Abstract group data - 864.2236

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• gps_groups •

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

  
  {'Agroup': False, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '8.2', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 3, 'aut_exponent': 12, 'aut_gen_orders': [2, 2, 2, 2, 3, 3, 3, 2, 2], 'aut_gens': [[1, 2, 24, 144], [1, 14, 120, 720], [1, 10, 552, 144], [1, 14, 24, 144], [13, 2, 24, 144], [17, 2, 456, 696], [1, 338, 24, 144], [97, 98, 24, 144], [433, 74, 24, 144], [1, 506, 24, 144]], 'aut_group': '1728.46116', 'aut_hash': 46116, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 1728, 'aut_permdeg': 54, 'aut_perms': [1530689906931956820987958667562774991532674383997767123233093227967, 63232141729261823401054829245524605307551258687160239798064850541648, 9327522704163120371983254089216102146592197590064120791883776000, 56809665994888577265306108959256299989696409963262788591717655838767644, 11274476011529488863020945887913196122973567767922843517884839013211778, 10829279796602294617577932493683225157854486786552836184563305505270, 61002378484090475882769967151247553925907117205020822735681772633991670, 4324550119232925694046616515849258738124345557235073570428788530156800, 51036090316002478531639515164682575660147317564127601305116832213880], 'aut_phi_ratio': 6.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 3, 1, 2], [2, 18, 2, 1], [3, 2, 1, 1], [3, 6, 1, 1], [3, 24, 1, 1], [3, 48, 1, 1], [4, 9, 2, 1], [4, 18, 2, 3], [4, 27, 2, 1], [6, 2, 1, 1], [6, 6, 1, 5], [6, 12, 1, 2], [6, 24, 1, 1], [6, 36, 2, 1], [6, 48, 1, 1], [12, 36, 2, 3], [12, 72, 2, 1]], 'aut_supersolvable': False, 'aut_tex': 'C_2^2\\times C_6^2:D_6', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 2, 'autcent_group': '4.2', 'autcent_hash': 2, 'autcent_nilpotent': True, 'autcent_order': 4, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^2', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 12, 'autcentquo_group': '432.523', 'autcentquo_hash': 523, 'autcentquo_nilpotent': False, 'autcentquo_order': 432, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'C_6^2:D_6', 'cc_stats': [[1, 1, 1], [2, 1, 1], [2, 3, 2], [2, 18, 2], [3, 2, 1], [3, 6, 1], [3, 24, 1], [3, 48, 1], [4, 9, 2], [4, 18, 6], [4, 27, 2], [6, 2, 1], [6, 6, 5], [6, 12, 2], [6, 24, 1], [6, 36, 2], [6, 48, 1], [12, 36, 6], [12, 72, 2]], 'center_label': '2.1', 'center_order': 2, 'central_product': False, 'central_quotient': '432.523', 'commutator_count': 1, 'commutator_label': '108.22', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '2.1', '3.1', '3.1', '3.1'], 'composition_length': 8, 'conjugacy_classes_known': True, 'counter': 2236, 'cyclic': False, 'derived_length': 3, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 3, 1, 2], [2, 18, 1, 2], [3, 2, 1, 1], [3, 6, 1, 1], [3, 24, 1, 1], [3, 48, 1, 1], [4, 9, 2, 1], [4, 18, 1, 2], [4, 18, 2, 2], [4, 27, 2, 1], [6, 2, 1, 1], [6, 6, 1, 5], [6, 12, 1, 2], [6, 24, 1, 1], [6, 36, 1, 2], [6, 48, 1, 1], [12, 36, 1, 2], [12, 36, 2, 2], [12, 72, 2, 1]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 54, 'exponent': 12, 'exponents_of_order': [5, 3], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [[6, -1, 2], [12, -1, 1]], 'familial': False, 'frattini_label': '6.2', 'frattini_quotient': '144.183', 'hash': 2236, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 12, 'inner_gen_orders': [2, 6, 6, 6], 'inner_gens': [[1, 10, 552, 144], [17, 2, 552, 312], [481, 482, 24, 144], [1, 842, 24, 144]], 'inner_hash': 523, 'inner_nilpotent': False, 'inner_order': 432, 'inner_split': True, 'inner_tex': 'C_6^2:D_6', 'inner_used': [1, 2, 3, 4], 'irrC_degree': 6, 'irrQ_degree': 6, 'irrQ_dim': 12, 'irrR_degree': 12, 'irrep_stats': [[1, 8], [2, 8], [3, 8], [4, 2], [6, 12], [12, 2]], 'label': '864.2236', 'linC_count': 2, 'linC_degree': 6, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 6, 'linQ_degree_count': 2, 'linQ_dim': 8, 'linQ_dim_count': 4, 'linR_count': 4, 'linR_degree': 8, 'maximal_subgroups_known': True, 'metabelian': False, 'metacyclic': False, 'monomial': True, 'name': 'C3^2:(C4*S4)', 'ngens': 8, 'nilpotency_class': -1, 'nilpotent': False, 'normal_counts': [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 29, 'number_characteristic_subgroups': 23, 'number_conjugacy_classes': 40, 'number_divisions': 33, 'number_normal_subgroups': 25, 'number_subgroup_autclasses': 205, 'number_subgroup_classes': 235, 'number_subgroups': 1994, 'old_label': None, 'order': 864, 'order_factorization_type': 33, 'order_stats': [[1, 1], [2, 43], [3, 80], [4, 180], [6, 200], [12, 360]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 2, 'outer_gen_orders': [2, 2], 'outer_gen_pows': [0, 0], 'outer_gens': [[1, 22, 456, 720], [13, 10, 456, 720]], 'outer_group': '4.2', 'outer_hash': 2, 'outer_nilpotent': True, 'outer_order': 4, 'outer_permdeg': 4, 'outer_perms': [1, 6], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^2', 'pc_rank': 4, 'perfect': False, 'permutation_degree': 17, 'pgroup': 0, 'primary_abelian_invariants': [2, 4], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 4], [2, 6], [3, 4], [4, 4], [6, 12], [12, 3]], 'representations': {'PC': {'code': 6586492797357651183710908862653263664355812478043121875172068124776213, 'gens': [1, 2, 5, 7], 'pres': [8, 2, 2, 2, 3, 2, 3, 2, 3, 96, 161, 41, 482, 66, 515, 22084, 11052, 5300, 2308, 116, 4613, 2317, 8750, 2374, 4902, 166, 19983, 5399, 3103]}, 'Perm': {'d': 17, 'gens': [355938468489, 2965618656729, 16, 23801712884040, 4036071473280, 47450457694080, 5160, 11520]}}, 'schur_multiplier': [2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 4], 'solvability_type': 11, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': 'C_3^2:(C_4\\times S_4)', 'transitive_degree': 36, 'wreath_data': None, 'wreath_product': False}
• gps_conj_classes •

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

  
  
  • id: 141605778
    {'aut_label': '1A', 'centralizer': '1.a1.a1', 'counter': 1, 'group_counter': 2236, 'group_order': 864, 'label': '1A', 'order': 1, 'powers': [1, 1], 'representative': 0, 'size': 1}
  • id: 141605789
    {'aut_label': '2A', 'centralizer': '1.a1.a1', 'counter': 2, 'group_counter': 2236, 'group_order': 864, 'label': '2A', 'order': 2, 'powers': [1, 2], 'representative': 12, 'size': 1}
  • id: 141605800
    {'aut_label': '2B', 'centralizer': '3.a1.a1', 'counter': 3, 'group_counter': 2236, 'group_order': 864, 'label': '2B', 'order': 2, 'powers': [1, 3], 'representative': 432, 'size': 3}
  • id: 141605811
    {'aut_label': '2C', 'centralizer': '3.a1.a1', 'counter': 4, 'group_counter': 2236, 'group_order': 864, 'label': '2C', 'order': 2, 'powers': [1, 4], 'representative': 84, 'size': 3}
  • id: 141605813
    {'aut_label': '2D', 'centralizer': '18.a1.a1', 'counter': 5, 'group_counter': 2236, 'group_order': 864, 'label': '2D', 'order': 2, 'powers': [1, 5], 'representative': 307, 'size': 18}
  • id: 141605814
    {'aut_label': '2D', 'centralizer': '18.a1.a1', 'counter': 6, 'group_counter': 2236, 'group_order': 864, 'label': '2E', 'order': 2, 'powers': [1, 6], 'representative': 7, 'size': 18}
  • id: 141605815
    {'aut_label': '3A', 'centralizer': '2.a1.a1', 'counter': 7, 'group_counter': 2236, 'group_order': 864, 'label': '3A', 'order': 3, 'powers': [7, 1], 'representative': 96, 'size': 2}
  • id: 141605816
    {'aut_label': '3B', 'centralizer': '6.j1.a1', 'counter': 8, 'group_counter': 2236, 'group_order': 864, 'label': '3B', 'order': 3, 'powers': [8, 1], 'representative': 288, 'size': 6}
  • id: 141605817
    {'aut_label': '3C', 'centralizer': '24.j1.a1', 'counter': 9, 'group_counter': 2236, 'group_order': 864, 'label': '3C', 'order': 3, 'powers': [9, 1], 'representative': 80, 'size': 24}
  • id: 141605779
    {'aut_label': '3D', 'centralizer': '48.c1.a1', 'counter': 10, 'group_counter': 2236, 'group_order': 864, 'label': '3D', 'order': 3, 'powers': [10, 1], 'representative': 784, 'size': 48}
  • id: 141605780
    {'aut_label': '4A1', 'centralizer': '9.c1.a1', 'counter': 11, 'group_counter': 2236, 'group_order': 864, 'label': '4A1', 'order': 4, 'powers': [2, 12], 'representative': 6, 'size': 9}
  • id: 141605781
    {'aut_label': '4A1', 'centralizer': '9.c1.a1', 'counter': 12, 'group_counter': 2236, 'group_order': 864, 'label': '4A-1', 'order': 4, 'powers': [2, 11], 'representative': 18, 'size': 9}
  • id: 141605782
    {'aut_label': '4B', 'centralizer': '18.e1.a1', 'counter': 13, 'group_counter': 2236, 'group_order': 864, 'label': '4B', 'order': 4, 'powers': [3, 13], 'representative': 203, 'size': 18}
  • id: 141605783
    {'aut_label': '4B', 'centralizer': '18.e1.a1', 'counter': 14, 'group_counter': 2236, 'group_order': 864, 'label': '4C', 'order': 4, 'powers': [3, 14], 'representative': 367, 'size': 18}
  • id: 141605784
    {'aut_label': '4D1', 'centralizer': '18.c1.a1', 'counter': 15, 'group_counter': 2236, 'group_order': 864, 'label': '4D1', 'order': 4, 'powers': [2, 16], 'representative': 13, 'size': 18}
  • id: 141605785
    {'aut_label': '4D1', 'centralizer': '18.c1.a1', 'counter': 16, 'group_counter': 2236, 'group_order': 864, 'label': '4D-1', 'order': 4, 'powers': [2, 15], 'representative': 1, 'size': 18}
  • id: 141605786
    {'aut_label': '4E1', 'centralizer': '18.g1.a1', 'counter': 17, 'group_counter': 2236, 'group_order': 864, 'label': '4E1', 'order': 4, 'powers': [4, 18], 'representative': 93, 'size': 18}
  • id: 141605787
    {'aut_label': '4E1', 'centralizer': '18.g1.a1', 'counter': 18, 'group_counter': 2236, 'group_order': 864, 'label': '4E-1', 'order': 4, 'powers': [4, 17], 'representative': 441, 'size': 18}
  • id: 141605788
    {'aut_label': '4F1', 'centralizer': '27.a1.a1', 'counter': 19, 'group_counter': 2236, 'group_order': 864, 'label': '4F1', 'order': 4, 'powers': [2, 20], 'representative': 150, 'size': 27}
  • id: 141605790
    {'aut_label': '4F1', 'centralizer': '27.a1.a1', 'counter': 20, 'group_counter': 2236, 'group_order': 864, 'label': '4F-1', 'order': 4, 'powers': [2, 19], 'representative': 162, 'size': 27}
  • id: 141605791
    {'aut_label': '6A', 'centralizer': '2.a1.a1', 'counter': 21, 'group_counter': 2236, 'group_order': 864, 'label': '6A', 'order': 6, 'powers': [7, 2], 'representative': 60, 'size': 2}
  • id: 141605792
    {'aut_label': '6B', 'centralizer': '6.j1.a1', 'counter': 22, 'group_counter': 2236, 'group_order': 864, 'label': '6B', 'order': 6, 'powers': [8, 3], 'representative': 144, 'size': 6}
  • id: 141605793
    {'aut_label': '6C', 'centralizer': '6.g1.a1', 'counter': 23, 'group_counter': 2236, 'group_order': 864, 'label': '6C', 'order': 6, 'powers': [7, 4], 'representative': 36, 'size': 6}
  • id: 141605794
    {'aut_label': '6D', 'centralizer': '6.j1.a1', 'counter': 24, 'group_counter': 2236, 'group_order': 864, 'label': '6D', 'order': 6, 'powers': [8, 2], 'representative': 588, 'size': 6}
  • id: 141605795
    {'aut_label': '6E', 'centralizer': '6.g1.a1', 'counter': 25, 'group_counter': 2236, 'group_order': 864, 'label': '6E', 'order': 6, 'powers': [7, 3], 'representative': 120, 'size': 6}
  • id: 141605796
    {'aut_label': '6F', 'centralizer': '6.j1.a1', 'counter': 26, 'group_counter': 2236, 'group_order': 864, 'label': '6F', 'order': 6, 'powers': [8, 4], 'representative': 180, 'size': 6}
  • id: 141605797
    {'aut_label': '6G', 'centralizer': '12.a1.a1', 'counter': 27, 'group_counter': 2236, 'group_order': 864, 'label': '6G', 'order': 6, 'powers': [8, 3], 'representative': 192, 'size': 12}
  • id: 141605798
    {'aut_label': '6H', 'centralizer': '12.a1.a1', 'counter': 28, 'group_counter': 2236, 'group_order': 864, 'label': '6H', 'order': 6, 'powers': [8, 4], 'representative': 204, 'size': 12}
  • id: 141605799
    {'aut_label': '6I', 'centralizer': '24.j1.a1', 'counter': 29, 'group_counter': 2236, 'group_order': 864, 'label': '6I', 'order': 6, 'powers': [9, 2], 'representative': 436, 'size': 24}
  • id: 141605801
    {'aut_label': '6J', 'centralizer': '36.b1.a1', 'counter': 30, 'group_counter': 2236, 'group_order': 864, 'label': '6J', 'order': 6, 'powers': [7, 5], 'representative': 355, 'size': 36}
  • id: 141605802
    {'aut_label': '6J', 'centralizer': '36.b1.a1', 'counter': 31, 'group_counter': 2236, 'group_order': 864, 'label': '6K', 'order': 6, 'powers': [7, 6], 'representative': 55, 'size': 36}
  • id: 141605803
    {'aut_label': '6L', 'centralizer': '48.c1.a1', 'counter': 32, 'group_counter': 2236, 'group_order': 864, 'label': '6L', 'order': 6, 'powers': [10, 2], 'representative': 668, 'size': 48}
  • id: 141605804
    {'aut_label': '12A', 'centralizer': '36.e1.a1', 'counter': 33, 'group_counter': 2236, 'group_order': 864, 'label': '12A', 'order': 12, 'powers': [25, 13], 'representative': 227, 'size': 36}
  • id: 141605805
    {'aut_label': '12A', 'centralizer': '36.e1.a1', 'counter': 34, 'group_counter': 2236, 'group_order': 864, 'label': '12B', 'order': 12, 'powers': [25, 14], 'representative': 847, 'size': 36}
  • id: 141605806
    {'aut_label': '12C1', 'centralizer': '36.l1.a1', 'counter': 35, 'group_counter': 2236, 'group_order': 864, 'label': '12C1', 'order': 12, 'powers': [24, 15], 'representative': 289, 'size': 36}
  • id: 141605807
    {'aut_label': '12C1', 'centralizer': '36.l1.a1', 'counter': 36, 'group_counter': 2236, 'group_order': 864, 'label': '12C-1', 'order': 12, 'powers': [24, 16], 'representative': 589, 'size': 36}
  • id: 141605808
    {'aut_label': '12D1', 'centralizer': '36.m1.a1', 'counter': 37, 'group_counter': 2236, 'group_order': 864, 'label': '12D1', 'order': 12, 'powers': [26, 17], 'representative': 777, 'size': 36}
  • id: 141605809
    {'aut_label': '12D1', 'centralizer': '36.m1.a1', 'counter': 38, 'group_counter': 2236, 'group_order': 864, 'label': '12D-1', 'order': 12, 'powers': [26, 18], 'representative': 621, 'size': 36}
  • id: 141605810
    {'aut_label': '12E1', 'centralizer': '72.o1.a1', 'counter': 39, 'group_counter': 2236, 'group_order': 864, 'label': '12E1', 'order': 12, 'powers': [29, 11], 'representative': 74, 'size': 72}
  • id: 141605812
    {'aut_label': '12E1', 'centralizer': '72.o1.a1', 'counter': 40, 'group_counter': 2236, 'group_order': 864, 'label': '12E-1', 'order': 12, 'powers': [29, 12], '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: 13153106
    {'cdim': 1, 'counter': 1, 'faithful': False, 'group': '864.2236', 'group_order': 864, 'image': None, 'label': '864.2236.1a', '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], 'schur_index': 1}
  • id: 13153117
    {'cdim': 1, 'counter': 2, 'faithful': False, 'group': '864.2236', 'group_order': 864, 'image': None, 'label': '864.2236.1b', '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], 'schur_index': 1}
  • id: 13153128
    {'cdim': 1, 'counter': 3, 'faithful': False, 'group': '864.2236', 'group_order': 864, 'image': None, 'label': '864.2236.1c', '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], 'schur_index': 1}
  • id: 13153133
    {'cdim': 1, 'counter': 4, 'faithful': False, 'group': '864.2236', 'group_order': 864, 'image': None, 'label': '864.2236.1d', '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], 'schur_index': 1}
  • id: 13153134
    {'cdim': 1, 'counter': 5, 'faithful': False, 'group': '864.2236', 'group_order': 864, 'image': None, 'label': '864.2236.1e', 'multiplicity': 2, 'nt': [4, 1], 'qdim': 2, 'qvalues': [2, -2, 2, -2, -2, 2, 2, 2, 2, 2, 0, 0, 0, 0, -2, 0, 0, 2, 0, 0, -2, 2, -2, 2, -2, -2, 2, -2, -2, -2, 2, -2, -2, 2, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 13153135
    {'cdim': 1, 'counter': 6, 'faithful': False, 'group': '864.2236', 'group_order': 864, 'image': None, 'label': '864.2236.1f', 'multiplicity': 2, 'nt': [4, 1], 'qdim': 2, 'qvalues': [2, -2, 2, -2, 2, -2, 2, 2, 2, 2, 0, 0, 0, 0, 2, 0, 0, -2, 0, 0, -2, 2, -2, 2, -2, -2, 2, -2, -2, 2, -2, -2, 2, -2, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 13153136
    {'cdim': 2, 'counter': 7, 'faithful': False, 'group': '864.2236', 'group_order': 864, 'image': None, 'label': '864.2236.2a', 'multiplicity': 1, 'nt': [3, 2], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 0, 0, 2, -1, 2, -1, 0, 0, 2, 2, 0, 2, 2, 0, 0, 0, 2, 2, -1, -1, 2, -1, -1, -1, 2, 0, 0, -1, 0, 0, -1, -1, -1, -1, 0, 0], 'schur_index': 1}
  • id: 13153137
    {'cdim': 2, 'counter': 8, 'faithful': False, 'group': '864.2236', 'group_order': 864, 'image': None, 'label': '864.2236.2b', 'multiplicity': 1, 'nt': [3, 2], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 0, 0, 2, 2, -1, -1, 2, 2, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -1, 0, 0, -1, 0, 0, 0, 0, 0, 0, -1, -1], 'schur_index': 1}
  • id: 13153138
    {'cdim': 2, 'counter': 9, 'faithful': False, 'group': '864.2236', 'group_order': 864, 'image': None, 'label': '864.2236.2c', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 0, 0, 2, -1, 2, -1, 0, 0, -2, -2, 0, -2, -2, 0, 0, 0, 2, 2, -1, -1, 2, -1, -1, -1, 2, 0, 0, -1, 0, 0, 1, 1, 1, 1, 0, 0], 'schur_index': 1}
  • id: 13153107
    {'cdim': 2, 'counter': 10, 'faithful': False, 'group': '864.2236', 'group_order': 864, 'image': None, 'label': '864.2236.2d', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 0, 0, 2, 2, -1, -1, -2, -2, 0, 0, 0, 0, 0, 0, -2, -2, 2, 2, 2, 2, 2, 2, 2, 2, -1, 0, 0, -1, 0, 0, 0, 0, 0, 0, 1, 1], 'schur_index': 1}
  • id: 13153110
    {'cdim': 3, 'counter': 13, 'faithful': False, 'group': '864.2236', 'group_order': 864, 'image': None, 'label': '864.2236.3a', 'multiplicity': 1, 'nt': [4, 5], 'qdim': 3, 'qvalues': [3, 3, -1, -1, 1, 1, 3, 3, 0, 0, 3, 3, 1, 1, -1, -1, -1, -1, -1, -1, 3, -1, -1, -1, -1, 3, -1, -1, 0, 1, 1, 0, -1, -1, 1, -1, -1, 1, 0, 0], 'schur_index': 1}
  • id: 13153111
    {'cdim': 3, 'counter': 14, 'faithful': False, 'group': '864.2236', 'group_order': 864, 'image': None, 'label': '864.2236.3b', 'multiplicity': 1, 'nt': [6, 8], 'qdim': 3, 'qvalues': [3, 3, -1, -1, -1, -1, 3, 3, 0, 0, 3, 3, -1, -1, 1, 1, 1, 1, -1, -1, 3, -1, -1, -1, -1, 3, -1, -1, 0, -1, -1, 0, 1, 1, -1, 1, 1, -1, 0, 0], 'schur_index': 1}
  • id: 13153112
    {'cdim': 3, 'counter': 15, 'faithful': False, 'group': '864.2236', 'group_order': 864, 'image': None, 'label': '864.2236.3c', 'multiplicity': 1, 'nt': [6, 11], 'qdim': 3, 'qvalues': [3, 3, -1, -1, -1, -1, 3, 3, 0, 0, -3, -3, 1, 1, 1, -1, -1, 1, 1, 1, 3, -1, -1, -1, -1, 3, -1, -1, 0, -1, -1, 0, 1, 1, 1, -1, -1, 1, 0, 0], 'schur_index': 1}
  • id: 13153113
    {'cdim': 3, 'counter': 16, 'faithful': False, 'group': '864.2236', 'group_order': 864, 'image': None, 'label': '864.2236.3d', 'multiplicity': 1, 'nt': [6, 11], 'qdim': 3, 'qvalues': [3, 3, -1, -1, 1, 1, 3, 3, 0, 0, -3, -3, -1, -1, -1, 1, 1, -1, 1, 1, 3, -1, -1, -1, -1, 3, -1, -1, 0, 1, 1, 0, -1, -1, -1, 1, 1, -1, 0, 0], 'schur_index': 1}
  • id: 13153108
    {'cdim': 2, 'counter': 11, 'faithful': False, 'group': '864.2236', 'group_order': 864, 'image': None, 'label': '864.2236.2e', 'multiplicity': 2, 'nt': [12, 11], 'qdim': 4, 'qvalues': [4, -4, 4, -4, 0, 0, 4, -2, 4, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 4, 2, -2, -4, 2, -2, 2, -4, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 13153109
    {'cdim': 2, 'counter': 12, 'faithful': False, 'group': '864.2236', 'group_order': 864, 'image': None, 'label': '864.2236.2f', 'multiplicity': 2, 'nt': [12, 11], 'qdim': 4, 'qvalues': [4, -4, 4, -4, 0, 0, 4, 4, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 4, -4, 4, -4, -4, 4, -4, 2, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 13153116
    {'cdim': 4, 'counter': 19, 'faithful': False, 'group': '864.2236', 'group_order': 864, 'image': None, 'label': '864.2236.4a', 'multiplicity': 1, 'nt': [6, 9], 'qdim': 4, 'qvalues': [4, 4, 4, 4, 0, 0, 4, -2, -2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, -2, -2, 4, -2, -2, -2, -2, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 13153118
    {'cdim': 4, 'counter': 20, 'faithful': False, 'group': '864.2236', 'group_order': 864, 'image': None, 'label': '864.2236.4b', 'multiplicity': 1, 'nt': [12, 39], 'qdim': 4, 'qvalues': [4, -4, 4, -4, 0, 0, 4, -2, -2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 4, 2, -2, -4, 2, -2, 2, 2, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 13153114
    {'cdim': 3, 'counter': 17, 'faithful': False, 'group': '864.2236', 'group_order': 864, 'image': None, 'label': '864.2236.3e', 'multiplicity': 2, 'nt': [12, 53], 'qdim': 6, 'qvalues': [6, -6, -2, 2, -2, 2, 6, 6, 0, 0, 0, 0, 0, 0, 2, 0, 0, -2, 0, 0, -6, -2, 2, -2, 2, -6, -2, 2, 0, -2, 2, 0, 2, -2, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 13153115
    {'cdim': 3, 'counter': 18, 'faithful': False, 'group': '864.2236', 'group_order': 864, 'image': None, 'label': '864.2236.3f', 'multiplicity': 2, 'nt': [12, 53], 'qdim': 6, 'qvalues': [6, -6, -2, 2, 2, -2, 6, 6, 0, 0, 0, 0, 0, 0, -2, 0, 0, 2, 0, 0, -6, -2, 2, -2, 2, -6, -2, 2, 0, 2, -2, 0, -2, 2, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 13153119
