains': ['144.bk1.a1', '144.bm1.a1', '144.bo1.a1', '216.p1.a1'], 'core': '288.e1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [469, 6, 864, 48], 'label': '1728.34767.72.cf1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.o1.a1', 'old_label': '72.cf1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.cf1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302430
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '72.cf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cd1.b1', '24.ce1.b1', '24.cf1.b1', '36.w1.a1'], 'contains': ['144.bk1.a1', '144.bm1.a1', '144.bo1.b1', '216.p1.b1'], 'core': '288.e1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [1405, 6, 864, 48], 'label': '1728.34767.72.cf1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.o1.a1', 'old_label': '72.cf1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.cf1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302431
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '72.cf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.i1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cd1.c1', '24.ce1.c1', '24.cf1.c1', '36.w1.b1'], 'contains': ['144.bk1.b1', '144.bm1.b1', '144.bo1.c1', '216.p1.c1'], 'core': '288.e1.b1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [937, 474, 864, 4], 'label': '1728.34767.72.cf1.c1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.f1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.o1.b1', 'old_label': '72.cf1.c1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.cf1.c1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302432
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '72.cf1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.i1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cd1.d1', '24.ce1.d1', '24.cf1.d1', '36.w1.b1'], 'contains': ['144.bk1.b1', '144.bm1.b1', '144.bo1.d1', '216.p1.d1'], 'core': '288.e1.b1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [1, 474, 864, 4], 'label': '1728.34767.72.cf1.d1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.f1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.o1.b1', 'old_label': '72.cf1.d1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.cf1.d1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302433
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '6.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.f1.a1', '3.a1.b1'], 'contains': ['12.b1.a1', '12.n1.b1', '12.q1.b1', '12.t1.a1', '12.bc1.b1', '12.bh1.a1', '12.br1.a1', '18.k1.a1', '18.r1.b1'], 'core': '12.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [1, 48, 864, 6, 576, 36, 936], 'label': '1728.34767.6.p1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.b1', 'old_label': '6.p1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.p1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302434
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '72.cg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cg1.a1', '24.ch1.a1', '24.ci1.a1', '36.bc1.a1'], 'contains': ['144.bl1.a1', '144.bo1.a1', '144.bp1.a1', '216.q1.a1'], 'core': '288.e1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [979, 432, 864, 48], 'label': '1728.34767.72.cg1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.k1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.t1.a1', 'old_label': '72.cg1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.cg1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302435
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '72.cg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cg1.b1', '24.ch1.b1', '24.ci1.b1', '36.bc1.a1'], 'contains': ['144.bl1.a1', '144.bo1.b1', '144.bp1.a1', '216.q1.b1'], 'core': '288.e1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [43, 432, 864, 48], 'label': '1728.34767.72.cg1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.k1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.t1.a1', 'old_label': '72.cg1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.cg1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302436
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '72.cg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cg1.c1', '24.ch1.c1', '24.ci1.a1', '36.bc1.b1'], 'contains': ['144.bl1.b1', '144.bo1.c1', '144.bp1.b1', '216.q1.a1'], 'core': '288.e1.b1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [979, 432, 864, 4], 'label': '1728.34767.72.cg1.c1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.k1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.t1.b1', 'old_label': '72.cg1.c1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.cg1.c1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302437
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '72.cg1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cg1.d1', '24.ch1.d1', '24.ci1.b1', '36.bc1.b1'], 'contains': ['144.bl1.b1', '144.bo1.d1', '144.bp1.b1', '216.q1.b1'], 'core': '288.e1.b1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [43, 432, 864, 4], 'label': '1728.34767.72.cg1.d1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.k1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.t1.b1', 'old_label': '72.cg1.d1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.cg1.d1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302438
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '72.ch1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cg1.a1', '24.cg1.c1', '24.cj1.a1', '24.cj1.b1', '36.bw1.a1'], 'contains': ['144.bq1.a1', '144.bs1.a1', '144.bt1.a1', '216.q1.a1'], 'core': '288.f1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [979, 432, 864, 576], 'label': '1728.34767.72.ch1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.k1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.x1.a1', 'old_label': '72.ch1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ch1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302439
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '72.ch1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cg1.b1', '24.cg1.d1', '24.cj1.c1', '24.cj1.d1', '36.bw1.a1'], 'contains': ['144.bq1.a1', '144.bs1.b1', '144.bt1.a1', '216.q1.b1'], 'core': '288.f1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [43, 432, 864, 576], 'label': '1728.34767.72.ch1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.k1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.x1.a1', 'old_label': '72.ch1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ch1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302440
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '72.ci1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cg1.a1', '24.ch1.c1', '24.ck1.a1', '24.ck1.b1', '36.ck1.a1'], 'contains': ['144.bu1.a1', '144.bw1.a1', '144.bx1.a1', '216.q1.a1'], 'core': '864.c1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [979, 432, 864, 1200], 'label': '1728.34767.72.ci1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.k1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.ck1.a1', 'old_label': '72.ci1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ci1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302441
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '72.ci1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cg1.b1', '24.ch1.d1', '24.ck1.c1', '24.ck1.d1', '36.ck1.a1'], 'contains': ['144.bu1.a1', '144.bw1.b1', '144.bx1.a1', '216.q1.b1'], 'core': '864.c1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [43, 432, 864, 1200], 'label': '1728.34767.72.ci1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.k1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.ck1.a1', 'old_label': '72.ci1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ci1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302442
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '72.ci1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cg1.c1', '24.ch1.a1', '24.ck1.a1', '24.ck1.b1', '36.ck1.b1'], 'contains': ['144.bu1.b1', '144.bw1.c1', '144.bx1.b1', '216.q1.a1'], 'core': '864.c1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [979, 432, 864, 1156], 'label': '1728.34767.72.ci1.c1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.k1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.ck1.b1', 'old_label': '72.ci1.c1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ci1.c1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302443
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '72.ci1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.cg1.d1', '24.ch1.b1', '24.ck1.c1', '24.ck1.d1', '36.ck1.b1'], 'contains': ['144.bu1.b1', '144.bw1.d1', '144.bx1.b1', '216.q1.b1'], 'core': '864.c1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [43, 432, 864, 1156], 'label': '1728.34767.72.ci1.d1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.k1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.ck1.b1', 'old_label': '72.ci1.d1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ci1.d1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302444
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '6.q1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.g1.a1', '3.a1.a1'], 'contains': ['12.c1.b1', '12.p1.a1', '12.r1.a1', '12.u1.b1', '12.bc1.a1', '12.bp1.b1', '12.bs1.b1', '18.l1.a1', '18.s1.a1'], 'core': '12.c1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [1, 4, 864, 6, 576, 468, 936], 'label': '1728.34767.6.q1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '6.q1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.q1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302445
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '72.cj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.ci1.a1', '24.cj1.a1', '24.ck1.a1', '36.cp1.a1'], 'contains': ['144.by1.a1', '144.bz1.a1', '144.ca1.a1', '216.q1.a1'], 'core': '864.c1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [979, 432, 864, 52], 'label': '1728.34767.72.cj1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.k1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bb1.a1', 'old_label': '72.cj1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.cj1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302446
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '72.cj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.ci1.a1', '24.cj1.b1', '24.ck1.b1', '36.cp1.a1'], 'contains': ['144.by1.b1', '144.bz1.a1', '144.ca1.a2', '216.q1.a1'], 'core': '864.c1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [979, 432, 864, 100], 'label': '1728.34767.72.cj1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.k1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bb1.a1', 'old_label': '72.cj1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.cj1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302447
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '72.cj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.ci1.b1', '24.cj1.c1', '24.ck1.c1', '36.cp1.a1'], 'contains': ['144.by1.a1', '144.bz1.b1', '144.ca1.a2', '216.q1.b1'], 'core': '864.c1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [43, 432, 864, 52], 'label': '1728.34767.72.cj1.c1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.k1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bb1.a1', 'old_label': '72.cj1.c1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.cj1.c1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302448
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '72.cj1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.ci1.b1', '24.cj1.d1', '24.ck1.d1', '36.cp1.a1'], 'contains': ['144.by1.b1', '144.bz1.b1', '144.ca1.a1', '216.q1.b1'], 'core': '864.c1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [43, 432, 864, 100], 'label': '1728.34767.72.cj1.d1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.k1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.bb1.a1', 'old_label': '72.cj1.d1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.cj1.d1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302449
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '72.ck1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.ch1.a1', '24.ch1.c1', '24.cj1.a1', '24.ck1.b1', '36.cu1.a1'], 'contains': ['144.cb1.a1', '144.cc1.a1', '144.cd1.a1', '216.q1.a1'], 'core': '864.c1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [979, 432, 864, 1204], 'label': '1728.34767.72.ck1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.k1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.cu1.a1', 'old_label': '72.ck1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ck1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302450
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '72.ck1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.ch1.a1', '24.ch1.c1', '24.cj1.b1', '24.ck1.a1', '36.cu1.a1'], 'contains': ['144.cb1.b1', '144.cc1.a1', '144.cd1.a2', '216.q1.a1'], 'core': '864.c1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [979, 432, 864, 676], 'label': '1728.34767.72.ck1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.k1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.cu1.a1', 'old_label': '72.ck1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ck1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302451