    {'cdim': 6, 'counter': 21, 'faithful': False, 'group': '864.2236', 'group_order': 864, 'image': None, 'label': '864.2236.6a', 'multiplicity': 1, 'nt': [9, 18], 'qdim': 6, 'qvalues': [6, 6, 6, 6, 2, 2, -3, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, -3, -3, 0, 0, -3, 0, 0, 0, 0, -1, -1, 0, -1, -1, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 13153120
    {'cdim': 6, 'counter': 22, 'faithful': False, 'group': '864.2236', 'group_order': 864, 'image': None, 'label': '864.2236.6b', 'multiplicity': 1, 'nt': [12, 83], 'qdim': 6, 'qvalues': [6, 6, -2, -2, 0, 0, 6, -3, 0, 0, 0, 0, 2, 2, 0, -2, -2, 0, 0, 0, 6, -2, 1, 1, -2, -3, 1, 1, 0, 0, 0, 0, 0, 0, -1, 1, 1, -1, 0, 0], 'schur_index': 1}
  • id: 13153121
    {'cdim': 6, 'counter': 23, 'faithful': False, 'group': '864.2236', 'group_order': 864, 'image': None, 'label': '864.2236.6c', 'multiplicity': 1, 'nt': [18, 51], 'qdim': 6, 'qvalues': [6, 6, 6, 6, -2, -2, -3, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, -2, 0, 0, -3, -3, 0, 0, -3, 0, 0, 0, 0, 1, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 13153122
    {'cdim': 6, 'counter': 24, 'faithful': False, 'group': '864.2236', 'group_order': 864, 'image': None, 'label': '864.2236.6d', 'multiplicity': 1, 'nt': [18, 69], 'qdim': 6, 'qvalues': [6, 6, -2, -2, 0, 0, 6, -3, 0, 0, 0, 0, -2, -2, 0, 2, 2, 0, 0, 0, 6, -2, 1, 1, -2, -3, 1, 1, 0, 0, 0, 0, 0, 0, 1, -1, -1, 1, 0, 0], 'schur_index': 1}
  • id: 13153123
    {'cdim': 6, 'counter': 25, 'faithful': False, 'group': '864.2236', 'group_order': 864, 'image': None, 'label': '864.2236.6e', 'multiplicity': 1, 'nt': [18, 152], 'qdim': 6, 'qvalues': [6, 6, -2, -2, -2, -2, -3, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, -3, 1, 4, 4, 1, 0, -2, -2, 0, 1, 1, 0, -1, -1, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 13153124
    {'cdim': 6, 'counter': 26, 'faithful': False, 'group': '864.2236', 'group_order': 864, 'image': None, 'label': '864.2236.6f', 'multiplicity': 1, 'nt': [18, 153], 'qdim': 6, 'qvalues': [6, 6, -2, -2, 2, 2, -3, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, -2, 0, 0, -3, 1, 4, 4, 1, 0, -2, -2, 0, -1, -1, 0, 1, 1, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 13153125
    {'cdim': 6, 'counter': 27, 'faithful': False, 'group': '864.2236', 'group_order': 864, 'image': None, 'label': '864.2236.6g', 'multiplicity': 1, 'nt': [36, 247], 'qdim': 6, 'qvalues': [6, -6, 6, -6, -2, 2, -3, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 2, 0, 0, 3, -3, 0, 0, 3, 0, 0, 0, 0, 1, -1, 0, 1, -1, 0, 0, 0, 0, 0, 0], 'schur_index': 2}
  • id: 13153126
    {'cdim': 6, 'counter': 28, 'faithful': False, 'group': '864.2236', 'group_order': 864, 'image': None, 'label': '864.2236.6h', 'multiplicity': 1, 'nt': [36, 247], 'qdim': 6, 'qvalues': [6, -6, 6, -6, 2, -2, -3, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, -2, 0, 0, 3, -3, 0, 0, 3, 0, 0, 0, 0, -1, 1, 0, -1, 1, 0, 0, 0, 0, 0, 0], 'schur_index': 2}
  • id: 13153127
    {'cdim': 6, 'counter': 29, 'faithful': True, 'group': '864.2236', 'group_order': 864, 'image': None, 'label': '864.2236.6i', 'multiplicity': 1, 'nt': [36, 1337], 'qdim': 6, 'qvalues': [6, -6, -2, 2, -2, 2, -3, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, -2, 0, 0, 3, 1, -4, 4, -1, 0, -2, 2, 0, 1, -1, 0, -1, 1, 0, 0, 0, 0, 0, 0], 'schur_index': 2}
  • id: 13153129
    {'cdim': 6, 'counter': 30, 'faithful': True, 'group': '864.2236', 'group_order': 864, 'image': None, 'label': '864.2236.6j', 'multiplicity': 1, 'nt': [36, 1337], 'qdim': 6, 'qvalues': [6, -6, -2, 2, 2, -2, -3, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 2, 0, 0, 3, 1, -4, 4, -1, 0, -2, 2, 0, -1, 1, 0, 1, -1, 0, 0, 0, 0, 0, 0], 'schur_index': 2}
  • id: 13153130
    {'cdim': 6, 'counter': 31, 'faithful': False, 'group': '864.2236', 'group_order': 864, 'image': None, 'label': '864.2236.6k', 'multiplicity': 2, 'nt': [36, 347], 'qdim': 12, 'qvalues': [12, -12, -4, 4, 0, 0, 12, -6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -12, -4, -2, 2, 4, 6, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 13153131
    {'cdim': 12, 'counter': 32, 'faithful': False, 'group': '864.2236', 'group_order': 864, 'image': None, 'label': '864.2236.12a', 'multiplicity': 1, 'nt': [36, 608], 'qdim': 12, 'qvalues': [12, 12, -4, -4, 0, 0, -6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -6, 2, -4, -4, 2, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 13153132
    {'cdim': 12, 'counter': 33, 'faithful': True, 'group': '864.2236', 'group_order': 864, 'image': None, 'label': '864.2236.12b', 'multiplicity': 1, 'nt': [72, 0], 'qdim': 12, 'qvalues': [12, -12, -4, 4, 0, 0, -6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 2, 4, -4, -2, 0, 2, -2, 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: 30987519
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 864, 'counter': 1, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '864.2236', 'group_counter': 2236, 'group_order': 864, 'image': None, 'image_isoclass': '1.1', 'image_order': 1, 'indicator': 1, 'kernel': '1.a1.a1', 'kernel_order': 864, 'label': '864.2236.1a', '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]]]}
  • id: 30987530
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 864, 'counter': 2, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '864.2236', 'group_counter': 2236, 'group_order': 864, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.c1.a1', 'kernel_order': 432, 'label': '864.2236.1b', '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]]]}
  • id: 30987541
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 864, 'counter': 3, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '864.2236', 'group_counter': 2236, 'group_order': 864, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.b1.a1', 'kernel_order': 432, 'label': '864.2236.1c', '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]]]}
  • id: 30987552
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 864, 'counter': 4, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '864.2236', 'group_counter': 2236, 'group_order': 864, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.a1.a1', 'kernel_order': 432, 'label': '864.2236.1d', '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]]]}
  • id: 30987554
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 864, 'counter': 5, 'cyclotomic_n': 4, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '864.2236', 'group_counter': 2236, 'group_order': 864, 'image': None, 'image_isoclass': '4.1', 'image_order': 4, 'indicator': 0, 'kernel': '4.b1.b1', 'kernel_order': 216, 'label': '864.2236.1e1', 'nt': [4, 1], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[-1, 0]], [[1, 1]], [[-1, 1]], [[1, 0]], [[-1, 1]], [[1, 1]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]]]}
  • id: 30987555
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 864, 'counter': 6, 'cyclotomic_n': 4, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '864.2236', 'group_counter': 2236, 'group_order': 864, 'image': None, 'image_isoclass': '4.1', 'image_order': 4, 'indicator': 0, 'kernel': '4.b1.b1', 'kernel_order': 216, 'label': '864.2236.1e2', 'nt': [4, 2], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[-1, 0]], [[-1, 1]], [[1, 1]], [[1, 0]], [[1, 1]], [[-1, 1]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]]]}
  • id: 30987556
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 864, 'counter': 7, 'cyclotomic_n': 4, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '864.2236', 'group_counter': 2236, 'group_order': 864, 'image': None, 'image_isoclass': '4.1', 'image_order': 4, 'indicator': 0, 'kernel': '4.b1.a1', 'kernel_order': 216, 'label': '864.2236.1f1', 'nt': [4, 1], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[1, 0]], [[-1, 1]], [[1, 1]], [[-1, 0]], [[-1, 1]], [[1, 1]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]]]}
  • id: 30987557
    {'center': '1.a1.a1', 'center_index': 1, 'center_order': 864, 'counter': 8, 'cyclotomic_n': 4, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '864.2236', 'group_counter': 2236, 'group_order': 864, 'image': None, 'image_isoclass': '4.1', 'image_order': 4, 'indicator': 0, 'kernel': '4.b1.a1', 'kernel_order': 216, 'label': '864.2236.1f2', 'nt': [4, 2], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 0]], [[1, 1]], [[-1, 1]], [[-1, 0]], [[1, 1]], [[-1, 1]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]]]}
  • id: 30987558
    {'center': '6.b1.a1', 'center_index': 6, 'center_order': 144, 'counter': 9, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '864.2236', 'group_counter': 2236, 'group_order': 864, 'image': None, 'image_isoclass': '6.1', 'image_order': 6, 'indicator': 1, 'kernel': '6.b1.a1', 'kernel_order': 144, 'label': '864.2236.2a', 'nt': [3, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]]]}
  • id: 30987520
    {'center': '6.a1.a1', 'center_index': 6, 'center_order': 144, 'counter': 10, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '864.2236', 'group_counter': 2236, 'group_order': 864, 'image': None, 'image_isoclass': '6.1', 'image_order': 6, 'indicator': 1, 'kernel': '6.a1.a1', 'kernel_order': 144, 'label': '864.2236.2b', 'nt': [3, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[2, 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]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 30987521
    {'center': '6.b1.a1', 'center_index': 6, 'center_order': 144, 'counter': 11, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '864.2236', 'group_counter': 2236, 'group_order': 864, 'image': None, 'image_isoclass': '12.4', 'image_order': 12, 'indicator': 1, 'kernel': '12.b1.a1', 'kernel_order': 72, 'label': '864.2236.2c', 'nt': [6, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]]]}
  • id: 30987522
    {'center': '6.a1.a1', 'center_index': 6, 'center_order': 144, 'counter': 12, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '864.2236', 'group_counter': 2236, 'group_order': 864, 'image': None, 'image_isoclass': '12.4', 'image_order': 12, 'indicator': 1, 'kernel': '12.a1.a1', 'kernel_order': 72, 'label': '864.2236.2d', 'nt': [6, 3], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-2, 0]], [[-2, 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]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]]]}
  • id: 30987523
    {'center': '6.b1.a1', 'center_index': 6, 'center_order': 144, 'counter': 13, 'cyclotomic_n': 4, 'dim': 2, 'faithful': False, 'field': [1, 0, 1], 'group': '864.2236', 'group_counter': 2236, 'group_order': 864, 'image': None, 'image_isoclass': '24.5', 'image_order': 24, 'indicator': 0, 'kernel': '24.c1.a1', 'kernel_order': 36, 'label': '864.2236.2e1', 'nt': [12, 11], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-2, 1]], [[2, 1]], [[0, 0]], [[-2, 1]], [[2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[1, 0]], [[-1, 0]], [[-2, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[0, 0]], [[0, 0]]]}
  • id: 30987524
    {'center': '6.b1.a1', 'center_index': 6, 'center_order': 144, 'counter': 14, 'cyclotomic_n': 4, 'dim': 2, 'faithful': False, 'field': [1, 0, 1], 'group': '864.2236', 'group_counter': 2236, 'group_order': 864, 'image': None, 'image_isoclass': '24.5', 'image_order': 24, 'indicator': 0, 'kernel': '24.c1.a1', 'kernel_order': 36, 'label': '864.2236.2e2', 'nt': [12, 2], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[2, 1]], [[-2, 1]], [[0, 0]], [[2, 1]], [[-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[1, 0]], [[-1, 0]], [[-2, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[0, 0]], [[0, 0]]]}
  • id: 30987525
    {'center': '6.a1.a1', 'center_index': 6, 'center_order': 144, 'counter': 15, 'cyclotomic_n': 4, 'dim': 2, 'faithful': False, 'field': [1, 0, 1], 'group': '864.2236', 'group_counter': 2236, 'group_order': 864, 'image': None, 'image_isoclass': '24.5', 'image_order': 24, 'indicator': 0, 'kernel': '24.b1.a1', 'kernel_order': 36, 'label': '864.2236.2f1', 'nt': [12, 11], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[-2, 1]], [[2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1]], [[2, 1]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1]], [[1, 1]]]}
  • id: 30987526
    {'center': '6.a1.a1', 'center_index': 6, 'center_order': 144, 'counter': 16, 'cyclotomic_n': 4, 'dim': 2, 'faithful': False, 'field': [1, 0, 1], 'group': '864.2236', 'group_counter': 2236, 'group_order': 864, 'image': None, 'image_isoclass': '24.5', 'image_order': 24, 'indicator': 0, 'kernel': '24.b1.a1', 'kernel_order': 36, 'label': '864.2236.2f2', 'nt': [12, 2], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[-1, 0]], [[2, 1]], [[-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1]], [[-2, 1]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1]], [[-1, 1]]]}
  • id: 30987527
    {'center': '24.a1.a1', 'center_index': 24, 'center_order': 36, 'counter': 17, 'cyclotomic_n': 1, 'dim': 3, 'faithful': False, 'field': [0, 1], 'group': '864.2236', 'group_counter': 2236, 'group_order': 864, 'image': None, 'image_isoclass': '24.12', 'image_order': 24, 'indicator': 1, 'kernel': '24.a1.a1', 'kernel_order': 36, 'label': '864.2236.3a', 'nt': [4, 5], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[3, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]]]}
  • id: 30987528
    {'center': '24.a1.a1', 'center_index': 24, 'center_order': 36, 'counter': 18, 'cyclotomic_n': 1, 'dim': 3, 'faithful': False, 'field': [0, 1], 'group': '864.2236', 'group_counter': 2236, 'group_order': 864, 'image': None, 'image_isoclass': '24.12', 'image_order': 24, 'indicator': 1, 'kernel': '24.a1.a1', 'kernel_order': 36, 'label': '864.2236.3b', 'nt': [6, 8], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]]]}
  • id: 30987529
    {'center': '24.a1.a1', 'center_index': 24, 'center_order': 36, 'counter': 19, 'cyclotomic_n': 1, 'dim': 3, 'faithful': False, 'field': [0, 1], 'group': '864.2236', 'group_counter': 2236, 'group_order': 864, 'image': None, 'image_isoclass': '48.48', 'image_order': 48, 'indicator': 1, 'kernel': '48.a1.a1', 'kernel_order': 18, 'label': '864.2236.3c', 'nt': [6, 11], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]]]}
  • id: 30987531
    {'center': '24.a1.a1', 'center_index': 24, 'center_order': 36, 'counter': 20, 'cyclotomic_n': 1, 'dim': 3, 'faithful': False, 'field': [0, 1], 'group': '864.2236', 'group_counter': 2236, 'group_order': 864, 'image': None, 'image_isoclass': '48.48', 'image_order': 48, 'indicator': 1, 'kernel': '48.a1.a1', 'kernel_order': 18, 'label': '864.2236.3d', 'nt': [6, 11], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]]]}
  • id: 30987532
    {'center': '24.a1.a1', 'center_index': 24, 'center_order': 36, 'counter': 21, 'cyclotomic_n': 4, 'dim': 3, 'faithful': False, 'field': [1, 0, 1], 'group': '864.2236', 'group_counter': 2236, 'group_order': 864, 'image': None, 'image_isoclass': '96.186', 'image_order': 96, 'indicator': 0, 'kernel': '96.a1.a1', 'kernel_order': 9, 'label': '864.2236.3e1', 'nt': [12, 53], 'q_character': None, 'values': [[[3, 0]], [[-3, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[-3, 1]], [[3, 1]], [[1, 1]], [[-1, 1]], [[1, 0]], [[-1, 1]], [[1, 1]], [[-1, 0]], [[1, 1]], [[-1, 1]], [[-3, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-3, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[0, 0]], [[0, 0]]]}
  • id: 30987533
    {'center': '24.a1.a1', 'center_index': 24, 'center_order': 36, 'counter': 22, 'cyclotomic_n': 4, 'dim': 3, 'faithful': False, 'field': [1, 0, 1], 'group': '864.2236', 'group_counter': 2236, 'group_order': 864, 'image': None, 'image_isoclass': '96.186', 'image_order': 96, 'indicator': 0, 'kernel': '96.a1.a1', 'kernel_order': 9, 'label': '864.2236.3e2', 'nt': [12, 2], 'q_character': None, 'values': [[[3, 0]], [[-3, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[3, 1]], [[-3, 1]], [[-1, 1]], [[1, 1]], [[1, 0]], [[1, 1]], [[-1, 1]], [[-1, 0]], [[-1, 1]], [[1, 1]], [[-3, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-3, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[0, 0]], [[0, 0]]]}
  • id: 30987534
    {'center': '24.a1.a1', 'center_index': 24, 'center_order': 36, 'counter': 23, 'cyclotomic_n': 4, 'dim': 3, 'faithful': False, 'field': [1, 0, 1], 'group': '864.2236', 'group_counter': 2236, 'group_order': 864, 'image': None, 'image_isoclass': '96.186', 'image_order': 96, 'indicator': 0, 'kernel': '96.a1.a1', 'kernel_order': 9, 'label': '864.2236.3f1', 'nt': [12, 53], 'q_character': None, 'values': [[[3, 0]], [[-3, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[-3, 1]], [[3, 1]], [[-1, 1]], [[1, 1]], [[-1, 0]], [[1, 1]], [[-1, 1]], [[1, 0]], [[1, 1]], [[-1, 1]], [[-3, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-3, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[0, 0]], [[0, 0]]]}
  • id: 30987535
    {'center': '24.a1.a1', 'center_index': 24, 'center_order': 36, 'counter': 24, 'cyclotomic_n': 4, 'dim': 3, 'faithful': False, 'field': [1, 0, 1], 'group': '864.2236', 'group_counter': 2236, 'group_order': 864, 'image': None, 'image_isoclass': '96.186', 'image_order': 96, 'indicator': 0, 'kernel': '96.a1.a1', 'kernel_order': 9, 'label': '864.2236.3f2', 'nt': [12, 2], 'q_character': None, 'values': [[[3, 0]], [[-3, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[3, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[3, 1]], [[-3, 1]], [[1, 1]], [[-1, 1]], [[-1, 0]], [[-1, 1]], [[1, 1]], [[1, 0]], [[-1, 1]], [[1, 1]], [[-3, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-3, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[0, 0]], [[0, 0]]]}
  • id: 30987536
    {'center': '36.a1.a1', 'center_index': 36, 'center_order': 24, 'counter': 25, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '864.2236', 'group_counter': 2236, 'group_order': 864, 'image': None, 'image_isoclass': '36.10', 'image_order': 36, 'indicator': 1, 'kernel': '36.a1.a1', 'kernel_order': 24, 'label': '864.2236.4a', 'nt': [6, 9], 'q_character': None, 'values': [[[4, 0]], [[4, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 30987537
    {'center': '36.a1.a1', 'center_index': 36, 'center_order': 24, 'counter': 26, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '864.2236', 'group_counter': 2236, 'group_order': 864, 'image': None, 'image_isoclass': '72.21', 'image_order': 72, 'indicator': 1, 'kernel': '72.a1.a1', 'kernel_order': 12, 'label': '864.2236.4b', 'nt': [12, 39], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[4, 0]], [[2, 0]], [[-2, 0]], [[-4, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 30987538
    {'center': '108.a1.a1', 'center_index': 108, 'center_order': 8, 'counter': 27, 'cyclotomic_n': 1, 'dim': 6, 'faithful': False, 'field': [0, 1], 'group': '864.2236', 'group_counter': 2236, 'group_order': 864, 'image': None, 'image_isoclass': '108.17', 'image_order': 108, 'indicator': 1, 'kernel': '108.a1.a1', 'kernel_order': 8, 'label': '864.2236.6a', 'nt': [9, 18], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[6, 0]], [[6, 0]], [[2, 0]], [[2, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 30987539
    {'center': '144.a1.a1', 'center_index': 144, 'center_order': 6, 'counter': 28, 'cyclotomic_n': 1, 'dim': 6, 'faithful': False, 'field': [0, 1], 'group': '864.2236', 'group_counter': 2236, 'group_order': 864, 'image': None, 'image_isoclass': '144.183', 'image_order': 144, 'indicator': 1, 'kernel': '144.a1.a1', 'kernel_order': 6, 'label': '864.2236.6b', 'nt': [12, 83], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[-3, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]]]}
  • id: 30987540
    {'center': '108.a1.a1', 'center_index': 108, 'center_order': 8, 'counter': 29, 'cyclotomic_n': 1, 'dim': 6, 'faithful': False, 'field': [0, 1], 'group': '864.2236', 'group_counter': 2236, 'group_order': 864, 'image': None, 'image_isoclass': '108.17', 'image_order': 108, 'indicator': 1, 'kernel': '108.a1.a1', 'kernel_order': 8, 'label': '864.2236.6c', 'nt': [18, 51], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[6, 0]], [[6, 0]], [[-2, 0]], [[-2, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 30987542
    {'center': '144.a1.a1', 'center_index': 144, 'center_order': 6, 'counter': 30, 'cyclotomic_n': 1, 'dim': 6, 'faithful': False, 'field': [0, 1], 'group': '864.2236', 'group_counter': 2236, 'group_order': 864, 'image': None, 'image_isoclass': '144.183', 'image_order': 144, 'indicator': 1, 'kernel': '144.a1.a1', 'kernel_order': 6, 'label': '864.2236.6d', 'nt': [18, 69], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[-2, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[-3, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]]]}
  • id: 30987543
    {'center': '432.a1.a1', 'center_index': 432, 'center_order': 2, 'counter': 31, 'cyclotomic_n': 1, 'dim': 6, 'faithful': False, 'field': [0, 1], 'group': '864.2236', 'group_counter': 2236, 'group_order': 864, 'image': None, 'image_isoclass': '432.523', 'image_order': 432, 'indicator': 1, 'kernel': '432.a1.a1', 'kernel_order': 2, 'label': '864.2236.6e', 'nt': [18, 152], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[1, 0]], [[4, 0]], [[4, 0]], [[1, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 30987544
    {'center': '432.a1.a1', 'center_index': 432, 'center_order': 2, 'counter': 32, 'cyclotomic_n': 1, 'dim': 6, 'faithful': False, 'field': [0, 1], 'group': '864.2236', 'group_counter': 2236, 'group_order': 864, 'image': None, 'image_isoclass': '432.523', 'image_order': 432, 'indicator': 1, 'kernel': '432.a1.a1', 'kernel_order': 2, 'label': '864.2236.6f', 'nt': [18, 153], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[1, 0]], [[4, 0]], [[4, 0]], [[1, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 30987545
    {'center': '108.a1.a1', 'center_index': 108, 'center_order': 8, 'counter': 33, 'cyclotomic_n': 1, 'dim': 6, 'faithful': False, 'field': [0, 1], 'group': '864.2236', 'group_counter': 2236, 'group_order': 864, 'image': None, 'image_isoclass': '216.36', 'image_order': 216, 'indicator': -1, 'kernel': '216.a1.a1', 'kernel_order': 4, 'label': '864.2236.6g', 'nt': [36, 247], 'q_character': None, 'values': [[[6, 0]], [[-6, 0]], [[6, 0]], [[-6, 0]], [[-2, 0]], [[2, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 30987546
    {'center': '108.a1.a1', 'center_index': 108, 'center_order': 8, 'counter': 34, 'cyclotomic_n': 1, 'dim': 6, 'faithful': False, 'field': [0, 1], 'group': '864.2236', 'group_counter': 2236, 'group_order': 864, 'image': None, 'image_isoclass': '216.36', 'image_order': 216, 'indicator': -1, 'kernel': '216.a1.a1', 'kernel_order': 4, 'label': '864.2236.6h', 'nt': [36, 247], 'q_character': None, 'values': [[[6, 0]], [[-6, 0]], [[6, 0]], [[-6, 0]], [[2, 0]], [[-2, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 30987547
    {'center': '432.a1.a1', 'center_index': 432, 'center_order': 2, 'counter': 35, 'cyclotomic_n': 1, 'dim': 6, 'faithful': True, 'field': [0, 1], 'group': '864.2236', 'group_counter': 2236, 'group_order': 864, 'image': None, 'image_isoclass': '864.2236', 'image_order': 864, 'indicator': -1, 'kernel': '864.a1.a1', 'kernel_order': 1, 'label': '864.2236.6i', 'nt': [36, 1337], 'q_character': None, 'values': [[[6, 0]], [[-6, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[1, 0]], [[-4, 0]], [[4, 0]], [[-1, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 30987548
    {'center': '432.a1.a1', 'center_index': 432, 'center_order': 2, 'counter': 36, 'cyclotomic_n': 1, 'dim': 6, 'faithful': True, 'field': [0, 1], 'group': '864.2236', 'group_counter': 2236, 'group_order': 864, 'image': None, 'image_isoclass': '864.2236', 'image_order': 864, 'indicator': -1, 'kernel': '864.a1.a1', 'kernel_order': 1, 'label': '864.2236.6j', 'nt': [36, 1337], 'q_character': None, 'values': [[[6, 0]], [[-6, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[1, 0]], [[-4, 0]], [[4, 0]], [[-1, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 30987549
    {'center': '144.a1.a1', 'center_index': 144, 'center_order': 6, 'counter': 37, 'cyclotomic_n': 4, 'dim': 6, 'faithful': False, 'field': [1, 0, 1], 'group': '864.2236', 'group_counter': 2236, 'group_order': 864, 'image': None, 'image_isoclass': '288.854', 'image_order': 288, 'indicator': 0, 'kernel': '288.a1.a1', 'kernel_order': 3, 'label': '864.2236.6k1', 'nt': [36, 347], 'q_character': None, 'values': [[[6, 0]], [[-6, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1]], [[2, 1]], [[0, 0]], [[2, 1]], [[-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[-2, 0]], [[-1, 0]], [[1, 0]], [[2, 0]], [[3, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[0, 0]], [[0, 0]]]}
  • id: 30987550
    {'center': '144.a1.a1', 'center_index': 144, 'center_order': 6, 'counter': 38, 'cyclotomic_n': 4, 'dim': 6, 'faithful': False, 'field': [1, 0, 1], 'group': '864.2236', 'group_counter': 2236, 'group_order': 864, 'image': None, 'image_isoclass': '288.854', 'image_order': 288, 'indicator': 0, 'kernel': '288.a1.a1', 'kernel_order': 3, 'label': '864.2236.6k2', 'nt': [36, 2], 'q_character': None, 'values': [[[6, 0]], [[-6, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[6, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1]], [[-2, 1]], [[0, 0]], [[-2, 1]], [[2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[-6, 0]], [[-2, 0]], [[-1, 0]], [[1, 0]], [[2, 0]], [[3, 0]], [[1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[0, 0]], [[0, 0]]]}
  • id: 30987551
    {'center': '432.a1.a1', 'center_index': 432, 'center_order': 2, 'counter': 39, 'cyclotomic_n': 1, 'dim': 12, 'faithful': False, 'field': [0, 1], 'group': '864.2236', 'group_counter': 2236, 'group_order': 864, 'image': None, 'image_isoclass': '432.523', 'image_order': 432, 'indicator': 1, 'kernel': '432.a1.a1', 'kernel_order': 2, 'label': '864.2236.12a', 'nt': [36, 608], 'q_character': None, 'values': [[[12, 0]], [[12, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 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]], [[-6, 0]], [[2, 0]], [[-4, 0]], [[-4, 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]]]}
  • id: 30987553
    {'center': '432.a1.a1', 'center_index': 432, 'center_order': 2, 'counter': 40, 'cyclotomic_n': 1, 'dim': 12, 'faithful': True, 'field': [0, 1], 'group': '864.2236', 'group_counter': 2236, 'group_order': 864, 'image': None, 'image_isoclass': '864.2236', 'image_order': 864, 'indicator': -1, 'kernel': '864.a1.a1', 'kernel_order': 1, 'label': '864.2236.12b', 'nt': [72, 0], 'q_character': None, 'values': [[[12, 0]], [[-12, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[0, 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]], [[6, 0]], [[2, 0]], [[4, 0]], [[-4, 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]]]}
• 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: 111526746
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '864.2236', 'ambient_counter': 2236, 'ambient_order': 864, 'ambient_tex': 'C_3^2:(C_4\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 864, 'counter': 1, 'cyclic': False, 'direct': True, 'hall': 6, 'label': '864.2236.1.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '1.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': False, 'quotient': '1.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 1, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_1', 'simple': False, 'solvable': True, 'special_labels': ['R', 'L0', 'D0', 'C0'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '864.2236', 'subgroup_hash': 2236, 'subgroup_order': 864, 'subgroup_tex': 'C_3^2:(C_4\\times S_4)', 'supersolvable': False, 'sylow': 0}
  • id: 111526857
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '864.2236', 'ambient_counter': 2236, 'ambient_order': 864, 'ambient_tex': 'C_3^2:(C_4\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': True, 'core_order': 432, 'counter': 2, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '864.2236.2.a1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': False, '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': False, 'standard_generators': False, 'stem': False, 'subgroup': '432.538', 'subgroup_hash': 538, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2:D_6', 'supersolvable': False, 'sylow': 0}
  • id: 111526904
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '864.2236', 'ambient_counter': 2236, 'ambient_order': 864, 'ambient_tex': 'C_3^2:(C_4\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 432, 'counter': 3, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '864.2236.2.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': '432.272', 'subgroup_hash': 272, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2:C_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 111526915
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '864.2236', 'ambient_counter': 2236, 'ambient_order': 864, 'ambient_tex': 'C_3^2:(C_4\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 432, 'counter': 4, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '864.2236.2.c1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': ['C1'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '432.251', 'subgroup_hash': 251, 'subgroup_order': 432, 'subgroup_tex': '(C_3\\times A_4):C_{12}', 'supersolvable': False, 'sylow': 0}
  • id: 111526926
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '864.2236', 'ambient_counter': 2236, 'ambient_order': 864, 'ambient_tex': 'C_3^2:(C_4\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 144, 'counter': 5, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '864.2236.3.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': '288.621', 'subgroup_hash': 621, 'subgroup_order': 288, 'subgroup_tex': 'C_2^3.S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 111526937
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '864.2236', 'ambient_counter': 2236, 'ambient_order': 864, 'ambient_tex': 'C_3^2:(C_4\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 144, 'counter': 6, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '864.2236.3.b1.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '3.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '288.853', 'subgroup_hash': 853, 'subgroup_order': 288, 'subgroup_tex': 'C_2^3.S_3^2', 'supersolvable': False, 'sylow': 0}
  • id: 111526948
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '864.2236', 'ambient_counter': 2236, 'ambient_order': 864, 'ambient_tex': 'C_3^2:(C_4\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': True, 'core_order': 216, 'counter': 7, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '864.2236.4.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': ['C2'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '216.107', 'subgroup_hash': 107, 'subgroup_order': 216, 'subgroup_tex': 'C_6^2:C_6', 'supersolvable': False, 'sylow': 0}
  • id: 111526959
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '864.2236', 'ambient_counter': 2236, 'ambient_order': 864, 'ambient_tex': 'C_3^2:(C_4\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 216, 'counter': 8, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '864.2236.4.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '216.95', 'subgroup_hash': 95, 'subgroup_order': 216, 'subgroup_tex': 'C_3^2:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 111526970
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '864.2236', 'ambient_counter': 2236, 'ambient_order': 864, 'ambient_tex': 'C_3^2:(C_4\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 216, 'counter': 9, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '864.2236.4.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '216.95', 'subgroup_hash': 95, 'subgroup_order': 216, 'subgroup_tex': 'C_3^2:S_4', 'supersolvable': False, 'sylow': 0}
  • id: 111526747
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '864.2236', 'ambient_counter': 2236, 'ambient_order': 864, 'ambient_tex': 'C_3^2:(C_4\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 36, 'counter': 10, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '864.2236.4.c1.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4.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': 4, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '216.36', 'subgroup_hash': 36, 'subgroup_order': 216, 'subgroup_tex': 'C_6.S_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 111526758
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '864.2236', 'ambient_counter': 2236, 'ambient_order': 864, 'ambient_tex': 'C_3^2:(C_4\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 144, 'counter': 11, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '864.2236.6.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': '144.176', 'subgroup_hash': 176, 'subgroup_order': 144, 'subgroup_tex': 'C_6^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 111526769
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '864.2236', 'ambient_counter': 2236, 'ambient_order': 864, 'ambient_tex': 'C_3^2:(C_4\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 144, 'counter': 12, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '864.2236.6.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, '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': True, 'standard_generators': False, 'stem': False, 'subgroup': '144.126', 'subgroup_hash': 126, 'subgroup_order': 144, 'subgroup_tex': 'C_6.S_4', 'supersolvable': False, 'sylow': 0}
  • id: 111526780
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '864.2236', 'ambient_counter': 2236, 'ambient_order': 864, 'ambient_tex': 'C_3^2:(C_4\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 36, 'counter': 13, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '864.2236.6.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': '144.146', 'subgroup_hash': 146, 'subgroup_order': 144, 'subgroup_tex': 'D_6.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 111526791
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '864.2236', 'ambient_counter': 2236, 'ambient_order': 864, 'ambient_tex': 'C_3^2:(C_4\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 18, 'counter': 14, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '864.2236.6.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': '144.64', 'subgroup_hash': 64, 'subgroup_order': 144, 'subgroup_tex': 'C_6.D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 111526802
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '864.2236', 'ambient_counter': 2236, 'ambient_order': 864, 'ambient_tex': 'C_3^2:(C_4\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 36, 'counter': 15, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '864.2236.6.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': '144.63', 'subgroup_hash': 63, 'subgroup_order': 144, 'subgroup_tex': 'C_3^2:C_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 111526813
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '864.2236', 'ambient_counter': 2236, 'ambient_order': 864, 'ambient_tex': 'C_3^2:(C_4\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 18, 'counter': 16, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '864.2236.6.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': '144.66', 'subgroup_hash': 66, 'subgroup_order': 144, 'subgroup_tex': 'C_6.D_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 111526824
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '864.2236', 'ambient_counter': 2236, 'ambient_order': 864, 'ambient_tex': 'C_3^2:(C_4\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 72, 'counter': 17, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '864.2236.6.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': '144.167', 'subgroup_hash': 167, 'subgroup_order': 144, 'subgroup_tex': 'C_6^2:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 111526835
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '864.2236', 'ambient_counter': 2236, 'ambient_order': 864, 'ambient_tex': 'C_3^2:(C_4\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 72, 'counter': 18, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '864.2236.6.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, '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': '144.188', 'subgroup_hash': 188, 'subgroup_order': 144, 'subgroup_tex': 'C_6\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 111526846
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '864.2236', 'ambient_counter': 2236, 'ambient_order': 864, 'ambient_tex': 'C_3^2:(C_4\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 24, 'counter': 19, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '864.2236.6.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, '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': '144.188', 'subgroup_hash': 188, 'subgroup_order': 144, 'subgroup_tex': 'C_6\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 111526858
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '864.2236', 'ambient_counter': 2236, 'ambient_order': 864, 'ambient_tex': 'C_3^2:(C_4\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 72, 'counter': 20, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '864.2236.6.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, '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': '144.84', 'subgroup_hash': 84, 'subgroup_order': 144, 'subgroup_tex': 'C_6^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 111526869
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '864.2236', 'ambient_counter': 2236, 'ambient_order': 864, 'ambient_tex': 'C_3^2:(C_4\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 72, 'counter': 21, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '864.2236.6.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': '144.129', 'subgroup_hash': 129, 'subgroup_order': 144, 'subgroup_tex': 'A_4\\times C_3:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 111526880
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '864.2236', 'ambient_counter': 2236, 'ambient_order': 864, 'ambient_tex': 'C_3^2:(C_4\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': True, 'core_order': 108, 'counter': 22, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '864.2236.8.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': '8.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_4', 'simple': False, 'solvable': True, 'special_labels': ['D', 'L1', 'D1', 'C3'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '108.22', 'subgroup_hash': 22, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:A_4', 'supersolvable': False, 'sylow': 0}
  • id: 111526891
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '864.2236', 'ambient_counter': 2236, 'ambient_order': 864, 'ambient_tex': 'C_3^2:(C_4\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 18, 'counter': 23, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '864.2236.8.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.28', 'subgroup_hash': 28, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:D_6', 'supersolvable': True, 'sylow': 0}
  • id: 111526898
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '864.2236', 'ambient_counter': 2236, 'ambient_order': 864, 'ambient_tex': 'C_3^2:(C_4\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 36, 'counter': 24, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '864.2236.8.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.8', 'subgroup_hash': 8, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 111526899
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '864.2236', 'ambient_counter': 2236, 'ambient_order': 864, 'ambient_tex': 'C_3^2:(C_4\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 18, 'counter': 25, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '864.2236.8.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '108.8', 'subgroup_hash': 8, 'subgroup_order': 108, 'subgroup_tex': 'C_3^2:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 111526900
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '864.2236', 'ambient_counter': 2236, 'ambient_order': 864, 'ambient_tex': 'C_3^2:(C_4\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 24, 'counter': 26, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '864.2236.9.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': '96.141', 'subgroup_hash': 141, 'subgroup_order': 96, 'subgroup_tex': 'C_2^3.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 111526901
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '864.2236', 'ambient_counter': 2236, 'ambient_order': 864, 'ambient_tex': 'C_3^2:(C_4\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 27, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '864.2236.9.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': '96.88', 'subgroup_hash': 88, 'subgroup_order': 96, 'subgroup_tex': 'C_2^3.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 111526902
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '864.2236', 'ambient_counter': 2236, 'ambient_order': 864, 'ambient_tex': 'C_3^2:(C_4\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 28, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '864.2236.9.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '9.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 9, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.186', 'subgroup_hash': 186, 'subgroup_order': 96, 'subgroup_tex': 'C_4\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 111526903