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '72.ck1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.ch1.b1', '24.ch1.d1', '24.cj1.c1', '24.ck1.d1', '36.cu1.a1'], 'contains': ['144.cb1.a1', '144.cc1.b1', '144.cd1.a2', '216.q1.b1'], 'core': '864.c1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [43, 432, 864, 1204], 'label': '1728.34767.72.ck1.c1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.k1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.cu1.a1', 'old_label': '72.ck1.c1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ck1.c1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302452
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '72.ck1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.ch1.b1', '24.ch1.d1', '24.cj1.d1', '24.ck1.c1', '36.cu1.a1'], 'contains': ['144.cb1.b1', '144.cc1.b1', '144.cd1.a1', '216.q1.b1'], 'core': '864.c1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': None, 'generators': [43, 432, 864, 676], 'label': '1728.34767.72.ck1.d1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.k1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.cu1.a1', 'old_label': '72.ck1.d1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.ck1.d1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302453
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '96.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.a1.b1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['32.a1.a1', '48.a1.a1', '48.c1.a1', '48.c1.b1', '48.i1.c1', '48.i1.d1', '48.k1.a1', '48.k1.b1'], 'contains': ['192.a1.a1', '288.a1.a1', '288.b1.a1', '288.g1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [936, 48, 576], 'label': '1728.34767.96.a1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '96.a1.a1', 'normal_contained_in': ['32.a1.a1', '48.a1.a1', '48.c1.a1', '48.c1.b1'], 'normal_contains': ['192.a1.a1', '288.a1.a1', '288.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '96.a1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.a1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302454
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '96.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['32.a1.a1', '48.a1.b1', '48.c1.c1', '48.c1.d1', '48.i1.a1', '48.i1.b1', '48.k1.c1', '48.k1.d1'], 'contains': ['192.a1.b1', '288.a1.b1', '288.b1.a1', '288.g1.b1'], 'core': '96.a1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [936, 4, 576], 'label': '1728.34767.96.a1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '96.a1.b1', 'normal_contained_in': ['32.a1.a1', '48.a1.b1', '48.c1.c1', '48.c1.d1'], 'normal_contains': ['192.a1.b1', '288.a1.b1', '288.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '96.a1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.a1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302455
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '6.q1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.g1.a1', '3.a1.b1'], 'contains': ['12.c1.a1', '12.p1.b1', '12.r1.b1', '12.u1.a1', '12.bc1.b1', '12.bp1.a1', '12.bs1.a1', '18.l1.a1', '18.s1.b1'], 'core': '12.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [1, 48, 864, 6, 576, 468, 936], 'label': '1728.34767.6.q1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.b1', 'old_label': '6.q1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.q1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302456
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '96.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.h1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['32.a1.a1', '48.b1.a1', '48.d1.a1', '48.d1.b1', '48.d1.c1', '48.d1.d1', '48.e1.a1', '48.e1.b1'], 'contains': ['192.b1.a1', '288.a1.a1', '288.a1.b1', '288.h1.a1'], 'core': '96.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [936, 4, 48], 'label': '1728.34767.96.b1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '96.b1.a1', 'normal_contained_in': ['32.a1.a1', '48.b1.a1', '48.d1.c1', '48.d1.a1', '48.d1.d1', '48.d1.b1', '48.e1.b1', '48.e1.a1'], 'normal_contains': ['192.b1.a1', '288.a1.b1', '288.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '96.b1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.b1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302457
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '96.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.a1.b1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['32.b1.a1', '48.a1.a1', '48.m1.b1', '48.n1.a1', '48.q1.a1', '48.r1.a1', '48.s1.a1', '48.t1.a1', '48.u1.a1', '48.v1.a1', '48.w1.a1'], 'contains': ['192.a1.a1', '288.c1.a1', '288.d1.a1', '288.j1.a1'], 'core': '96.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [72, 48, 576], 'label': '1728.34767.96.c1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '96.c1.a1', 'normal_contained_in': ['32.b1.a1', '48.a1.a1'], 'normal_contains': ['192.a1.a1', '288.c1.a1', '288.d1.a1'], 'normalizer': '1.a1.a1', 'old_label': '96.c1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.c1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302458
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '96.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['32.b1.a1', '48.a1.b1', '48.m1.a1', '48.n1.b1', '48.q1.b1', '48.r1.b1', '48.s1.b1', '48.t1.b1', '48.u1.b1', '48.v1.b1', '48.w1.b1'], 'contains': ['192.a1.b1', '288.c1.b1', '288.d1.a1', '288.j1.b1'], 'core': '96.c1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [72, 4, 576], 'label': '1728.34767.96.c1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '96.c1.b1', 'normal_contained_in': ['32.b1.a1', '48.a1.b1'], 'normal_contains': ['192.a1.b1', '288.c1.b1', '288.d1.a1'], 'normalizer': '1.a1.a1', 'old_label': '96.c1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.c1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302459
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '96.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.h1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['32.b1.a1', '48.b1.a1', '48.p1.a1', '48.p1.b1', '48.z1.a1', '48.ba1.a1', '48.ba1.b1', '48.bb1.a1', '48.bc1.a1', '48.bd1.a1', '48.bd1.b1'], 'contains': ['192.b1.a1', '288.c1.a1', '288.c1.b1', '288.k1.a1'], 'core': '96.d1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [72, 4, 48], 'label': '1728.34767.96.d1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '96.d1.a1', 'normal_contained_in': ['32.b1.a1', '48.b1.a1'], 'normal_contains': ['192.b1.a1', '288.c1.b1', '288.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '96.d1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.d1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302460
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '96.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.a1.b1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['32.c1.a1', '48.a1.a1', '48.bh1.b1', '48.bi1.a1', '48.bl1.a1', '48.bm1.a1', '48.bn1.a1', '48.bo1.a1', '48.bo1.b1', '48.bp1.a1'], 'contains': ['192.a1.a1', '288.e1.a1', '288.f1.a1', '288.m1.a1'], 'core': '96.e1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [864, 48, 576], 'label': '1728.34767.96.e1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '96.e1.a1', 'normal_contained_in': ['32.c1.a1', '48.a1.a1'], 'normal_contains': ['192.a1.a1', '288.e1.a1', '288.f1.a1'], 'normalizer': '1.a1.a1', 'old_label': '96.e1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.e1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302461
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '96.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['32.c1.a1', '48.a1.b1', '48.bh1.a1', '48.bi1.b1', '48.bl1.b1', '48.bm1.b1', '48.bn1.b1', '48.bo1.c1', '48.bo1.d1', '48.bp1.b1'], 'contains': ['192.a1.b1', '288.e1.b1', '288.f1.a1', '288.m1.b1'], 'core': '96.e1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [864, 4, 576], 'label': '1728.34767.96.e1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '96.e1.b1', 'normal_contained_in': ['32.c1.a1', '48.a1.b1'], 'normal_contains': ['192.a1.b1', '288.e1.b1', '288.f1.a1'], 'normalizer': '1.a1.a1', 'old_label': '96.e1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.e1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302462
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '96.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.h1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['32.c1.a1', '48.b1.a1', '48.bk1.a1', '48.bk1.b1', '48.bu1.a1', '48.bv1.a1', '48.bv1.b1', '48.bw1.a1', '48.bw1.b1', '48.bx1.a1'], 'contains': ['192.b1.a1', '288.e1.a1', '288.e1.b1', '288.n1.a1'], 'core': '96.f1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [864, 4, 48], 'label': '1728.34767.96.f1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '96.f1.a1', 'normal_contained_in': ['32.c1.a1', '48.b1.a1'], 'normal_contains': ['192.b1.a1', '288.e1.b1', '288.e1.a1'], 'normalizer': '1.a1.a1', 'old_label': '96.f1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.f1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302463
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '96.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.a1.a1', '48.f1.a1', '48.j1.a1', '48.j1.b1'], 'contains': ['192.c1.a1', '288.a1.a1', '288.g1.b1', '288.i1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [936, 1156, 48], 'label': '1728.34767.96.g1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '32.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '96.g1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.g1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302464
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '96.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.a1.a1', '48.f1.b1', '48.j1.c1', '48.j1.d1'], 'contains': ['192.c1.b1', '288.a1.b1', '288.g1.a1', '288.i1.a1'], 'core': '288.a1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [936, 4, 1200], 'label': '1728.34767.96.g1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '32.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.b1', 'old_label': '96.g1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.g1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302465
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '96.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.a1.a1', '48.g1.a1', '48.l1.a1', '48.l1.b1'], 'contains': ['192.d1.a1', '288.b1.a1', '288.h1.a1', '288.i1.a1'], 'core': '288.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [936, 100, 576], 'label': '1728.34767.96.h1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '32.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.h1.a1', 'old_label': '96.h1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.h1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302466
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '6.r1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.f1.a1', '3.b1.a1'], 'contains': ['12.f1.a1', '12.y1.a1', '12.y1.b1', '12.ba1.a1', '12.ba1.b1', '12.cd1.a1', '12.ck1.a1', '18.r1.a1', '18.r1.b1'], 'core': '12.f1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [1, 4, 864, 6, 48, 36, 936], 'label': '1728.34767.6.r1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '6.r1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.r1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302467
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '96.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.a1.a1', '48.h1.a1'], 'contains': ['192.e1.a1', '288.g1.a1', '288.g1.b1', '288.h1.a1', '288.i1.a1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [936, 1156, 1200], 'label': '1728.34767.96.i1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '32.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.k1.a1', 'old_label': '96.i1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.i1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302468
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '96.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.b1.a1', '48.f1.a1', '48.o1.a1', '48.x1.a1', '48.y1.a1'], 'contains': ['192.c1.a1', '288.c1.a1', '288.j1.b1', '288.l1.a1'], 'core': '288.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [72, 1156, 48], 'label': '1728.34767.96.j1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '32.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '96.j1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.j1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302469
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '96.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.b1.a1', '48.f1.b1', '48.o1.b1', '48.x1.b1', '48.y1.b1'], 'contains': ['192.c1.b1', '288.c1.b1', '288.j1.a1', '288.l1.a1'], 'core': '288.c1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [72, 4, 1200], 'label': '1728.34767.96.j1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '32.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.b1', 'old_label': '96.j1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.j1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302470
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '96.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.b1.a1', '48.g1.a1', '48.be1.a1', '48.bf1.a1', '48.bg1.a1'], 'contains': ['192.d1.a1', '288.d1.a1', '288.k1.a1', '288.l1.a1'], 'core': '288.d1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [72, 100, 576], 'label': '1728.34767.96.k1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '32.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.h1.a1', 'old_label': '96.k1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.k1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302471