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '864.2236', 'ambient_counter': 2236, 'ambient_order': 864, 'ambient_tex': 'C_3^2:(C_4\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': True, 'core_order': 72, 'counter': 29, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '864.2236.12.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '12.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '12.4', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_6', 'simple': False, 'solvable': True, 'special_labels': ['F'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '72.50', 'subgroup_hash': 50, 'subgroup_order': 72, 'subgroup_tex': 'C_2\\times C_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 111526905
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '864.2236', 'ambient_counter': 2236, 'ambient_order': 864, 'ambient_tex': 'C_3^2:(C_4\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': True, 'core_order': 72, 'counter': 30, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '864.2236.12.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': '72.47', 'subgroup_hash': 47, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 111526906
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '864.2236', 'ambient_counter': 2236, 'ambient_order': 864, 'ambient_tex': 'C_3^2:(C_4\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 18, 'counter': 31, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '864.2236.12.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.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': 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': '72.48', 'subgroup_hash': 48, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 111526907
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '864.2236', 'ambient_counter': 2236, 'ambient_order': 864, 'ambient_tex': 'C_3^2:(C_4\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 36, 'counter': 32, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '864.2236.12.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.34', 'subgroup_hash': 34, 'subgroup_order': 72, 'subgroup_tex': 'C_6.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 111526908
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '864.2236', 'ambient_counter': 2236, 'ambient_order': 864, 'ambient_tex': 'C_3^2:(C_4\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 18, 'counter': 33, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '864.2236.12.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.29', 'subgroup_hash': 29, 'subgroup_order': 72, 'subgroup_tex': 'C_6:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 111526909
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '864.2236', 'ambient_counter': 2236, 'ambient_order': 864, 'ambient_tex': 'C_3^2:(C_4\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 18, 'counter': 34, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '864.2236.12.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.29', 'subgroup_hash': 29, 'subgroup_order': 72, 'subgroup_tex': 'C_6:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 111526910
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '864.2236', 'ambient_counter': 2236, 'ambient_order': 864, 'ambient_tex': 'C_3^2:(C_4\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 18, 'counter': 35, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '864.2236.12.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.29', 'subgroup_hash': 29, 'subgroup_order': 72, 'subgroup_tex': 'C_6:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 111526911
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '864.2236', 'ambient_counter': 2236, 'ambient_order': 864, 'ambient_tex': 'C_3^2:(C_4\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 18, 'counter': 36, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '864.2236.12.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.34', 'subgroup_hash': 34, 'subgroup_order': 72, 'subgroup_tex': 'C_6.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 111526912
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '864.2236', 'ambient_counter': 2236, 'ambient_order': 864, 'ambient_tex': 'C_3^2:(C_4\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 24, 'counter': 37, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '864.2236.12.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.47', 'subgroup_hash': 47, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 111526913
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '864.2236', 'ambient_counter': 2236, 'ambient_order': 864, 'ambient_tex': 'C_3^2:(C_4\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 36, 'counter': 38, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '864.2236.12.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.20', 'subgroup_hash': 20, 'subgroup_order': 72, 'subgroup_tex': 'C_6.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 111526914
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '864.2236', 'ambient_counter': 2236, 'ambient_order': 864, 'ambient_tex': 'C_3^2:(C_4\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 18, 'counter': 39, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '864.2236.12.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.20', 'subgroup_hash': 20, 'subgroup_order': 72, 'subgroup_tex': 'C_6.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 111526916
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '864.2236', 'ambient_counter': 2236, 'ambient_order': 864, 'ambient_tex': 'C_3^2:(C_4\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 6, 'counter': 40, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '864.2236.12.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.l1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.20', 'subgroup_hash': 20, 'subgroup_order': 72, 'subgroup_tex': 'C_6.D_6', 'supersolvable': True, 'sylow': 0}
  • id: 111526917
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '864.2236', 'ambient_counter': 2236, 'ambient_order': 864, 'ambient_tex': 'C_3^2:(C_4\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 9, 'counter': 41, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '864.2236.12.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.m1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.30', 'subgroup_hash': 30, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 111526918
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '864.2236', 'ambient_counter': 2236, 'ambient_order': 864, 'ambient_tex': 'C_3^2:(C_4\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 9, 'counter': 42, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '864.2236.12.m1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '72.30', 'subgroup_hash': 30, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 111526919
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '864.2236', 'ambient_counter': 2236, 'ambient_order': 864, 'ambient_tex': 'C_3^2:(C_4\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 36, 'counter': 43, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '864.2236.12.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.n1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.30', 'subgroup_hash': 30, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 111526920
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '864.2236', 'ambient_counter': 2236, 'ambient_order': 864, 'ambient_tex': 'C_3^2:(C_4\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 36, 'counter': 44, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '864.2236.12.n1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, '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': '72.30', 'subgroup_hash': 30, 'subgroup_order': 72, 'subgroup_tex': 'C_6\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 111526921
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '864.2236', 'ambient_counter': 2236, 'ambient_order': 864, 'ambient_tex': 'C_3^2:(C_4\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 36, 'counter': 45, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '864.2236.12.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, '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': '72.42', 'subgroup_hash': 42, 'subgroup_order': 72, 'subgroup_tex': 'C_3\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 111526922
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '864.2236', 'ambient_counter': 2236, 'ambient_order': 864, 'ambient_tex': 'C_3^2:(C_4\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 36, 'counter': 46, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '864.2236.12.o1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, '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': '72.42', 'subgroup_hash': 42, 'subgroup_order': 72, 'subgroup_tex': 'C_3\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 111526923
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '864.2236', 'ambient_counter': 2236, 'ambient_order': 864, 'ambient_tex': 'C_3^2:(C_4\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 12, 'counter': 47, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '864.2236.12.p1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '12.p1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '72.42', 'subgroup_hash': 42, 'subgroup_order': 72, 'subgroup_tex': 'C_3\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 111526924
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '864.2236', 'ambient_counter': 2236, 'ambient_order': 864, 'ambient_tex': 'C_3^2:(C_4\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 12, 'counter': 48, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '864.2236.12.p1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, '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': '72.42', 'subgroup_hash': 42, 'subgroup_order': 72, 'subgroup_tex': 'C_3\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 111526925
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '864.2236', 'ambient_counter': 2236, 'ambient_order': 864, 'ambient_tex': 'C_3^2:(C_4\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 18, 'counter': 49, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '864.2236.16.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '16.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '54.10', 'subgroup_hash': 10, 'subgroup_order': 54, 'subgroup_tex': 'C_2\\times \\He_3', 'supersolvable': True, 'sylow': 0}
  • id: 111526927
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '864.2236', 'ambient_counter': 2236, 'ambient_order': 864, 'ambient_tex': 'C_3^2:(C_4\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 9, 'counter': 50, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '864.2236.16.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.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': 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': '54.8', 'subgroup_hash': 8, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 111526928
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '864.2236', 'ambient_counter': 2236, 'ambient_order': 864, 'ambient_tex': 'C_3^2:(C_4\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 9, 'counter': 51, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '864.2236.16.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.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': 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': '54.8', 'subgroup_hash': 8, 'subgroup_order': 54, 'subgroup_tex': 'C_3^2:S_3', 'supersolvable': True, 'sylow': 0}
  • id: 111526929
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '864.2236', 'ambient_counter': 2236, 'ambient_order': 864, 'ambient_tex': 'C_3^2:(C_4\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 52, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '864.2236.18.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '48.42', 'subgroup_hash': 42, 'subgroup_order': 48, 'subgroup_tex': 'C_6.C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 111526930
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '864.2236', 'ambient_counter': 2236, 'ambient_order': 864, 'ambient_tex': 'C_3^2:(C_4\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 53, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '864.2236.18.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, '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': '48.19', 'subgroup_hash': 19, 'subgroup_order': 48, 'subgroup_tex': 'C_6.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 111526931
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '864.2236', 'ambient_counter': 2236, 'ambient_order': 864, 'ambient_tex': 'C_3^2:(C_4\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 54, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '864.2236.18.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': '48.35', 'subgroup_hash': 35, 'subgroup_order': 48, 'subgroup_tex': 'C_4\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 111526932
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '864.2236', 'ambient_counter': 2236, 'ambient_order': 864, 'ambient_tex': 'C_3^2:(C_4\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 55, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '864.2236.18.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.14', 'subgroup_hash': 14, 'subgroup_order': 48, 'subgroup_tex': 'D_6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 111526933
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '864.2236', 'ambient_counter': 2236, 'ambient_order': 864, 'ambient_tex': 'C_3^2:(C_4\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 56, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '864.2236.18.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, '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': '48.11', 'subgroup_hash': 11, 'subgroup_order': 48, 'subgroup_tex': 'C_{12}:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 111526934
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '864.2236', 'ambient_counter': 2236, 'ambient_order': 864, 'ambient_tex': 'C_3^2:(C_4\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 6, 'counter': 57, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '864.2236.18.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, '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': '48.13', 'subgroup_hash': 13, 'subgroup_order': 48, 'subgroup_tex': 'C_{12}:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 111526935
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '864.2236', 'ambient_counter': 2236, 'ambient_order': 864, 'ambient_tex': 'C_3^2:(C_4\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 58, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '864.2236.18.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, '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': '48.11', 'subgroup_hash': 11, 'subgroup_order': 48, 'subgroup_tex': 'C_{12}:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 111526936
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '864.2236', 'ambient_counter': 2236, 'ambient_order': 864, 'ambient_tex': 'C_3^2:(C_4\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 59, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '864.2236.18.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.12', 'subgroup_hash': 12, 'subgroup_order': 48, 'subgroup_tex': 'C_6.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 111526938
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '864.2236', 'ambient_counter': 2236, 'ambient_order': 864, 'ambient_tex': 'C_3^2:(C_4\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 24, 'counter': 60, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '864.2236.18.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '48.45', 'subgroup_hash': 45, 'subgroup_order': 48, 'subgroup_tex': 'C_6\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 111526939
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '864.2236', 'ambient_counter': 2236, 'ambient_order': 864, 'ambient_tex': 'C_3^2:(C_4\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 8, 'counter': 61, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '864.2236.18.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.43', 'subgroup_hash': 43, 'subgroup_order': 48, 'subgroup_tex': 'C_6:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 111526940
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '864.2236', 'ambient_counter': 2236, 'ambient_order': 864, 'ambient_tex': 'C_3^2:(C_4\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 8, 'counter': 62, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '864.2236.18.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, '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': '48.48', 'subgroup_hash': 48, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 111526941
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '864.2236', 'ambient_counter': 2236, 'ambient_order': 864, 'ambient_tex': 'C_3^2:(C_4\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 8, 'counter': 63, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '864.2236.18.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, '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': '48.48', 'subgroup_hash': 48, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times S_4', 'supersolvable': False, 'sylow': 0}
  • id: 111526942
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '864.2236', 'ambient_counter': 2236, 'ambient_order': 864, 'ambient_tex': 'C_3^2:(C_4\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 24, 'counter': 64, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '864.2236.18.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': '48.42', 'subgroup_hash': 42, 'subgroup_order': 48, 'subgroup_tex': 'C_6.C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 111526943
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '864.2236', 'ambient_counter': 2236, 'ambient_order': 864, 'ambient_tex': 'C_3^2:(C_4\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 24, 'counter': 65, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '864.2236.18.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '18.n1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 18, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.19', 'subgroup_hash': 19, 'subgroup_order': 48, 'subgroup_tex': 'C_6.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 111526944
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '864.2236', 'ambient_counter': 2236, 'ambient_order': 864, 'ambient_tex': 'C_3^2:(C_4\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 66, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '864.2236.18.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': '48.42', 'subgroup_hash': 42, 'subgroup_order': 48, 'subgroup_tex': 'C_6.C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 111526945
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '864.2236', 'ambient_counter': 2236, 'ambient_order': 864, 'ambient_tex': 'C_3^2:(C_4\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 8, 'counter': 67, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '864.2236.18.p1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '48.21', 'subgroup_hash': 21, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 111526946
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '864.2236', 'ambient_counter': 2236, 'ambient_order': 864, 'ambient_tex': 'C_3^2:(C_4\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 68, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '864.2236.18.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': '48.31', 'subgroup_hash': 31, 'subgroup_order': 48, 'subgroup_tex': 'C_4\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 111526947
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '864.2236', 'ambient_counter': 2236, 'ambient_order': 864, 'ambient_tex': 'C_3^2:(C_4\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 69, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '864.2236.18.r1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, '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': '48.30', 'subgroup_hash': 30, 'subgroup_order': 48, 'subgroup_tex': 'A_4:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 111526949
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '864.2236', 'ambient_counter': 2236, 'ambient_order': 864, 'ambient_tex': 'C_3^2:(C_4\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 36, 'counter': 70, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '864.2236.24.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': '24.12', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 12, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'S_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '36.7', 'subgroup_hash': 7, 'subgroup_order': 36, 'subgroup_tex': 'C_3^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 111526950