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '96.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.b1.a1', '48.h1.a1'], 'contains': ['192.e1.a1', '288.j1.a1', '288.j1.b1', '288.k1.a1', '288.l1.a1'], 'core': '864.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [72, 1156, 1200], 'label': '1728.34767.96.l1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '32.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.k1.a1', 'old_label': '96.l1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.l1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302472
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '96.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.c1.a1', '48.f1.a1', '48.bj1.a1', '48.bq1.a1', '48.br1.a1', '48.bs1.a1', '48.bs1.b1', '48.bt1.a1'], 'contains': ['192.c1.a1', '288.e1.a1', '288.m1.b1', '288.o1.a1'], 'core': '288.e1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [864, 1156, 48], 'label': '1728.34767.96.m1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '32.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '96.m1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.m1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302473
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '96.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.c1.a1', '48.f1.b1', '48.bj1.b1', '48.bq1.b1', '48.br1.b1', '48.bs1.c1', '48.bs1.d1', '48.bt1.b1'], 'contains': ['192.c1.b1', '288.e1.b1', '288.m1.a1', '288.o1.a1'], 'core': '288.e1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [864, 4, 1200], 'label': '1728.34767.96.m1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '32.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.b1', 'old_label': '96.m1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.m1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302474
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '96.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.c1.a1', '48.g1.a1', '48.by1.a1', '48.by1.b1', '48.bz1.a1', '48.bz1.b1', '48.ca1.a1', '48.ca1.a2'], 'contains': ['192.d1.a1', '288.f1.a1', '288.n1.a1', '288.o1.a1'], 'core': '288.f1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [864, 100, 576], 'label': '1728.34767.96.n1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '32.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.h1.a1', 'old_label': '96.n1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.n1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302475
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '96.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.c1.a1', '48.h1.a1', '48.cb1.a1', '48.cb1.b1', '48.cc1.a1', '48.cc1.b1', '48.cd1.a1', '48.cd1.a2'], 'contains': ['192.e1.a1', '288.m1.a1', '288.m1.b1', '288.n1.a1', '288.o1.a1'], 'core': '864.c1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [864, 1156, 1200], 'label': '1728.34767.96.o1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '32.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.k1.a1', 'old_label': '96.o1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.o1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302476
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '96.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.n1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.d1.a1', '48.i1.a1', '48.m1.a1', '48.bh1.a1'], 'contains': ['192.a1.b1', '288.p1.a1', '288.q1.a1', '288.r1.a1'], 'core': '192.a1.b1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [6, 4, 576], 'label': '1728.34767.96.p1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '16.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.e1.a1', 'old_label': '96.p1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.p1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302477
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '6.s1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.g1.a1', '3.b1.a1'], 'contains': ['12.f1.a1', '12.z1.a1', '12.z1.b1', '12.bb1.a1', '12.bb1.b1', '12.ci1.a1', '12.cl1.a1', '18.s1.a1', '18.s1.b1'], 'core': '12.f1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [1, 4, 864, 6, 48, 468, 936], 'label': '1728.34767.6.s1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '6.s1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.s1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302478
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '96.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.n1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.d1.b1', '48.i1.b1', '48.m1.a1', '48.bh1.a1'], 'contains': ['192.a1.b1', '288.p1.b1', '288.q1.b1', '288.r1.b1'], 'core': '192.a1.b1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [870, 4, 576], 'label': '1728.34767.96.p1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '16.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.e1.a1', 'old_label': '96.p1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.p1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302479
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '96.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.n1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.d1.c1', '48.i1.c1', '48.m1.b1', '48.bh1.b1'], 'contains': ['192.a1.a1', '288.p1.c1', '288.q1.c1', '288.r1.c1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [1, 48, 576], 'label': '1728.34767.96.p1.c1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '16.b1.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.e1.b1', 'old_label': '96.p1.c1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.p1.c1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302480
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '96.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.n1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.d1.d1', '48.i1.d1', '48.m1.b1', '48.bh1.b1'], 'contains': ['192.a1.a1', '288.p1.d1', '288.q1.d1', '288.r1.d1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [865, 48, 576], 'label': '1728.34767.96.p1.d1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '16.b1.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.e1.b1', 'old_label': '96.p1.d1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.p1.d1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302481
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '96.q1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.e1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.d1.a1', '48.c1.a1', '48.n1.a1', '48.bi1.a1'], 'contains': ['192.a1.a1', '288.q1.a1', '288.s1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [6, 576, 48], 'label': '1728.34767.96.q1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '48.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '96.q1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.q1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302482
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '96.q1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.e1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.d1.b1', '48.c1.b1', '48.n1.a1', '48.bi1.a1'], 'contains': ['192.a1.a1', '288.q1.b1', '288.s1.b1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [870, 576, 48], 'label': '1728.34767.96.q1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '48.c1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '96.q1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.q1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302483
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '96.q1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.d1.c1', '48.c1.c1', '48.n1.b1', '48.bi1.b1'], 'contains': ['192.a1.b1', '288.q1.c1', '288.s1.c1'], 'core': '192.a1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [1, 576, 4], 'label': '1728.34767.96.q1.c1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '48.c1.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.b1', 'old_label': '96.q1.c1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.q1.c1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302484
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '96.q1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.d1.d1', '48.c1.d1', '48.n1.b1', '48.bi1.b1'], 'contains': ['192.a1.b1', '288.q1.d1', '288.s1.d1'], 'core': '192.a1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [865, 576, 4], 'label': '1728.34767.96.q1.d1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '48.c1.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.b1', 'old_label': '96.q1.d1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.q1.d1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302485
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '96.r1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.d1.a1', '48.j1.a1', '48.o1.a1', '48.bj1.a1'], 'contains': ['192.c1.a1', '288.r1.a1', '288.s1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [6, 1156, 48], 'label': '1728.34767.96.r1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '16.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.f1.a1', 'old_label': '96.r1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.r1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302486
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '96.r1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.d1.b1', '48.j1.b1', '48.o1.a1', '48.bj1.a1'], 'contains': ['192.c1.a1', '288.r1.b1', '288.s1.b1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [870, 1156, 48], 'label': '1728.34767.96.r1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '16.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.f1.a1', 'old_label': '96.r1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.r1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302487
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '96.r1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.d1.c1', '48.j1.c1', '48.o1.b1', '48.bj1.b1'], 'contains': ['192.c1.b1', '288.r1.c1', '288.s1.c1'], 'core': '576.a1.b1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [1, 1200, 4], 'label': '1728.34767.96.r1.c1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '16.b1.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.f1.b1', 'old_label': '96.r1.c1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.r1.c1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302488
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '2.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': ['864.d1.a1', '864.d1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.c1.b1', '4.d1.b1', '4.e1.b1', '4.o1.b1', '4.q1.b1', '4.t1.a1', '4.w1.a1', '6.f1.b1', '6.i1.b1', '6.n1.b1'], 'core': '2.d1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [1, 864, 4, 438, 72, 576, 48, 468], 'label': '1728.34767.2.d1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.d1.b1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.c1.b1', '4.d1.b1', '4.e1.b1', '4.o1.b1', '4.q1.b1', '4.t1.a1', '4.w1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.d1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2.d1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302489
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '6.t1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.h1.a1', '3.a1.b1'], 'contains': ['12.g1.a1', '12.bd1.a1', '12.bf1.a1', '12.bh1.a1', '12.bi1.a1', '12.bp1.a1', '12.bq1.a1', '18.t1.a1', '18.x1.a1'], 'core': '12.g1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [7, 48, 864, 36, 576, 432, 936], 'label': '1728.34767.6.t1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.h1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.b1', 'old_label': '6.t1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.t1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302490
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '96.r1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '48.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.d1.d1', '48.j1.d1', '48.o1.b1', '48.bj1.b1'], 'contains': ['192.c1.b1', '288.r1.d1', '288.s1.d1'], 'core': '576.a1.b1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [865, 1200, 4], 'label': '1728.34767.96.r1.d1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '16.b1.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.f1.b1', 'old_label': '96.r1.d1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.r1.d1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302491
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '96.s1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.d1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.d1.a1', '48.d1.a1', '48.p1.a1', '48.bk1.a1'], 'contains': ['192.b1.a1', '288.p1.a1', '288.s1.a1'], 'core': '192.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [6, 4, 48], 'label': '1728.34767.96.s1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '48.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '96.s1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.s1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302492
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '96.s1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.d1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.d1.b1', '48.d1.b1', '48.p1.a1', '48.bk1.a1'], 'contains': ['192.b1.a1', '288.p1.b1', '288.s1.b1'], 'core': '192.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [870, 4, 48], 'label': '1728.34767.96.s1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '48.d1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '96.s1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.s1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302493
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '96.s1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.d1.c1', '48.d1.c1', '48.p1.b1', '48.bk1.b1'], 'contains': ['192.b1.a1', '288.p1.c1', '288.s1.c1'], 'core': '192.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [1, 48, 4], 'label': '1728.34767.96.s1.c1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '48.d1.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.b1', 'old_label': '96.s1.c1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.s1.c1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302494
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '96.s1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.d1.d1', '48.d1.d1', '48.p1.b1', '48.bk1.b1'], 'contains': ['192.b1.a1', '288.p1.d1', '288.s1.d1'], 'core': '192.b1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [865, 48, 4], 'label': '1728.34767.96.s1.d1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '48.d1.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.b1', 'old_label': '96.s1.d1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.s1.d1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302495
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '108.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.r1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.a1.a1', '36.c1.a1', '36.i1.a1', '36.o1.a1', '54.a1.a1', '54.b1.a1', '54.e1.a1'], 'contains': ['216.a1.a1', '216.b1.a1', '216.d1.b1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [6, 432], 'label': '1728.34767.108.a1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '108.a1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.a1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302496
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '108.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.r1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.a1.b1', '36.c1.b1', '36.i1.b1', '36.o1.b1', '54.a1.b1', '54.b1.b1', '54.e1.a1'], 'contains': ['216.a1.a1', '216.b1.b1', '216.d1.a1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [1, 432], 'label': '1728.34767.108.a1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.b1', 'old_label': '108.a1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.a1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302497
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '108.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '36.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.d1.a1', '36.j1.a1', '36.s1.a1', '54.a1.a1', '54.c1.a1', '54.f1.a1'], 'contains': ['216.b1.a1', '216.c1.a1', '216.h1.a1', '216.m1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [6, 36, 864], 'label': '1728.34767.108.b1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1.a1', 'old_label': '108.b1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.b1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302498
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '108.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '36.d1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.d1.b1', '36.j1.b1', '36.s1.b1', '54.a1.b1', '54.c1.b1', '54.f1.a1'], 'contains': ['216.b1.b1', '216.c1.a1', '216.h1.b1', '216.m1.b1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [1, 36, 864], 'label': '1728.34767.108.b1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1.b1', 'old_label': '108.b1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.b1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302499
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '108.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '36.k1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.e1.a1', '36.k1.a1', '36.t1.a1', '54.c1.a1', '54.d1.a1', '54.e1.a1'], 'contains': ['216.b1.a1', '216.d1.a1', '216.g1.a1', '216.n1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [433, 6, 864], 'label': '1728.34767.108.c1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '108.c1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.c1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302500
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '6.t1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.h1.a1', '3.a1.a1'], 'contains': ['12.g1.b1', '12.bd1.b1', '12.bf1.b1', '12.bh1.b1', '12.bi1.b1', '12.bp1.b1', '12.bq1.b1', '18.t1.b1', '18.x1.a1'], 'core': '12.g1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [7, 4, 864, 36, 576, 432, 936], 'label': '1728.34767.6.t1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.h1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '6.t1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.t1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302501
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '108.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '36.k1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.e1.b1', '36.k1.b1', '36.t1.b1', '54.c1.b1', '54.d1.b1', '54.e1.a1'], 'contains': ['216.b1.b1', '216.d1.b1', '216.g1.a1', '216.n1.b1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [1, 438, 864], 'label': '1728.34767.108.c1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.e1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '108.c1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.c1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302502
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '108.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.s1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.f1.a1', '36.l1.a1', '36.u1.a1', '54.a1.a1', '54.d1.a1', '54.g1.a1'], 'contains': ['216.b1.a1', '216.e1.a1', '216.i1.b1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [6, 468], 'label': '1728.34767.108.d1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1.a1', 'old_label': '108.d1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.d1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302503
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '108.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.s1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.f1.b1', '36.l1.b1', '36.u1.b1', '54.a1.b1', '54.d1.b1', '54.g1.a1'], 'contains': ['216.b1.b1', '216.e1.a1', '216.i1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [1, 468], 'label': '1728.34767.108.d1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.c1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1.b1', 'old_label': '108.d1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.d1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302504
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '108.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.g1.a1', '36.m1.a1', '36.p1.a1', '36.v1.a1', '54.b1.a1', '54.d1.a1', '54.f1.a1'], 'contains': ['216.b1.a1', '216.h1.b1', '216.k1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [37, 6], 'label': '1728.34767.108.e1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1.a1', 'old_label': '108.e1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.e1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302505
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '108.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.g1.b1', '36.m1.b1', '36.p1.b1', '36.v1.b1', '54.b1.b1', '54.d1.b1', '54.f1.a1'], 'contains': ['216.b1.b1', '216.h1.a1', '216.k1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [1, 42], 'label': '1728.34767.108.e1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.e1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1.a1', 'old_label': '108.e1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.e1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302506
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '108.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '108.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.h1.a1', '36.n1.a1', '36.q1.a1', '36.w1.a1', '54.b1.a1', '54.c1.a1', '54.g1.a1'], 'contains': ['216.b1.a1', '216.i1.a1', '216.j1.a1', '216.p1.a1', '216.p1.b1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [469, 6, 936], 'label': '1728.34767.108.f1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1.a1', 'old_label': '108.f1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.f1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302507
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '108.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '108.f1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.h1.b1', '36.n1.b1', '36.q1.b1', '36.w1.b1', '54.b1.b1', '54.c1.b1', '54.g1.a1'], 'contains': ['216.b1.b1', '216.i1.b1', '216.j1.a1', '216.p1.c1', '216.p1.d1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [1, 474, 936], 'label': '1728.34767.108.f1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.f1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1.a1', 'old_label': '108.f1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.f1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302508
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '108.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '36.bz1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.r1.a1', '36.x1.a1', '36.x1.b1', '54.e1.a1', '54.f1.a1', '54.g1.a1'], 'contains': ['216.b1.a1', '216.b1.b1', '216.f1.a1', '216.l1.a1', '216.l1.b1', '216.l1.c1', '216.l1.d1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [1, 6, 864], 'label': '1728.34767.108.g1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '108.g1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.g1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302509
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '108.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.k1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.b1.a1', '36.y1.a1', '36.y1.b1', '36.cn1.a1', '54.a1.a1', '54.a1.b1', '54.h1.a1'], 'contains': ['216.a1.a1', '216.c1.a1', '216.e1.a1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [36, 432], 'label': '1728.34767.108.h1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '36.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '108.h1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.h1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302510
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '108.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '36.bu1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.z1.a1', '36.z1.b1', '36.bu1.a1', '36.co1.a1', '54.e1.a1', '54.h1.a1', '54.i1.a1'], 'contains': ['216.a1.a1', '216.f1.a1', '216.g1.a1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [7, 432], 'label': '1728.34767.108.i1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.k1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '108.i1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.i1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302511
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '6.u1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.i1.a1', '3.a1.b1'], 'contains': ['12.h1.a1', '12.bd1.a1', '12.be1.a1', '12.br1.a1', '12.bs1.a1', '12.bt1.a1', '12.bu1.a1', '18.u1.a1', '18.y1.a1'], 'core': '12.h1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [37, 48, 864, 42, 576, 432, 72], 'label': '1728.34767.6.u1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.i1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.b1', 'old_label': '6.u1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.u1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302512
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '108.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.ba1.b1', '36.bb1.a1', '36.bv1.a1', '36.cj1.a1', '54.a1.a1', '54.b1.b1', '54.i1.a1'], 'contains': ['216.a1.a1', '216.h1.a1', '216.i1.b1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [42, 432], 'label': '1728.34767.108.j1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.h1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1.a1', 'old_label': '108.j1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.j1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302513
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '108.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.ba1.a1', '36.bb1.b1', '36.bv1.b1', '36.cj1.b1', '54.a1.b1', '54.b1.a1', '54.i1.a1'], 'contains': ['216.a1.a1', '216.h1.b1', '216.i1.a1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [37, 432], 'label': '1728.34767.108.j1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.h1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1.b1', 'old_label': '108.j1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.j1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302514
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '108.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.bc1.a1', '36.bc1.b1', '36.bw1.a1', '36.ck1.a1', '36.ck1.b1', '36.cp1.a1', '36.cu1.a1', '54.b1.a1', '54.b1.b1', '54.h1.a1'], 'contains': ['216.a1.a1', '216.j1.a1', '216.k1.a1', '216.q1.a1', '216.q1.b1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [43, 432, 936], 'label': '1728.34767.108.k1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.k1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1.a1', 'old_label': '108.k1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.k1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302515