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '864.2236', 'ambient_counter': 2236, 'ambient_order': 864, 'ambient_tex': 'C_3^2:(C_4\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': True, 'core_order': 36, 'counter': 71, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '864.2236.24.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '24.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '24.5', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4\\times S_3', 'simple': False, 'solvable': True, 'special_labels': ['C4'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '36.14', 'subgroup_hash': 14, 'subgroup_order': 36, 'subgroup_tex': 'C_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 111526951
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '864.2236', 'ambient_counter': 2236, 'ambient_order': 864, 'ambient_tex': 'C_3^2:(C_4\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': True, 'core_order': 36, 'counter': 72, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '864.2236.24.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '24.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '24.5', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4\\times S_3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '36.11', 'subgroup_hash': 11, 'subgroup_order': 36, 'subgroup_tex': 'C_3\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 111526952
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '864.2236', 'ambient_counter': 2236, 'ambient_order': 864, 'ambient_tex': 'C_3^2:(C_4\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 18, 'counter': 73, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '864.2236.24.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.14', 'subgroup_hash': 14, 'subgroup_order': 36, 'subgroup_tex': 'C_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 111526953
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '864.2236', 'ambient_counter': 2236, 'ambient_order': 864, 'ambient_tex': 'C_3^2:(C_4\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 18, 'counter': 74, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '864.2236.24.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 111526954
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '864.2236', 'ambient_counter': 2236, 'ambient_order': 864, 'ambient_tex': 'C_3^2:(C_4\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 6, 'counter': 75, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '864.2236.24.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 111526955
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '864.2236', 'ambient_counter': 2236, 'ambient_order': 864, 'ambient_tex': 'C_3^2:(C_4\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 6, 'counter': 76, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '864.2236.24.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 111526956
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '864.2236', 'ambient_counter': 2236, 'ambient_order': 864, 'ambient_tex': 'C_3^2:(C_4\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 18, 'counter': 77, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '864.2236.24.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.6', 'subgroup_hash': 6, 'subgroup_order': 36, 'subgroup_tex': 'C_3:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 111526957
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '864.2236', 'ambient_counter': 2236, 'ambient_order': 864, 'ambient_tex': 'C_3^2:(C_4\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 18, 'counter': 78, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '864.2236.24.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.7', 'subgroup_hash': 7, 'subgroup_order': 36, 'subgroup_tex': 'C_3^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 111526958
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '864.2236', 'ambient_counter': 2236, 'ambient_order': 864, 'ambient_tex': 'C_3^2:(C_4\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 6, 'counter': 79, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '864.2236.24.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.6', 'subgroup_hash': 6, 'subgroup_order': 36, 'subgroup_tex': 'C_3:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 111526960
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '864.2236', 'ambient_counter': 2236, 'ambient_order': 864, 'ambient_tex': 'C_3^2:(C_4\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 6, 'counter': 80, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '864.2236.24.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.7', 'subgroup_hash': 7, 'subgroup_order': 36, 'subgroup_tex': 'C_3^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 111526961
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '864.2236', 'ambient_counter': 2236, 'ambient_order': 864, 'ambient_tex': 'C_3^2:(C_4\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 9, 'counter': 81, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '864.2236.24.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.l1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.14', 'subgroup_hash': 14, 'subgroup_order': 36, 'subgroup_tex': 'C_6^2', 'supersolvable': True, 'sylow': 0}
  • id: 111526962
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '864.2236', 'ambient_counter': 2236, 'ambient_order': 864, 'ambient_tex': 'C_3^2:(C_4\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 9, 'counter': 82, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '864.2236.24.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.m1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 111526963
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '864.2236', 'ambient_counter': 2236, 'ambient_order': 864, 'ambient_tex': 'C_3^2:(C_4\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 9, 'counter': 83, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '864.2236.24.m1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.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': 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': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 111526964
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '864.2236', 'ambient_counter': 2236, 'ambient_order': 864, 'ambient_tex': 'C_3^2:(C_4\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 9, 'counter': 84, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '864.2236.24.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '24.n1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '36.6', 'subgroup_hash': 6, 'subgroup_order': 36, 'subgroup_tex': 'C_3:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 111526965
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '864.2236', 'ambient_counter': 2236, 'ambient_order': 864, 'ambient_tex': 'C_3^2:(C_4\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 9, 'counter': 85, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '864.2236.24.n1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '36.6', 'subgroup_hash': 6, 'subgroup_order': 36, 'subgroup_tex': 'C_3:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 111526966
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '864.2236', 'ambient_counter': 2236, 'ambient_order': 864, 'ambient_tex': 'C_3^2:(C_4\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 12, 'counter': 86, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '864.2236.24.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': '36.11', 'subgroup_hash': 11, 'subgroup_order': 36, 'subgroup_tex': 'C_3\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 111526967
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '864.2236', 'ambient_counter': 2236, 'ambient_order': 864, 'ambient_tex': 'C_3^2:(C_4\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 9, 'counter': 87, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '864.2236.24.p1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '36.12', 'subgroup_hash': 12, 'subgroup_order': 36, 'subgroup_tex': 'C_6\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 111526968
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '864.2236', 'ambient_counter': 2236, 'ambient_order': 864, 'ambient_tex': 'C_3^2:(C_4\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 9, 'counter': 88, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '864.2236.24.q1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '36.6', 'subgroup_hash': 6, 'subgroup_order': 36, 'subgroup_tex': 'C_3:C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 111526969
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '864.2236', 'ambient_counter': 2236, 'ambient_order': 864, 'ambient_tex': 'C_3^2:(C_4\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 89, 'cyclic': False, 'direct': None, 'hall': 2, 'label': '864.2236.27.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': '32.25', 'subgroup_hash': 25, 'subgroup_order': 32, 'subgroup_tex': 'C_4\\times D_4', 'supersolvable': True, 'sylow': 2}
  • id: 111526971
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '864.2236', 'ambient_counter': 2236, 'ambient_order': 864, 'ambient_tex': 'C_3^2:(C_4\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 9, 'counter': 90, 'cyclic': False, 'direct': None, 'hall': 3, 'label': '864.2236.32.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '32.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': 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': '27.3', 'subgroup_hash': 3, 'subgroup_order': 27, 'subgroup_tex': '\\He_3', 'supersolvable': True, 'sylow': 3}
  • id: 111526972
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '864.2236', 'ambient_counter': 2236, 'ambient_order': 864, 'ambient_tex': 'C_3^2:(C_4\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': True, 'core_order': 24, 'counter': 91, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '864.2236.36.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': ['S'], 'split': False, '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: 111526973
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '864.2236', 'ambient_counter': 2236, 'ambient_order': 864, 'ambient_tex': 'C_3^2:(C_4\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 6, 'counter': 92, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '864.2236.36.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.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': 36, 'quotient_simple': 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: 111526974
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '864.2236', 'ambient_counter': 2236, 'ambient_order': 864, 'ambient_tex': 'C_3^2:(C_4\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 2, 'counter': 93, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '864.2236.36.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
  • id: 111526975
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '864.2236', 'ambient_counter': 2236, 'ambient_order': 864, 'ambient_tex': 'C_3^2:(C_4\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 6, 'counter': 94, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '864.2236.36.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '24.7', 'subgroup_hash': 7, 'subgroup_order': 24, 'subgroup_tex': 'C_6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 111526976
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '864.2236', 'ambient_counter': 2236, 'ambient_order': 864, 'ambient_tex': 'C_3^2:(C_4\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 6, 'counter': 95, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '864.2236.36.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '24.9', 'subgroup_hash': 9, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 111526977
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '864.2236', 'ambient_counter': 2236, 'ambient_order': 864, 'ambient_tex': 'C_3^2:(C_4\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 6, 'counter': 96, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '864.2236.36.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.7', 'subgroup_hash': 7, 'subgroup_order': 24, 'subgroup_tex': 'C_6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 111526978
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '864.2236', 'ambient_counter': 2236, 'ambient_order': 864, 'ambient_tex': 'C_3^2:(C_4\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 6, 'counter': 97, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '864.2236.36.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': '24.7', 'subgroup_hash': 7, 'subgroup_order': 24, 'subgroup_tex': 'C_6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 111526979
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '864.2236', 'ambient_counter': 2236, 'ambient_order': 864, 'ambient_tex': 'C_3^2:(C_4\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 98, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '864.2236.36.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, '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': '24.7', 'subgroup_hash': 7, 'subgroup_order': 24, 'subgroup_tex': 'C_6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 111526980
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '864.2236', 'ambient_counter': 2236, 'ambient_order': 864, 'ambient_tex': 'C_3^2:(C_4\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 99, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '864.2236.36.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.7', 'subgroup_hash': 7, 'subgroup_order': 24, 'subgroup_tex': 'C_6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 111526748
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '864.2236', 'ambient_counter': 2236, 'ambient_order': 864, 'ambient_tex': 'C_3^2:(C_4\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 100, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '864.2236.36.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.7', 'subgroup_hash': 7, 'subgroup_order': 24, 'subgroup_tex': 'C_6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 111526749
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '864.2236', 'ambient_counter': 2236, 'ambient_order': 864, 'ambient_tex': 'C_3^2:(C_4\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 2, 'counter': 101, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '864.2236.36.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.7', 'subgroup_hash': 7, 'subgroup_order': 24, 'subgroup_tex': 'C_6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 111526750
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '864.2236', 'ambient_counter': 2236, 'ambient_order': 864, 'ambient_tex': 'C_3^2:(C_4\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 2, 'counter': 102, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '864.2236.36.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.l1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.9', 'subgroup_hash': 9, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 111526751
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '864.2236', 'ambient_counter': 2236, 'ambient_order': 864, 'ambient_tex': 'C_3^2:(C_4\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 2, 'counter': 103, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '864.2236.36.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.m1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.9', 'subgroup_hash': 9, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 111526752
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '864.2236', 'ambient_counter': 2236, 'ambient_order': 864, 'ambient_tex': 'C_3^2:(C_4\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 104, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '864.2236.36.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.n1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.7', 'subgroup_hash': 7, 'subgroup_order': 24, 'subgroup_tex': 'C_6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 111526753
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '864.2236', 'ambient_counter': 2236, 'ambient_order': 864, 'ambient_tex': 'C_3^2:(C_4\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 105, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '864.2236.36.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.o1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.7', 'subgroup_hash': 7, 'subgroup_order': 24, 'subgroup_tex': 'C_6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 111526754
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '864.2236', 'ambient_counter': 2236, 'ambient_order': 864, 'ambient_tex': 'C_3^2:(C_4\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 8, 'counter': 106, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '864.2236.36.p1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.p1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.15', 'subgroup_hash': 15, 'subgroup_order': 24, 'subgroup_tex': 'C_2^2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 111526755
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '864.2236', 'ambient_counter': 2236, 'ambient_order': 864, 'ambient_tex': 'C_3^2:(C_4\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 8, 'counter': 107, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '864.2236.36.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': '24.13', 'subgroup_hash': 13, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 111526756
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '864.2236', 'ambient_counter': 2236, 'ambient_order': 864, 'ambient_tex': 'C_3^2:(C_4\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 8, 'counter': 108, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '864.2236.36.r1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.r1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.13', 'subgroup_hash': 13, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times A_4', 'supersolvable': False, 'sylow': 0}
  • id: 111526757
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '864.2236', 'ambient_counter': 2236, 'ambient_order': 864, 'ambient_tex': 'C_3^2:(C_4\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 109, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '864.2236.36.s1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, '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': '24.7', 'subgroup_hash': 7, 'subgroup_order': 24, 'subgroup_tex': 'C_6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 111526759
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '864.2236', 'ambient_counter': 2236, 'ambient_order': 864, 'ambient_tex': 'C_3^2:(C_4\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 6, 'counter': 110, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '864.2236.36.t1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.t1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.7', 'subgroup_hash': 7, 'subgroup_order': 24, 'subgroup_tex': 'C_6:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 111526760
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '864.2236', 'ambient_counter': 2236, 'ambient_order': 864, 'ambient_tex': 'C_3^2:(C_4\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 111, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '864.2236.36.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': '24.5', 'subgroup_hash': 5, 'subgroup_order': 24, 'subgroup_tex': 'C_4\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 111526761
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '864.2236', 'ambient_counter': 2236, 'ambient_order': 864, 'ambient_tex': 'C_3^2:(C_4\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 112, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '864.2236.36.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': '24.5', 'subgroup_hash': 5, 'subgroup_order': 24, 'subgroup_tex': 'C_4\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 111526762
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '864.2236', 'ambient_counter': 2236, 'ambient_order': 864, 'ambient_tex': 'C_3^2:(C_4\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 113, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '864.2236.36.w1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.w1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.5', 'subgroup_hash': 5, 'subgroup_order': 24, 'subgroup_tex': 'C_4\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 111526763
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '864.2236', 'ambient_counter': 2236, 'ambient_order': 864, 'ambient_tex': 'C_3^2:(C_4\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 114, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '864.2236.36.x1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.x1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.10', 'subgroup_hash': 10, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 111526764
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '864.2236', 'ambient_counter': 2236, 'ambient_order': 864, 'ambient_tex': 'C_3^2:(C_4\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 3, 'counter': 115, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '864.2236.36.x1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '24.10', 'subgroup_hash': 10, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 111526765
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '864.2236', 'ambient_counter': 2236, 'ambient_order': 864, 'ambient_tex': 'C_3^2:(C_4\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 116, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '864.2236.36.y1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '24.8', 'subgroup_hash': 8, 'subgroup_order': 24, 'subgroup_tex': 'C_3:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 111526766
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '864.2236', 'ambient_counter': 2236, 'ambient_order': 864, 'ambient_tex': 'C_3^2:(C_4\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 117, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '864.2236.36.y1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '24.8', 'subgroup_hash': 8, 'subgroup_order': 24, 'subgroup_tex': 'C_3:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 111526767
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '864.2236', 'ambient_counter': 2236, 'ambient_order': 864, 'ambient_tex': 'C_3^2:(C_4\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 12, 'counter': 118, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '864.2236.36.z1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '36.z1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.10', 'subgroup_hash': 10, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 111526768
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '864.2236', 'ambient_counter': 2236, 'ambient_order': 864, 'ambient_tex': 'C_3^2:(C_4\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 12, 'counter': 119, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '864.2236.36.z1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '24.10', 'subgroup_hash': 10, 'subgroup_order': 24, 'subgroup_tex': 'C_3\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 111526770
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '864.2236', 'ambient_counter': 2236, 'ambient_order': 864, 'ambient_tex': 'C_3^2:(C_4\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 4, 'counter': 120, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '864.2236.36.ba1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '36.ba1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 36, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.8', 'subgroup_hash': 8, 'subgroup_order': 24, 'subgroup_tex': 'C_3:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 111526771
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '864.2236', 'ambient_counter': 2236, 'ambient_order': 864, 'ambient_tex': 'C_3^2:(C_4\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 4, 'counter': 121, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '864.2236.36.ba1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '24.8', 'subgroup_hash': 8, 'subgroup_order': 24, 'subgroup_tex': 'C_3:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 111526772
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '864.2236', 'ambient_counter': 2236, 'ambient_order': 864, 'ambient_tex': 'C_3^2:(C_4\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 4, 'counter': 122, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '864.2236.36.bb1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, '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': '24.12', 'subgroup_hash': 12, 'subgroup_order': 24, 'subgroup_tex': 'S_4', 'supersolvable': False, 'sylow': 0}
  • id: 111526773
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '864.2236', 'ambient_counter': 2236, 'ambient_order': 864, 'ambient_tex': 'C_3^2:(C_4\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 4, 'counter': 123, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '864.2236.36.bb1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, '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': '24.12', 'subgroup_hash': 12, 'subgroup_order': 24, 'subgroup_tex': 'S_4', 'supersolvable': False, 'sylow': 0}
  • id: 111526774
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '864.2236', 'ambient_counter': 2236, 'ambient_order': 864, 'ambient_tex': 'C_3^2:(C_4\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 4, 'counter': 124, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '864.2236.36.bc1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, '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': '24.12', 'subgroup_hash': 12, 'subgroup_order': 24, 'subgroup_tex': 'S_4', 'supersolvable': False, 'sylow': 0}
  • id: 111526775
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '864.2236', 'ambient_counter': 2236, 'ambient_order': 864, 'ambient_tex': 'C_3^2:(C_4\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 4, 'counter': 125, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '864.2236.36.bc1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, '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': '24.12', 'subgroup_hash': 12, 'subgroup_order': 24, 'subgroup_tex': 'S_4', 'supersolvable': False, 'sylow': 0}
  • id: 111526776
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '864.2236', 'ambient_counter': 2236, 'ambient_order': 864, 'ambient_tex': 'C_3^2:(C_4\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': True, 'core_order': 18, 'counter': 126, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '864.2236.48.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': '48.48', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 48, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 48, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_2\\times S_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 111526777
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '864.2236', 'ambient_counter': 2236, 'ambient_order': 864, 'ambient_tex': 'C_3^2:(C_4\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 6, 'counter': 127, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '864.2236.48.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 111526778
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '864.2236', 'ambient_counter': 2236, 'ambient_order': 864, 'ambient_tex': 'C_3^2:(C_4\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 6, 'counter': 128, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '864.2236.48.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 111526779
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '864.2236', 'ambient_counter': 2236, 'ambient_order': 864, 'ambient_tex': 'C_3^2:(C_4\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 9, 'counter': 129, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '864.2236.48.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 111526781
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '864.2236', 'ambient_counter': 2236, 'ambient_order': 864, 'ambient_tex': 'C_3^2:(C_4\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 9, 'counter': 130, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '864.2236.48.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '18.5', 'subgroup_hash': 5, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 111526782
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '864.2236', 'ambient_counter': 2236, 'ambient_order': 864, 'ambient_tex': 'C_3^2:(C_4\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 9, 'counter': 131, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '864.2236.48.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 111526783
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '864.2236', 'ambient_counter': 2236, 'ambient_order': 864, 'ambient_tex': 'C_3^2:(C_4\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 9, 'counter': 132, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '864.2236.48.f1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 111526784
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '864.2236', 'ambient_counter': 2236, 'ambient_order': 864, 'ambient_tex': 'C_3^2:(C_4\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 133, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '864.2236.48.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 111526785
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '864.2236', 'ambient_counter': 2236, 'ambient_order': 864, 'ambient_tex': 'C_3^2:(C_4\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 134, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '864.2236.48.g1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.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': 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': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 111526786
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '864.2236', 'ambient_counter': 2236, 'ambient_order': 864, 'ambient_tex': 'C_3^2:(C_4\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 135, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '864.2236.48.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 111526787
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '864.2236', 'ambient_counter': 2236, 'ambient_order': 864, 'ambient_tex': 'C_3^2:(C_4\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 136, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '864.2236.48.h1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '48.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': 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': '18.3', 'subgroup_hash': 3, 'subgroup_order': 18, 'subgroup_tex': 'C_3\\times S_3', 'supersolvable': True, 'sylow': 0}
  • id: 111526788
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '864.2236', 'ambient_counter': 2236, 'ambient_order': 864, 'ambient_tex': 'C_3^2:(C_4\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 137, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '864.2236.54.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': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 111526789
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '864.2236', 'ambient_counter': 2236, 'ambient_order': 864, 'ambient_tex': 'C_3^2:(C_4\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 138, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '864.2236.54.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': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 111526790
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '864.2236', 'ambient_counter': 2236, 'ambient_order': 864, 'ambient_tex': 'C_3^2:(C_4\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 139, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '864.2236.54.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '16.2', 'subgroup_hash': 2, 'subgroup_order': 16, 'subgroup_tex': 'C_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 111526792
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '864.2236', 'ambient_counter': 2236, 'ambient_order': 864, 'ambient_tex': 'C_3^2:(C_4\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 140, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '864.2236.54.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '16.4', 'subgroup_hash': 4, 'subgroup_order': 16, 'subgroup_tex': 'C_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 111526793
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '864.2236', 'ambient_counter': 2236, 'ambient_order': 864, 'ambient_tex': 'C_3^2:(C_4\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 8, 'counter': 141, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '864.2236.54.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': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 111526794
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '864.2236', 'ambient_counter': 2236, 'ambient_order': 864, 'ambient_tex': 'C_3^2:(C_4\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 142, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '864.2236.54.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': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 111526795
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '864.2236', 'ambient_counter': 2236, 'ambient_order': 864, 'ambient_tex': 'C_3^2:(C_4\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 8, 'counter': 143, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '864.2236.54.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': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 111526796
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '864.2236', 'ambient_counter': 2236, 'ambient_order': 864, 'ambient_tex': 'C_3^2:(C_4\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': True, 'core_order': 12, 'counter': 144, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '864.2236.72.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '72.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '72.21', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 21, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 72, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6.D_6', 'simple': False, 'solvable': True, 'special_labels': ['D2', 'C5'], '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: 111526797
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '864.2236', 'ambient_counter': 2236, 'ambient_order': 864, 'ambient_tex': 'C_3^2:(C_4\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 6, 'counter': 145, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '864.2236.72.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 111526798
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '864.2236', 'ambient_counter': 2236, 'ambient_order': 864, 'ambient_tex': 'C_3^2:(C_4\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 2, 'counter': 146, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '864.2236.72.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 111526799
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '864.2236', 'ambient_counter': 2236, 'ambient_order': 864, 'ambient_tex': 'C_3^2:(C_4\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 2, 'counter': 147, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '864.2236.72.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 111526800
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '864.2236', 'ambient_counter': 2236, 'ambient_order': 864, 'ambient_tex': 'C_3^2:(C_4\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 6, 'counter': 148, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '864.2236.72.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 111526801
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '864.2236', 'ambient_counter': 2236, 'ambient_order': 864, 'ambient_tex': 'C_3^2:(C_4\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 2, 'counter': 149, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '864.2236.72.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 111526803
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '864.2236', 'ambient_counter': 2236, 'ambient_order': 864, 'ambient_tex': 'C_3^2:(C_4\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 2, 'counter': 150, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '864.2236.72.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 111526804
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '864.2236', 'ambient_counter': 2236, 'ambient_order': 864, 'ambient_tex': 'C_3^2:(C_4\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 2, 'counter': 151, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '864.2236.72.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 111526805
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '864.2236', 'ambient_counter': 2236, 'ambient_order': 864, 'ambient_tex': 'C_3^2:(C_4\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 6, 'counter': 152, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '864.2236.72.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '12.1', 'subgroup_hash': 1, 'subgroup_order': 12, 'subgroup_tex': 'C_3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 111526806
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '864.2236', 'ambient_counter': 2236, 'ambient_order': 864, 'ambient_tex': 'C_3^2:(C_4\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 6, 'counter': 153, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '864.2236.72.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '12.1', 'subgroup_hash': 1, 'subgroup_order': 12, 'subgroup_tex': 'C_3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 111526807
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '864.2236', 'ambient_counter': 2236, 'ambient_order': 864, 'ambient_tex': 'C_3^2:(C_4\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 6, 'counter': 154, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '864.2236.72.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '12.1', 'subgroup_hash': 1, 'subgroup_order': 12, 'subgroup_tex': 'C_3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 111526808
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '864.2236', 'ambient_counter': 2236, 'ambient_order': 864, 'ambient_tex': 'C_3^2:(C_4\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 155, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '864.2236.72.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.l1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.1', 'subgroup_hash': 1, 'subgroup_order': 12, 'subgroup_tex': 'C_3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 111526809
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '864.2236', 'ambient_counter': 2236, 'ambient_order': 864, 'ambient_tex': 'C_3^2:(C_4\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 2, 'counter': 156, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '864.2236.72.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.m1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 111526810
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '864.2236', 'ambient_counter': 2236, 'ambient_order': 864, 'ambient_tex': 'C_3^2:(C_4\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 157, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '864.2236.72.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.n1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.1', 'subgroup_hash': 1, 'subgroup_order': 12, 'subgroup_tex': 'C_3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 111526811
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '864.2236', 'ambient_counter': 2236, 'ambient_order': 864, 'ambient_tex': 'C_3^2:(C_4\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 158, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '864.2236.72.n2.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.n2.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': 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: 111526812
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '864.2236', 'ambient_counter': 2236, 'ambient_order': 864, 'ambient_tex': 'C_3^2:(C_4\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 2, 'counter': 159, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '864.2236.72.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': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 111526814
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '864.2236', 'ambient_counter': 2236, 'ambient_order': 864, 'ambient_tex': 'C_3^2:(C_4\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 160, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '864.2236.72.p1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.p1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.1', 'subgroup_hash': 1, 'subgroup_order': 12, 'subgroup_tex': 'C_3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 111526815
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '864.2236', 'ambient_counter': 2236, 'ambient_order': 864, 'ambient_tex': 'C_3^2:(C_4\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 3, 'counter': 161, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '864.2236.72.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': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 111526816
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '864.2236', 'ambient_counter': 2236, 'ambient_order': 864, 'ambient_tex': 'C_3^2:(C_4\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 1, 'counter': 162, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '864.2236.72.r1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.r1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 111526817
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '864.2236', 'ambient_counter': 2236, 'ambient_order': 864, 'ambient_tex': 'C_3^2:(C_4\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 1, 'counter': 163, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '864.2236.72.s1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.s1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 111526818