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '108.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.bd1.a1', '36.be1.b1', '36.bx1.a1', '54.a1.b1', '54.c1.a1', '54.j1.a1'], 'contains': ['216.c1.a1', '216.d1.a1', '216.i1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [433, 36], 'label': '1728.34767.108.l1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.i1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1.b1', 'old_label': '108.l1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.l1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302516
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '108.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.bd1.b1', '36.be1.a1', '36.bx1.b1', '54.a1.a1', '54.c1.b1', '54.j1.a1'], 'contains': ['216.c1.a1', '216.d1.b1', '216.i1.b1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [438, 36], 'label': '1728.34767.108.l1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.i1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1.a1', 'old_label': '108.l1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.l1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302517
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '108.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '108.m1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.bf1.a1', '36.bf1.b1', '36.by1.a1', '36.cq1.a1', '54.f1.a1', '54.h1.a1', '54.j1.a1'], 'contains': ['216.c1.a1', '216.f1.a1', '216.k1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [7, 36], 'label': '1728.34767.108.m1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.m1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1.a1', 'old_label': '108.m1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.m1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302518
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '108.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '108.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.bg1.a1', '36.bg1.b1', '36.bz1.a1', '36.cr1.a1', '54.c1.a1', '54.c1.b1', '54.h1.a1'], 'contains': ['216.c1.a1', '216.g1.a1', '216.j1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [439, 36], 'label': '1728.34767.108.n1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.n1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1.a1', 'old_label': '108.n1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.n1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302519
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '108.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.bh1.a1', '36.bk1.b1', '36.ca1.a1', '54.a1.b1', '54.d1.a1', '54.k1.a1'], 'contains': ['216.d1.a1', '216.e1.a1', '216.h1.b1', '216.o1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [433, 468, 864], 'label': '1728.34767.108.o1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.j1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1.b1', 'old_label': '108.o1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.o1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302520
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '108.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '144.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.bh1.b1', '36.bk1.a1', '36.ca1.b1', '54.a1.a1', '54.d1.b1', '54.k1.a1'], 'contains': ['216.d1.b1', '216.e1.a1', '216.h1.a1', '216.o1.b1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [438, 468, 864], 'label': '1728.34767.108.o1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.j1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1.a1', 'old_label': '108.o1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.o1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302521
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '108.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.bi1.a1', '36.bl1.b1', '36.cb1.a1', '36.cl1.a1', '54.b1.b1', '54.c1.a1', '54.k1.a1'], 'contains': ['216.d1.a1', '216.h1.a1', '216.j1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [433, 42], 'label': '1728.34767.108.p1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.p1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1.a1', 'old_label': '108.p1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.p1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302522
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '6.u1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.i1.a1', '3.a1.a1'], 'contains': ['12.h1.b1', '12.bd1.b1', '12.be1.b1', '12.br1.b1', '12.bs1.b1', '12.bt1.b1', '12.bu1.b1', '18.u1.b1', '18.y1.a1'], 'core': '12.h1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [37, 4, 864, 42, 576, 432, 72], 'label': '1728.34767.6.u1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.i1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '6.u1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.u1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302523
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '108.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.bi1.b1', '36.bl1.a1', '36.cb1.b1', '36.cl1.b1', '54.b1.a1', '54.c1.b1', '54.k1.a1'], 'contains': ['216.d1.b1', '216.h1.b1', '216.j1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [37, 438], 'label': '1728.34767.108.p1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.p1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1.a1', 'old_label': '108.p1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.p1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302524
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '108.q1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.bj1.a1', '36.bm1.b1', '36.cc1.a1', '36.cm1.a1', '54.b1.b1', '54.d1.a1', '54.j1.a1'], 'contains': ['216.d1.a1', '216.i1.b1', '216.k1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [433, 474], 'label': '1728.34767.108.q1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.q1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1.a1', 'old_label': '108.q1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.q1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302525
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '108.q1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.bj1.b1', '36.bm1.a1', '36.cc1.b1', '36.cm1.b1', '54.b1.a1', '54.d1.b1', '54.j1.a1'], 'contains': ['216.d1.b1', '216.i1.a1', '216.k1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [469, 438], 'label': '1728.34767.108.q1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.q1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1.a1', 'old_label': '108.q1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.q1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302526
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '108.r1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.w1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.bn1.a1', '36.bn1.b1', '36.cd1.a1', '54.e1.a1', '54.j1.a1', '54.k1.a1'], 'contains': ['216.d1.a1', '216.d1.b1', '216.f1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [433, 438], 'label': '1728.34767.108.r1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '12.l1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '108.r1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.r1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302527
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '108.s1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '108.s1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.bo1.a1', '36.bo1.b1', '36.ce1.a1', '36.cs1.a1', '54.g1.a1', '54.h1.a1', '54.k1.a1'], 'contains': ['216.e1.a1', '216.f1.a1', '216.j1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [7, 468], 'label': '1728.34767.108.s1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.s1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1.a1', 'old_label': '108.s1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.s1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302528
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '108.t1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.bp1.a1', '36.bp1.b1', '36.cf1.a1', '36.ct1.a1', '54.d1.a1', '54.d1.b1', '54.h1.a1'], 'contains': ['216.e1.a1', '216.g1.a1', '216.k1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [439, 468], 'label': '1728.34767.108.t1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.t1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1.a1', 'old_label': '108.t1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.t1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302529
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '108.u1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.bq1.a1', '36.bq1.b1', '36.cg1.a1', '54.f1.a1', '54.i1.a1', '54.k1.a1'], 'contains': ['216.f1.a1', '216.h1.a1', '216.h1.b1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [37, 42], 'label': '1728.34767.108.u1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.u1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1.a1', 'old_label': '108.u1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.u1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302530
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '108.v1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.br1.a1', '36.br1.b1', '36.ch1.a1', '54.g1.a1', '54.i1.a1', '54.j1.a1'], 'contains': ['216.f1.a1', '216.i1.a1', '216.i1.b1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [469, 474], 'label': '1728.34767.108.v1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.v1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1.a1', 'old_label': '108.v1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.v1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302531
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '108.w1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.bs1.b1', '36.bt1.a1', '36.ci1.a1', '54.c1.a1', '54.d1.b1', '54.i1.a1'], 'contains': ['216.g1.a1', '216.h1.a1', '216.i1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [469, 42], 'label': '1728.34767.108.w1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.w1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1.a1', 'old_label': '108.w1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.w1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302532
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '108.w1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.bs1.a1', '36.bt1.b1', '36.ci1.b1', '54.c1.b1', '54.d1.a1', '54.i1.a1'], 'contains': ['216.g1.a1', '216.h1.b1', '216.i1.b1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': None, 'generators': [37, 474], 'label': '1728.34767.108.w1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.w1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1.a1', 'old_label': '108.w1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.w1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302533
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '6.v1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.j1.a1', '3.a1.b1'], 'contains': ['12.i1.a1', '12.bg1.a1', '12.bh1.a1', '12.bl1.a1', '12.bn1.a1', '12.bo1.a1', '12.bs1.a1', '18.v1.a1', '18.z1.a1'], 'core': '12.i1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [433, 48, 864, 438, 576, 36, 72], 'label': '1728.34767.6.v1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.j1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.b1', 'old_label': '6.v1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.v1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302534
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '144.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2.a1.b1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['48.a1.a1', '48.b1.a1', '48.f1.a1', '72.a1.a1', '72.b1.a1', '72.c1.a1', '72.g1.b1', '72.j1.a1', '72.k1.a1', '72.l1.a1', '72.m1.a1', '72.n1.a1', '72.o1.a1', '72.p1.a1', '72.q1.a1', '72.r1.a1', '72.s1.a1', '72.t1.a1'], 'contains': ['288.a1.a1', '288.c1.a1', '288.e1.a1', '432.a1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [936, 864, 48], 'label': '1728.34767.144.a1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '144.a1.a1', 'normal_contained_in': ['48.a1.a1', '48.b1.a1', '72.a1.a1', '72.b1.a1', '72.c1.a1'], 'normal_contains': ['288.a1.a1', '288.c1.a1', '288.e1.a1', '432.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '144.a1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.a1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302535
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '144.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['48.a1.b1', '48.b1.a1', '48.f1.b1', '72.a1.b1', '72.b1.b1', '72.c1.b1', '72.g1.a1', '72.j1.b1', '72.k1.b1', '72.l1.b1', '72.m1.b1', '72.n1.b1', '72.o1.b1', '72.p1.b1', '72.q1.b1', '72.r1.b1', '72.s1.b1', '72.t1.b1'], 'contains': ['288.a1.b1', '288.c1.b1', '288.e1.b1', '432.a1.a1'], 'core': '144.a1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [936, 864, 4], 'label': '1728.34767.144.a1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '144.a1.b1', 'normal_contained_in': ['48.a1.b1', '48.b1.a1', '72.a1.b1', '72.b1.b1', '72.c1.b1'], 'normal_contains': ['288.a1.b1', '288.c1.b1', '288.e1.b1', '432.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '144.a1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.a1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302536
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '144.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2.e1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['48.a1.a1', '48.a1.b1', '48.g1.a1', '72.d1.a1', '72.e1.a1', '72.f1.a1', '72.h1.a1', '72.h1.b1', '72.u1.a1', '72.u1.b1', '72.v1.a1', '72.w1.a1', '72.x1.a1', '72.x1.b1', '72.y1.a1', '72.y1.b1', '72.z1.a1', '72.ba1.a1'], 'contains': ['288.b1.a1', '288.d1.a1', '288.f1.a1', '432.a1.a1'], 'core': '144.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [936, 864, 576], 'label': '1728.34767.144.b1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '144.b1.a1', 'normal_contained_in': ['48.a1.b1', '48.a1.a1', '72.d1.a1', '72.e1.a1', '72.f1.a1'], 'normal_contains': ['288.b1.a1', '288.d1.a1', '288.f1.a1', '432.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '144.b1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.b1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302537
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '144.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12.i1.b1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['48.c1.a1', '48.d1.a1', '48.j1.a1', '72.a1.a1', '72.bs1.c1', '72.bs1.d1'], 'contains': ['288.a1.a1', '288.s1.a1', '432.b1.a1'], 'core': '144.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [6, 936, 48], 'label': '1728.34767.144.c1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '144.c1.a1', 'normal_contained_in': ['48.c1.a1', '48.d1.a1', '72.a1.a1'], 'normal_contains': ['288.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '144.c1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.c1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302538
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '144.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12.i1.b1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['48.c1.b1', '48.d1.b1', '48.j1.b1', '72.a1.a1', '72.bs1.g1', '72.bs1.h1'], 'contains': ['288.a1.a1', '288.s1.b1', '432.b1.b1'], 'core': '144.c1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [870, 936, 48], 'label': '1728.34767.144.c1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '144.c1.b1', 'normal_contained_in': ['48.c1.b1', '48.d1.b1', '72.a1.a1'], 'normal_contains': ['288.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '144.c1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.c1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302539
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '144.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12.i1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['48.c1.c1', '48.d1.c1', '48.j1.c1', '72.a1.b1', '72.bs1.a1', '72.bs1.e1'], 'contains': ['288.a1.b1', '288.s1.c1', '432.b1.c1'], 'core': '144.c1.c1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [1, 936, 4], 'label': '1728.34767.144.c1.c1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '144.c1.c1', 'normal_contained_in': ['48.c1.c1', '48.d1.c1', '72.a1.b1'], 'normal_contains': ['288.a1.b1'], 'normalizer': '1.a1.a1', 'old_label': '144.c1.c1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.c1.c1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302540
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '144.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12.i1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['48.c1.d1', '48.d1.d1', '48.j1.d1', '72.a1.b1', '72.bs1.b1', '72.bs1.f1'], 'contains': ['288.a1.b1', '288.s1.d1', '432.b1.d1'], 'core': '144.c1.d1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [865, 936, 4], 'label': '1728.34767.144.c1.d1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '144.c1.d1', 'normal_contained_in': ['48.c1.d1', '48.d1.d1', '72.a1.b1'], 'normal_contains': ['288.a1.b1'], 'normalizer': '1.a1.a1', 'old_label': '144.c1.d1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.c1.d1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302541
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '144.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.a1.a1', '48.f1.b1', '48.h1.a1', '72.i1.b1', '72.bb1.a1', '72.bc1.a1', '72.bd1.a1', '72.be1.a1', '72.bf1.a1', '72.bg1.a1'], 'contains': ['288.g1.a1', '288.j1.a1', '288.m1.a1', '432.a1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [936, 864, 1200], 'label': '1728.34767.144.d1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '48.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.b1', 'old_label': '144.d1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.d1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302542
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '144.d1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.a1.b1', '48.f1.a1', '48.h1.a1', '72.i1.a1', '72.bb1.b1', '72.bc1.b1', '72.bd1.b1', '72.be1.b1', '72.bf1.b1', '72.bg1.b1'], 'contains': ['288.g1.b1', '288.j1.b1', '288.m1.b1', '432.a1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [936, 864, 1156], 'label': '1728.34767.144.d1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '48.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1.a1', 'old_label': '144.d1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.d1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302543
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '144.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.b1.a1', '48.g1.a1', '48.h1.a1', '72.bh1.a1', '72.bi1.a1', '72.bj1.a1', '72.bk1.a1', '72.bl1.a1', '72.bm1.a1', '72.bn1.a1'], 'contains': ['288.h1.a1', '288.k1.a1', '288.n1.a1', '432.a1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [936, 864, 100], 'label': '1728.34767.144.e1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '48.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.h1.a1', 'old_label': '144.e1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.e1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302544
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '6.v1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.j1.a1', '3.a1.a1'], 'contains': ['12.i1.b1', '12.bg1.b1', '12.bh1.b1', '12.bl1.b1', '12.bn1.b1', '12.bo1.b1', '12.bs1.b1', '18.v1.b1', '18.z1.a1'], 'core': '12.i1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [433, 4, 864, 438, 576, 36, 72], 'label': '1728.34767.6.v1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.j1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '6.v1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.v1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302545
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '144.f1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '8.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.f1.a1', '48.f1.b1', '48.g1.a1', '48.h1.a1', '72.bo1.a1', '72.bp1.a1', '72.bq1.a1'], 'contains': ['288.i1.a1', '288.l1.a1', '288.o1.a1', '432.a1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': None, 'generators': [936, 864, 1204], 'label': '1728.34767.144.f1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '16.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.k1.a1', 'old_label': '144.f1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.f1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302546
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '144.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12.n1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.d1.a1', '48.i1.a1', '72.g1.a1', '72.bs1.a1', '72.bs1.b1'], 'contains': ['288.a1.b1', '288.p1.a1', '432.b1.a1'], 'core': '288.a1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [6, 936, 4], 'label': '1728.34767.144.g1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '48.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '144.g1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.g1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302547
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '144.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12.n1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.d1.b1', '48.i1.b1', '72.g1.a1', '72.bs1.e1', '72.bs1.f1'], 'contains': ['288.a1.b1', '288.p1.b1', '432.b1.b1'], 'core': '288.a1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [870, 936, 4], 'label': '1728.34767.144.g1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '48.d1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '144.g1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.g1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302548
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '144.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12.n1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.d1.c1', '48.i1.c1', '72.g1.b1', '72.bs1.c1', '72.bs1.g1'], 'contains': ['288.a1.a1', '288.p1.c1', '432.b1.c1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [1, 936, 48], 'label': '1728.34767.144.g1.c1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '48.d1.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.b1', 'old_label': '144.g1.c1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.g1.c1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302549
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '144.g1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12.n1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.d1.d1', '48.i1.d1', '72.g1.b1', '72.bs1.d1', '72.bs1.h1'], 'contains': ['288.a1.a1', '288.p1.d1', '432.b1.d1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [865, 936, 48], 'label': '1728.34767.144.g1.d1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '48.d1.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.b1', 'old_label': '144.g1.d1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.g1.d1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302550
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '144.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12.o1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.c1.a1', '48.i1.a1', '72.h1.a1', '72.br1.a1', '72.br1.b1'], 'contains': ['288.b1.a1', '288.q1.a1', '432.b1.a1'], 'core': '288.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [6, 936, 576], 'label': '1728.34767.144.h1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '48.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '144.h1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.h1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302551
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '144.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12.o1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.c1.b1', '48.i1.b1', '72.h1.a1', '72.br1.c1', '72.br1.d1'], 'contains': ['288.b1.a1', '288.q1.b1', '432.b1.b1'], 'core': '288.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [870, 936, 576], 'label': '1728.34767.144.h1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '48.c1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '144.h1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.h1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302552
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '144.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12.o1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.c1.c1', '48.i1.c1', '72.h1.b1', '72.br1.a1', '72.br1.c1'], 'contains': ['288.b1.a1', '288.q1.c1', '432.b1.c1'], 'core': '288.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [1, 936, 576], 'label': '1728.34767.144.h1.c1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '48.c1.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.b1', 'old_label': '144.h1.c1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.h1.c1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302553
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '144.h1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12.o1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.c1.d1', '48.i1.d1', '72.h1.b1', '72.br1.b1', '72.br1.d1'], 'contains': ['288.b1.a1', '288.q1.d1', '432.b1.d1'], 'core': '288.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [865, 936, 576], 'label': '1728.34767.144.h1.d1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '48.c1.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.b1', 'old_label': '144.h1.d1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.h1.d1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302554
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '144.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.n1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.i1.a1', '48.j1.a1', '72.i1.a1'], 'contains': ['288.g1.b1', '288.r1.a1', '432.b1.a1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [6, 936, 1156], 'label': '1728.34767.144.i1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '16.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.a1', 'old_label': '144.i1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.i1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302555
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '6.w1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.k1.a1', '3.a1.b1'], 'contains': ['12.j1.a1', '12.bj1.a1', '12.bk1.a1', '12.bm1.a1', '12.bo1.a1', '12.bp1.a1', '12.br1.a1', '18.w1.a1', '18.ba1.a1'], 'core': '12.j1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [433, 48, 864, 438, 576, 468, 72], 'label': '1728.34767.6.w1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.k1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.b1', 'old_label': '6.w1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.w1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302556