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '864.2236', 'ambient_counter': 2236, 'ambient_order': 864, 'ambient_tex': 'C_3^2:(C_4\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 3, 'counter': 164, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '864.2236.72.t1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.t1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 111526819
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '864.2236', 'ambient_counter': 2236, 'ambient_order': 864, 'ambient_tex': 'C_3^2:(C_4\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 3, 'counter': 165, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '864.2236.72.t1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, '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': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 111526820
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '864.2236', 'ambient_counter': 2236, 'ambient_order': 864, 'ambient_tex': 'C_3^2:(C_4\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 166, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '864.2236.72.u1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.u1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 111526821
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '864.2236', 'ambient_counter': 2236, 'ambient_order': 864, 'ambient_tex': 'C_3^2:(C_4\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 167, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '864.2236.72.u1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 111526822
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '864.2236', 'ambient_counter': 2236, 'ambient_order': 864, 'ambient_tex': 'C_3^2:(C_4\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 3, 'counter': 168, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '864.2236.72.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': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 111526823
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '864.2236', 'ambient_counter': 2236, 'ambient_order': 864, 'ambient_tex': 'C_3^2:(C_4\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 3, 'counter': 169, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '864.2236.72.v1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.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': 72, 'quotient_simple': 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: 111526825
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '864.2236', 'ambient_counter': 2236, 'ambient_order': 864, 'ambient_tex': 'C_3^2:(C_4\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 170, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '864.2236.72.w1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.w1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.1', 'subgroup_hash': 1, 'subgroup_order': 12, 'subgroup_tex': 'C_3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 111526826
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '864.2236', 'ambient_counter': 2236, 'ambient_order': 864, 'ambient_tex': 'C_3^2:(C_4\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 171, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '864.2236.72.w1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.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': 72, 'quotient_simple': 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: 111526827
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '864.2236', 'ambient_counter': 2236, 'ambient_order': 864, 'ambient_tex': 'C_3^2:(C_4\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 4, 'counter': 172, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '864.2236.72.x1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.x1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 111526828
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '864.2236', 'ambient_counter': 2236, 'ambient_order': 864, 'ambient_tex': 'C_3^2:(C_4\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 4, 'counter': 173, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '864.2236.72.y1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '72.y1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.3', 'subgroup_hash': 3, 'subgroup_order': 12, 'subgroup_tex': 'A_4', 'supersolvable': False, 'sylow': 0}
  • id: 111526829
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '864.2236', 'ambient_counter': 2236, 'ambient_order': 864, 'ambient_tex': 'C_3^2:(C_4\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 4, 'counter': 174, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '864.2236.72.z1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, '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': '12.3', 'subgroup_hash': 3, 'subgroup_order': 12, 'subgroup_tex': 'A_4', 'supersolvable': False, 'sylow': 0}
  • id: 111526830
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '864.2236', 'ambient_counter': 2236, 'ambient_order': 864, 'ambient_tex': 'C_3^2:(C_4\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 3, 'counter': 175, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '864.2236.72.ba1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.ba1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
  • id: 111526831
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '864.2236', 'ambient_counter': 2236, 'ambient_order': 864, 'ambient_tex': 'C_3^2:(C_4\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 176, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '864.2236.72.bb1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
  • id: 111526832
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '864.2236', 'ambient_counter': 2236, 'ambient_order': 864, 'ambient_tex': 'C_3^2:(C_4\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 3, 'counter': 177, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '864.2236.72.bc1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '12.1', 'subgroup_hash': 1, 'subgroup_order': 12, 'subgroup_tex': 'C_3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 111526833
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '864.2236', 'ambient_counter': 2236, 'ambient_order': 864, 'ambient_tex': 'C_3^2:(C_4\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 178, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '864.2236.72.bd1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '72.bd1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 72, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
  • id: 111526834
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '864.2236', 'ambient_counter': 2236, 'ambient_order': 864, 'ambient_tex': 'C_3^2:(C_4\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': True, 'core_order': 9, 'counter': 179, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '864.2236.96.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': '96.186', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 186, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 96, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_4\\times S_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 111526836
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '864.2236', 'ambient_counter': 2236, 'ambient_order': 864, 'ambient_tex': 'C_3^2:(C_4\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 3, 'counter': 180, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '864.2236.96.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.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': 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': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 111526837
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '864.2236', 'ambient_counter': 2236, 'ambient_order': 864, 'ambient_tex': 'C_3^2:(C_4\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 3, 'counter': 181, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '864.2236.96.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.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': 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': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
  • id: 111526838
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '864.2236', 'ambient_counter': 2236, 'ambient_order': 864, 'ambient_tex': 'C_3^2:(C_4\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': True, 'core_order': 8, 'counter': 182, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '864.2236.108.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '108.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '108.17', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 17, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 108, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3^2:D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 111526839
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '864.2236', 'ambient_counter': 2236, 'ambient_order': 864, 'ambient_tex': 'C_3^2:(C_4\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 2, 'counter': 183, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '864.2236.108.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': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 111526840
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '864.2236', 'ambient_counter': 2236, 'ambient_order': 864, 'ambient_tex': 'C_3^2:(C_4\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 184, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '864.2236.108.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 111526841
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '864.2236', 'ambient_counter': 2236, 'ambient_order': 864, 'ambient_tex': 'C_3^2:(C_4\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 2, 'counter': 185, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '864.2236.108.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 111526842
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '864.2236', 'ambient_counter': 2236, 'ambient_order': 864, 'ambient_tex': 'C_3^2:(C_4\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 2, 'counter': 186, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '864.2236.108.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 111526843
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '864.2236', 'ambient_counter': 2236, 'ambient_order': 864, 'ambient_tex': 'C_3^2:(C_4\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 2, 'counter': 187, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '864.2236.108.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 111526844
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '864.2236', 'ambient_counter': 2236, 'ambient_order': 864, 'ambient_tex': 'C_3^2:(C_4\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 188, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '864.2236.108.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 111526845
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '864.2236', 'ambient_counter': 2236, 'ambient_order': 864, 'ambient_tex': 'C_3^2:(C_4\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 189, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '864.2236.108.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': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 111526847
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '864.2236', 'ambient_counter': 2236, 'ambient_order': 864, 'ambient_tex': 'C_3^2:(C_4\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 190, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '864.2236.108.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': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 111526848
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '864.2236', 'ambient_counter': 2236, 'ambient_order': 864, 'ambient_tex': 'C_3^2:(C_4\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 191, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '864.2236.108.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': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 111526849
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '864.2236', 'ambient_counter': 2236, 'ambient_order': 864, 'ambient_tex': 'C_3^2:(C_4\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 192, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '864.2236.108.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': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 111526850
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '864.2236', 'ambient_counter': 2236, 'ambient_order': 864, 'ambient_tex': 'C_3^2:(C_4\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 4, 'counter': 193, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '864.2236.108.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 108, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 111526851
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '864.2236', 'ambient_counter': 2236, 'ambient_order': 864, 'ambient_tex': 'C_3^2:(C_4\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 4, 'counter': 194, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '864.2236.108.k1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '108.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': 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': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 111526852
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '864.2236', 'ambient_counter': 2236, 'ambient_order': 864, 'ambient_tex': 'C_3^2:(C_4\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 432, 'characteristic': True, 'core_order': 6, 'counter': 195, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '864.2236.144.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': '144.183', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 183, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 144, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'S_3\\times S_4', 'simple': False, 'solvable': True, 'special_labels': ['Phi'], '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: 111526853
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '864.2236', 'ambient_counter': 2236, 'ambient_order': 864, 'ambient_tex': 'C_3^2:(C_4\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 2, 'counter': 196, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '864.2236.144.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.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': 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': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 111526854
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '864.2236', 'ambient_counter': 2236, 'ambient_order': 864, 'ambient_tex': 'C_3^2:(C_4\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 2, 'counter': 197, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '864.2236.144.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 111526855
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '864.2236', 'ambient_counter': 2236, 'ambient_order': 864, 'ambient_tex': 'C_3^2:(C_4\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 2, 'counter': 198, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '864.2236.144.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': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 111526856
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '864.2236', 'ambient_counter': 2236, 'ambient_order': 864, 'ambient_tex': 'C_3^2:(C_4\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 3, 'counter': 199, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '864.2236.144.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': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 111526859
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '864.2236', 'ambient_counter': 2236, 'ambient_order': 864, 'ambient_tex': 'C_3^2:(C_4\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 1, 'counter': 200, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '864.2236.144.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': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 111526860
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '864.2236', 'ambient_counter': 2236, 'ambient_order': 864, 'ambient_tex': 'C_3^2:(C_4\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 1, 'counter': 201, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '864.2236.144.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': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 111526861
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '864.2236', 'ambient_counter': 2236, 'ambient_order': 864, 'ambient_tex': 'C_3^2:(C_4\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 3, 'counter': 202, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '864.2236.144.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': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 111526862
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '864.2236', 'ambient_counter': 2236, 'ambient_order': 864, 'ambient_tex': 'C_3^2:(C_4\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 1, 'counter': 203, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '864.2236.144.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': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 111526863
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '864.2236', 'ambient_counter': 2236, 'ambient_order': 864, 'ambient_tex': 'C_3^2:(C_4\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 72, 'characteristic': False, 'core_order': 1, 'counter': 204, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '864.2236.144.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '144.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 144, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 111526864
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '864.2236', 'ambient_counter': 2236, 'ambient_order': 864, 'ambient_tex': 'C_3^2:(C_4\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 3, 'counter': 205, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '864.2236.144.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': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 111526865
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '864.2236', 'ambient_counter': 2236, 'ambient_order': 864, 'ambient_tex': 'C_3^2:(C_4\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 3, 'counter': 206, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '864.2236.144.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': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
  • id: 111526866
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '864.2236', 'ambient_counter': 2236, 'ambient_order': 864, 'ambient_tex': 'C_3^2:(C_4\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 207, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '864.2236.144.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': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
  • id: 111526867
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '864.2236', 'ambient_counter': 2236, 'ambient_order': 864, 'ambient_tex': 'C_3^2:(C_4\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 1, 'counter': 208, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '864.2236.144.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': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
  • id: 111526868
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '864.2236', 'ambient_counter': 2236, 'ambient_order': 864, 'ambient_tex': 'C_3^2:(C_4\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 209, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '864.2236.144.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
  • id: 111526870
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '864.2236', 'ambient_counter': 2236, 'ambient_order': 864, 'ambient_tex': 'C_3^2:(C_4\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 12, 'characteristic': False, 'core_order': 1, 'counter': 210, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '864.2236.144.m1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
  • id: 111526871
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '864.2236', 'ambient_counter': 2236, 'ambient_order': 864, 'ambient_tex': 'C_3^2:(C_4\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 211, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '864.2236.144.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
  • id: 111526872
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '864.2236', 'ambient_counter': 2236, 'ambient_order': 864, 'ambient_tex': 'C_3^2:(C_4\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 212, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '864.2236.144.n1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