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '144.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.n1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.i1.b1', '48.j1.b1', '72.i1.a1'], 'contains': ['288.g1.b1', '288.r1.b1', '432.b1.b1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [870, 936, 1156], 'label': '1728.34767.144.i1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '16.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.a1', 'old_label': '144.i1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.i1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302557
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '144.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.n1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.i1.c1', '48.j1.c1', '72.i1.b1'], 'contains': ['288.g1.a1', '288.r1.c1', '432.b1.c1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [1, 936, 1200], 'label': '1728.34767.144.i1.c1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '16.b1.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.b1', 'old_label': '144.i1.c1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.i1.c1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302558
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '144.i1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.n1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.i1.d1', '48.j1.d1', '72.i1.b1'], 'contains': ['288.g1.a1', '288.r1.d1', '432.b1.d1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [865, 936, 1200], 'label': '1728.34767.144.i1.d1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '16.b1.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.b1', 'old_label': '144.i1.d1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.i1.d1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302559
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '144.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '36.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.e1.a1', '48.k1.a1', '72.m1.a1', '72.bs1.c1', '72.bs1.h1'], 'contains': ['288.a1.a1', '432.c1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [7, 936, 48], 'label': '1728.34767.144.j1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '48.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.b1', 'old_label': '144.j1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.j1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302560
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '144.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '36.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.e1.b1', '48.k1.b1', '72.m1.a1', '72.bs1.d1', '72.bs1.g1'], 'contains': ['288.a1.a1', '432.c1.b1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [871, 936, 48], 'label': '1728.34767.144.j1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '48.e1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.b1', 'old_label': '144.j1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.j1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302561
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '144.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '36.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.e1.a1', '48.k1.c1', '72.m1.b1', '72.bs1.a1', '72.bs1.f1'], 'contains': ['288.a1.b1', '432.c1.a1'], 'core': '288.a1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [7, 936, 4], 'label': '1728.34767.144.j1.c1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '48.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '144.j1.c1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.j1.c1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302562
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '144.j1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '36.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.e1.b1', '48.k1.d1', '72.m1.b1', '72.bs1.b1', '72.bs1.e1'], 'contains': ['288.a1.b1', '432.c1.b1'], 'core': '288.a1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [871, 936, 4], 'label': '1728.34767.144.j1.d1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '48.e1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '144.j1.d1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.j1.d1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302563
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '144.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '36.bu1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.k1.a1', '48.k1.c1', '48.l1.a1', '72.v1.a1', '72.br1.a1', '72.br1.d1'], 'contains': ['288.b1.a1', '432.c1.a1'], 'core': '288.b1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [7, 576, 936], 'label': '1728.34767.144.k1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '16.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '144.k1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.k1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302564
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '144.k1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '36.bu1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.k1.b1', '48.k1.d1', '48.l1.b1', '72.v1.a1', '72.br1.b1', '72.br1.c1'], 'contains': ['288.b1.a1', '432.c1.b1'], 'core': '288.b1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': None, 'generators': [871, 576, 936], 'label': '1728.34767.144.k1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '16.c1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '144.k1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.k1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302565
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '144.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '36.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.e1.a1', '48.l1.a1', '72.bk1.a1'], 'contains': ['288.h1.a1', '432.c1.a1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [7, 936, 100], 'label': '1728.34767.144.l1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '48.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.bb1.a1', 'old_label': '144.l1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.l1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302566
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '6.w1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.k1.a1', '3.a1.a1'], 'contains': ['12.j1.b1', '12.bj1.b1', '12.bk1.b1', '12.bm1.b1', '12.bo1.b1', '12.bp1.b1', '12.br1.b1', '18.w1.b1', '18.ba1.a1'], 'core': '12.j1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [433, 4, 864, 438, 576, 468, 72], 'label': '1728.34767.6.w1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.k1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '6.w1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.w1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302567
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '144.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '36.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.e1.b1', '48.l1.b1', '72.bk1.a1'], 'contains': ['288.h1.a1', '432.c1.b1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [871, 936, 100], 'label': '1728.34767.144.l1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '48.e1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.bb1.a1', 'old_label': '144.l1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.l1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302568
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '144.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12.n1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.m1.a1', '48.p1.a1', '72.g1.a1', '72.bt1.a1', '72.bu1.a1'], 'contains': ['288.c1.b1', '288.p1.a1', '288.p1.b1', '432.d1.a1'], 'core': '288.c1.b1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [6, 72, 4], 'label': '1728.34767.144.m1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.e1.a1', 'old_label': '144.m1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.m1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302569
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '144.m1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12.n1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.m1.b1', '48.p1.b1', '72.g1.b1', '72.bt1.b1', '72.bu1.b1'], 'contains': ['288.c1.a1', '288.p1.c1', '288.p1.d1', '432.d1.b1'], 'core': '288.c1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [1, 72, 48], 'label': '1728.34767.144.m1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.e1.b1', 'old_label': '144.m1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.m1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302570
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '144.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12.o1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.m1.a1', '48.n1.a1', '72.h1.a1', '72.bv1.a1', '72.bw1.a1'], 'contains': ['288.d1.a1', '288.q1.a1', '288.q1.b1', '432.d1.a1'], 'core': '288.d1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [6, 72, 576], 'label': '1728.34767.144.n1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.e1.a1', 'old_label': '144.n1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.n1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302571
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '144.n1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12.o1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.m1.b1', '48.n1.b1', '72.h1.b1', '72.bv1.b1', '72.bw1.b1'], 'contains': ['288.d1.a1', '288.q1.c1', '288.q1.d1', '432.d1.b1'], 'core': '288.d1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [1, 72, 576], 'label': '1728.34767.144.n1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.e1.b1', 'old_label': '144.n1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.n1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302572
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '144.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.n1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.m1.a1', '48.o1.a1', '72.i1.a1'], 'contains': ['288.j1.b1', '288.r1.a1', '288.r1.b1', '432.d1.a1'], 'core': '864.b1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [6, 72, 1156], 'label': '1728.34767.144.o1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.r1.a1', 'old_label': '144.o1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.o1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302573
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '144.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.n1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.m1.b1', '48.o1.b1', '72.i1.b1'], 'contains': ['288.j1.a1', '288.r1.c1', '288.r1.d1', '432.d1.b1'], 'core': '864.b1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': None, 'generators': [1, 72, 1200], 'label': '1728.34767.144.o1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.r1.b1', 'old_label': '144.o1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.o1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302574
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '144.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12.i1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.n1.a1', '48.o1.a1', '48.p1.a1', '72.a1.a1', '72.bx1.a1', '72.by1.a1'], 'contains': ['288.c1.a1', '288.s1.a1', '288.s1.b1', '432.d1.a1'], 'core': '288.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [6, 72, 48], 'label': '1728.34767.144.p1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '72.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.a1', 'old_label': '144.p1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.p1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302575
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '144.p1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.n1.b1', '48.o1.b1', '48.p1.b1', '72.a1.b1', '72.bx1.b1', '72.by1.b1'], 'contains': ['288.c1.b1', '288.s1.c1', '288.s1.d1', '432.d1.b1'], 'core': '288.c1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [1, 72, 4], 'label': '1728.34767.144.p1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '72.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1.b1', 'old_label': '144.p1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.p1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302576
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '144.q1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12.y1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.q1.a1', '48.z1.a1', '72.j1.a1', '72.bt1.b1', '72.bx1.a1'], 'contains': ['288.c1.a1', '432.e1.a1'], 'core': '288.c1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [36, 48, 72], 'label': '1728.34767.144.q1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.d1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.r1.a1', 'old_label': '144.q1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.q1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302577
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '6.x1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.h1.a1', '3.b1.a1'], 'contains': ['12.k1.a1', '12.bz1.a1', '12.cb1.a1', '12.cd1.a1', '12.ce1.a1', '12.ci1.a1', '12.cj1.a1', '18.t1.a1', '18.t1.b1', '18.bb1.a1'], 'core': '12.k1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [7, 4, 864, 36, 48, 432, 936], 'label': '1728.34767.6.x1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.h1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '6.x1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.x1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302578
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '144.q1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12.y1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.q1.b1', '48.z1.a1', '72.j1.b1', '72.bt1.a1', '72.bx1.b1'], 'contains': ['288.c1.b1', '432.e1.a1'], 'core': '288.c1.b1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [36, 4, 72], 'label': '1728.34767.144.q1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.d1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.r1.a1', 'old_label': '144.q1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.q1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302579
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '144.r1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.p1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.r1.a1', '48.ba1.a1', '72.k1.a1', '72.by1.a1', '72.bz1.a1'], 'contains': ['288.c1.a1', '432.f1.a1'], 'core': '288.c1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [433, 48, 72], 'label': '1728.34767.144.r1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.j1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.i1.a1', 'old_label': '144.r1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.r1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302580
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '144.r1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.p1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.r1.b1', '48.ba1.b1', '72.k1.b1', '72.by1.b1', '72.bz1.b1'], 'contains': ['288.c1.b1', '432.f1.b1'], 'core': '288.c1.b1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [438, 4, 72], 'label': '1728.34767.144.r1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.j1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.i1.b1', 'old_label': '144.r1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.r1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302581
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '144.s1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.s1.a1', '48.x1.a1', '48.ba1.b1', '72.c1.a1', '72.bu1.b1', '72.ca1.a1'], 'contains': ['288.c1.a1', '432.f1.b1'], 'core': '288.c1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [438, 72, 48], 'label': '1728.34767.144.s1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '72.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.b1', 'old_label': '144.s1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.s1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302582
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '144.s1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.s1.b1', '48.x1.b1', '48.ba1.a1', '72.c1.b1', '72.bu1.a1', '72.ca1.b1'], 'contains': ['288.c1.b1', '432.f1.a1'], 'core': '288.c1.b1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [433, 72, 4], 'label': '1728.34767.144.s1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '72.c1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1.a1', 'old_label': '144.s1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.s1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302583
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '144.t1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.bd1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.t1.a1', '48.bb1.a1', '72.l1.a1', '72.bz1.a1', '72.ca1.a1'], 'contains': ['288.c1.a1', '432.g1.a1'], 'core': '288.c1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [468, 48, 72], 'label': '1728.34767.144.t1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.ba1.a1', 'old_label': '144.t1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.t1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302584
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '144.t1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.bd1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.t1.b1', '48.bb1.a1', '72.l1.b1', '72.bz1.b1', '72.ca1.b1'], 'contains': ['288.c1.b1', '432.g1.a1'], 'core': '288.c1.b1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [468, 4, 72], 'label': '1728.34767.144.t1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.f1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.ba1.a1', 'old_label': '144.t1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.t1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302585
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '144.u1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '36.i1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.u1.a1', '48.bc1.a1', '72.n1.a1', '72.bu1.b1', '72.by1.a1'], 'contains': ['288.c1.a1', '432.h1.a1'], 'core': '288.c1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [439, 72, 48], 'label': '1728.34767.144.u1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.l1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.o1.b1', 'old_label': '144.u1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.u1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302586
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '144.u1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '36.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.u1.b1', '48.bc1.a1', '72.n1.b1', '72.bu1.a1', '72.by1.b1'], 'contains': ['288.c1.b1', '432.h1.a1'], 'core': '288.c1.b1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [439, 72, 4], 'label': '1728.34767.144.u1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.l1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.o1.a1', 'old_label': '144.u1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.u1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302587
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '144.v1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '36.d1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.v1.a1', '48.y1.a1', '48.bd1.b1', '72.o1.a1', '72.bt1.b1', '72.bz1.a1'], 'contains': ['288.c1.a1', '432.i1.b1'], 'core': '288.c1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [37, 48, 72], 'label': '1728.34767.144.v1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.h1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1.b1', 'old_label': '144.v1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.v1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302588
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '6.y1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.i1.a1', '3.b1.a1'], 'contains': ['12.k1.a1', '12.ca1.a1', '12.ca1.b1', '12.ck1.a1', '12.cl1.a1', '12.cm1.a1', '12.cm1.b1', '18.u1.a1', '18.u1.b1'], 'core': '12.k1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [37, 4, 864, 42, 48, 432, 72], 'label': '1728.34767.6.y1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.i1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '6.y1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.y1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302589
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '144.v1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '36.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.v1.b1', '48.y1.b1', '48.bd1.a1', '72.o1.b1', '72.bt1.a1', '72.bz1.b1'], 'contains': ['288.c1.b1', '432.i1.a1'], 'core': '288.c1.b1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [42, 4, 72], 'label': '1728.34767.144.v1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.h1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1.a1', 'old_label': '144.v1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.v1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302590
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '144.w1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.j1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.w1.a1', '48.bd1.a1', '72.p1.a1', '72.bx1.a1', '72.ca1.a1'], 'contains': ['288.c1.a1', '432.i1.a1'], 'core': '288.c1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [42, 72, 48], 'label': '1728.34767.144.w1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.k1.a1', 'old_label': '144.w1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.w1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302591
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '144.w1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.w1.b1', '48.bd1.b1', '72.p1.b1', '72.bx1.b1', '72.ca1.b1'], 'contains': ['288.c1.b1', '432.i1.b1'], 'core': '288.c1.b1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [37, 72, 4], 'label': '1728.34767.144.w1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.g1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.k1.b1', 'old_label': '144.w1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.w1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302592
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '144.x1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.q1.a1', '48.q1.b1', '48.be1.a1', '72.e1.a1', '72.bv1.a1', '72.bv1.b1'], 'contains': ['288.d1.a1', '432.e1.a1'], 'core': '288.d1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [36, 72, 576], 'label': '1728.34767.144.x1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '72.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.f1.a1', 'old_label': '144.x1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.x1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302593
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '144.y1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12.s1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.r1.a1', '48.s1.b1', '72.u1.a1', '72.bw1.a1', '72.cb1.a1'], 'contains': ['288.d1.a1', '432.f1.a1'], 'core': '288.d1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [433, 576, 72], 'label': '1728.34767.144.y1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.e1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.i1.a1', 'old_label': '144.y1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.y1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302594
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '144.y1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '12.s1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.r1.b1', '48.s1.a1', '72.u1.b1', '72.bw1.b1', '72.cb1.b1'], 'contains': ['288.d1.a1', '432.f1.b1'], 'core': '288.d1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [438, 576, 72], 'label': '1728.34767.144.y1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.e1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.i1.b1', 'old_label': '144.y1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.y1.b1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302595
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '144.z1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.k1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.t1.a1', '48.t1.b1', '48.bf1.a1', '72.f1.a1', '72.cb1.a1', '72.cb1.b1'], 'contains': ['288.d1.a1', '432.g1.a1'], 'core': '288.d1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [468, 72, 576], 'label': '1728.34767.144.z1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '72.f1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.k1.a1', 'old_label': '144.z1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.z1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302596
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '144.ba1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '18.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.u1.a1', '48.u1.b1', '48.bg1.a1', '72.w1.a1', '72.bw1.a1', '72.bw1.b1'], 'contains': ['288.d1.a1', '432.h1.a1'], 'core': '288.d1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': None, 'generators': [439, 576, 72], 'label': '1728.34767.144.ba1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.j1.a1', 'old_label': '144.ba1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.ba1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302597
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '144.bb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.v1.b1', '48.w1.a1', '72.x1.a1', '72.bv1.a1', '72.cb1.b1'], 'contains': ['288.d1.a1', '432.i1.a1'], 'core': '288.d1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [42, 72, 576], 'label': '1728.34767.144.bb1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.g1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.c1.a1', 'old_label': '144.bb1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.bb1.a1', 'subgroup_fusion': None, 'weyl_group': None}
  • id: 93302598
    {'ambient': '1728.34767', 'aut_centralizer_order': None, 'aut_label': '144.bb1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.g1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.v1.a1', '48.w1.b1', '72.x1.b1', '72.bv1.b1', '72.cb1.a1'], 'contains': ['288.d1.a1', '432.i1.b1'], 'core': '288.d1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': None, 'generators': [37, 72, 576], 'label': '1728.34767.144.bb1.b1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '24.g1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.c1.b1', 'old_label': '144.bb1.b1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.bb1.b1', 'subgroup_fusion': None, 'weyl_group': None}