  • id: 111526873
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '864.2236', 'ambient_counter': 2236, 'ambient_order': 864, 'ambient_tex': 'C_3^2:(C_4\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': True, 'core_order': 4, 'counter': 213, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '864.2236.216.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '216.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '216.36', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 36, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 216, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6.S_3^2', 'simple': False, 'solvable': True, 'special_labels': ['C6'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 111526874
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '864.2236', 'ambient_counter': 2236, 'ambient_order': 864, 'ambient_tex': 'C_3^2:(C_4\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 288, 'characteristic': False, 'core_order': 2, 'counter': 214, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '864.2236.216.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '216.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 216, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 111526875
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '864.2236', 'ambient_counter': 2236, 'ambient_order': 864, 'ambient_tex': 'C_3^2:(C_4\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 2, 'counter': 215, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '864.2236.216.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': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 111526876
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '864.2236', 'ambient_counter': 2236, 'ambient_order': 864, 'ambient_tex': 'C_3^2:(C_4\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 2, 'counter': 216, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '864.2236.216.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': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 111526877
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '864.2236', 'ambient_counter': 2236, 'ambient_order': 864, 'ambient_tex': 'C_3^2:(C_4\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 2, 'counter': 217, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '864.2236.216.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': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 111526878
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '864.2236', 'ambient_counter': 2236, 'ambient_order': 864, 'ambient_tex': 'C_3^2:(C_4\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 218, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '864.2236.216.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': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 111526879
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '864.2236', 'ambient_counter': 2236, 'ambient_order': 864, 'ambient_tex': 'C_3^2:(C_4\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 1, 'counter': 219, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '864.2236.216.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': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 111526881
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '864.2236', 'ambient_counter': 2236, 'ambient_order': 864, 'ambient_tex': 'C_3^2:(C_4\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 220, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '864.2236.216.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': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 111526882
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '864.2236', 'ambient_counter': 2236, 'ambient_order': 864, 'ambient_tex': 'C_3^2:(C_4\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 221, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '864.2236.216.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': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 111526883
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '864.2236', 'ambient_counter': 2236, 'ambient_order': 864, 'ambient_tex': 'C_3^2:(C_4\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 222, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '864.2236.216.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': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 111526884
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '864.2236', 'ambient_counter': 2236, 'ambient_order': 864, 'ambient_tex': 'C_3^2:(C_4\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 223, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '864.2236.216.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': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 111526885
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '864.2236', 'ambient_counter': 2236, 'ambient_order': 864, 'ambient_tex': 'C_3^2:(C_4\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 224, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '864.2236.216.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': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 111526886
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '864.2236', 'ambient_counter': 2236, 'ambient_order': 864, 'ambient_tex': 'C_3^2:(C_4\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 225, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '864.2236.216.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': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 111526887
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '864.2236', 'ambient_counter': 2236, 'ambient_order': 864, 'ambient_tex': 'C_3^2:(C_4\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 432, 'characteristic': True, 'core_order': 3, 'counter': 226, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '864.2236.288.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '288.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '288.854', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 854, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 288, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_2^3.S_3^2', 'simple': True, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '3.1', 'subgroup_hash': 1, 'subgroup_order': 3, 'subgroup_tex': 'C_3', 'supersolvable': True, 'sylow': 0}
  • id: 111526888
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '864.2236', 'ambient_counter': 2236, 'ambient_order': 864, 'ambient_tex': 'C_3^2:(C_4\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 144, 'characteristic': False, 'core_order': 1, 'counter': 227, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '864.2236.288.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '288.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': 288, '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: 111526889
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '864.2236', 'ambient_counter': 2236, 'ambient_order': 864, 'ambient_tex': 'C_3^2:(C_4\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 36, 'characteristic': False, 'core_order': 1, 'counter': 228, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '864.2236.288.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '288.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': 288, '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: 111526890
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '864.2236', 'ambient_counter': 2236, 'ambient_order': 864, 'ambient_tex': 'C_3^2:(C_4\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 18, 'characteristic': False, 'core_order': 1, 'counter': 229, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '864.2236.288.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '288.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': 288, '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: 111526892
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '864.2236', 'ambient_counter': 2236, 'ambient_order': 864, 'ambient_tex': 'C_3^2:(C_4\\times S_4)', 'central': True, 'central_factor': False, 'centralizer_order': 864, 'characteristic': True, 'core_order': 2, 'counter': 230, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '864.2236.432.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '432.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '432.523', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 523, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 432, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_6^2:D_6', 'simple': True, 'solvable': True, 'special_labels': ['Z', 'U0'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
  • id: 111526893
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '864.2236', 'ambient_counter': 2236, 'ambient_order': 864, 'ambient_tex': 'C_3^2:(C_4\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 288, 'characteristic': False, 'core_order': 1, 'counter': 231, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '864.2236.432.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, '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': 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: 111526894
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '864.2236', 'ambient_counter': 2236, 'ambient_order': 864, 'ambient_tex': 'C_3^2:(C_4\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 288, 'characteristic': False, 'core_order': 1, 'counter': 232, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '864.2236.432.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
  • id: 111526895
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '864.2236', 'ambient_counter': 2236, 'ambient_order': 864, 'ambient_tex': 'C_3^2:(C_4\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 233, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '864.2236.432.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '432.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 432, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
  • id: 111526896
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '864.2236', 'ambient_counter': 2236, 'ambient_order': 864, 'ambient_tex': 'C_3^2:(C_4\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 48, 'characteristic': False, 'core_order': 1, 'counter': 234, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '864.2236.432.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, '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': 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: 111526897
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '864.2236', 'ambient_counter': 2236, 'ambient_order': 864, 'ambient_tex': 'C_3^2:(C_4\\times S_4)', 'central': True, 'central_factor': False, 'centralizer_order': 864, 'characteristic': True, 'core_order': 1, 'counter': 235, 'cyclic': True, 'direct': True, 'hall': 1, 'label': '864.2236.864.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '864.a1.a1', 'outer_equivalence': False, 'perfect': True, 'proper': False, 'quotient': '864.2236', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 2236, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 864, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_3^2:(C_4\\times S_4)', 'simple': False, 'solvable': True, 'special_labels': ['PC', 'U1', 'D3', 'C7'], 'split': True, 'standard_generators': False, 'stem': True, 'subgroup': '1.1', 'subgroup_hash': 1, 'subgroup_order': 1, 'subgroup_tex': 'C_1', 'supersolvable': True, 'sylow': 1}
• gps_subgroup_data •

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

  
  
  • id: 111526746
    {'ambient': '864.2236', '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': ['864.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': [], 'contains': ['2.a1.a1', '2.b1.a1', '2.c1.a1', '3.a1.a1', '3.b1.a1', '4.c1.a1'], 'core': '1.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3275, 5061, 3461, 5279, 7599, 5078, 6223, 5036], 'generators': [1, 288, 48, 6, 8, 432, 504, 12], 'label': '864.2236.1.a1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '1.a1.a1', 'normal_contained_in': [], 'normal_contains': ['2.a1.a1', '2.b1.a1', '2.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '1.a1.a1', 'projective_image': '432.523', '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': '432.523'}
  • id: 111526747
    {'ambient': '864.2236', 'aut_centralizer_order': 1, 'aut_label': '4.c1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '432.545', 'aut_weyl_index': 4, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['8.b1.a1', '8.c1.a1', '8.d1.a1', '12.j1.a1', '12.l1.a1'], 'core': '24.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [3231, -1, 3400, -1, 7528, -1, 6285, -1], 'generators': [1, 48, 288, 6, 12, 8], 'label': '864.2236.4.c1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1.a1', 'old_label': '4.c1.a1', 'projective_image': '432.523', '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': '108.17'}
  • id: 111526748
    {'ambient': '864.2236', 'aut_centralizer_order': 8, 'aut_label': '36.j1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '12.4', 'aut_weyl_index': 144, 'centralizer': '108.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.d1.a1', '18.o1.a1'], 'contains': ['72.d1.a1', '72.l1.a1', '72.n2.a1', '108.c1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [8309, -1, 9638, -1, 1149, -1, 820, -1], 'generators': [6, 504, 12, 288], 'label': '864.2236.36.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.o1.a1', 'old_label': '36.j1.a1', 'projective_image': '432.523', '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': '6.1'}
  • id: 111526749
    {'ambient': '864.2236', 'aut_centralizer_order': 24, 'aut_label': '36.k1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '24.14', 'aut_weyl_index': 72, 'centralizer': '36.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.e1.a1', '18.g1.a1', '18.h1.a1', '18.j1.a1'], 'contains': ['72.c1.a1', '72.w1.a1', '72.w1.b1', '108.d1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [9305, -1, 5322, -1, 2460, -1, 4116, -1], 'generators': [511, 12, 432, 288], 'label': '864.2236.36.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '36.k1.a1', 'projective_image': '432.523', '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': '12.4'}
  • id: 111526750
    {'ambient': '864.2236', 'aut_centralizer_order': 24, 'aut_label': '36.l1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '8.5', 'aut_weyl_index': 216, 'centralizer': '36.l1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.f1.a1', '18.c1.a1', '18.h1.a1', '18.p1.a1'], 'contains': ['72.c1.a1', '72.m1.a1', '108.e1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [9103, -1, 7569, -1, 1502, -1, 1313, -1], 'generators': [1, 432, 288, 12], 'label': '864.2236.36.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1.a1', 'old_label': '36.l1.a1', 'projective_image': '432.523', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.l1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 111526751
    {'ambient': '864.2236', 'aut_centralizer_order': 24, 'aut_label': '36.m1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '8.5', 'aut_weyl_index': 216, 'centralizer': '36.m1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.g1.a1', '18.d1.a1', '18.g1.a1', '18.p1.a1'], 'contains': ['72.c1.a1', '72.bd1.a1', '108.f1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [9553, -1, 9852, -1, 92, -1, 266, -1], 'generators': [505, 432, 288, 444], 'label': '864.2236.36.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1.a1', 'old_label': '36.m1.a1', 'projective_image': '432.523', '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': '4.2'}
  • id: 111526752
    {'ambient': '864.2236', 'aut_centralizer_order': 8, 'aut_label': '36.n1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '24.14', 'aut_weyl_index': 72, 'centralizer': '108.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.h1.a1', '18.d1.a1', '18.h1.a1', '18.o1.a1'], 'contains': ['72.c1.a1', '72.n2.a1', '108.g1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [9754, -1, 8854, -1, 513, -1, 449, -1], 'generators': [510, 432, 12, 288], 'label': '864.2236.36.n1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1.a1', 'old_label': '36.n1.a1', 'projective_image': '432.523', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.n1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 111526753
    {'ambient': '864.2236', 'aut_centralizer_order': 8, 'aut_label': '36.o1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '12.4', 'aut_weyl_index': 144, 'centralizer': '108.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.h1.a1', '18.o1.a1'], 'contains': ['72.d1.a1', '72.n1.a1', '72.n2.a1', '108.g1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [8901, -1, 9030, -1, 725, -1, 634, -1], 'generators': [438, 504, 12, 288], 'label': '864.2236.36.o1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.o1.a1', 'old_label': '36.o1.a1', 'projective_image': '432.523', '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': '6.1'}
  • id: 111526754
    {'ambient': '864.2236', 'aut_centralizer_order': 144, 'aut_label': '36.p1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '4.2', 'aut_weyl_index': 432, 'centralizer': '12.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.a1.a1', '18.j1.a1', '18.o1.a1', '18.p1.a1'], 'contains': ['72.c1.a1', '72.d1.a1', '72.r1.a1', '72.s1.a1', '72.x1.a1', '108.a1.a1'], 'core': '108.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7620, -1, 6322, -1, 3420, -1, 4295, -1], 'generators': [12, 504, 432, 288], 'label': '864.2236.36.p1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '36.p1.a1', 'projective_image': '432.523', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.p1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 111526755
    {'ambient': '864.2236', 'aut_centralizer_order': 24, 'aut_label': '36.q1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '24.12', 'aut_weyl_index': 72, 'centralizer': '72.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.b1.a1', '18.k1.a1', '18.q1.a1', '18.r1.a1'], 'contains': ['72.y1.a1', '108.a1.a1', '144.c1.a1'], 'core': '108.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [2808, -1, 3032, -1, 8204, -1, 7712, -1], 'generators': [12, 8, 504, 432], 'label': '864.2236.36.q1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '36.q1.a1', 'projective_image': '432.523', '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': '24.12'}
  • id: 111526756
    {'ambient': '864.2236', 'aut_centralizer_order': 12, 'aut_label': '36.r1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '24.12', 'aut_weyl_index': 72, 'centralizer': '144.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.i1.a1', '18.l1.a1'], 'contains': ['72.z1.a1', '108.a1.a1', '144.d1.a1'], 'core': '108.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [724, -1, 463, -1, 9834, -1, 9539, -1], 'generators': [12, 584, 504, 432], 'label': '864.2236.36.r1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.i1.a1', 'old_label': '36.r1.a1', 'projective_image': '432.523', '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': '24.12'}
  • id: 111526757
    {'ambient': '864.2236', 'aut_centralizer_order': 4, 'aut_label': '36.s1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '24.14', 'aut_weyl_index': 72, 'centralizer': '108.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.j1.a1', '12.l1.a1', '18.a1.a1'], 'contains': ['72.e1.a1', '72.i1.a1', '72.j1.a1', '108.h1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [4125, -1, 4906, -1, 6063, -1, 5106, -1], 'generators': [1, 6, 12, 48], 'label': '864.2236.36.s1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1.a1', 'old_label': '36.s1.a1', 'projective_image': '432.523', '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': '6.1'}
  • id: 111526758
    {'ambient': '864.2236', 'aut_centralizer_order': 8, 'aut_label': '6.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '216.102', 'aut_weyl_index': 8, 'centralizer': '108.a1.a1', 'complements': ['144.m1.b1', '144.n1.b1', '144.m1.a1', '144.n1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '3.a1.a1'], 'contains': ['12.a1.a1', '12.d1.a1', '12.h1.a1', '18.m1.a1', '18.o1.a1'], 'core': '6.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6159, 1642, 7822, 8701, 3678, 1306, 3112, 8948], 'generators': [6, 48, 288, 504, 432, 12], 'label': '864.2236.6.a1.a1', 'mobius_quo': 0, 'mobius_sub': 3, 'normal_closure': '6.a1.a1', 'normal_contained_in': ['2.b1.a1'], 'normal_contains': ['12.a1.a1', '24.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '6.a1.a1', 'projective_image': '432.523', 'quotient_action_image': '6.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '6.a1.a1', 'subgroup_fusion': None, 'weyl_group': '108.17'}
  • id: 111526759
    {'ambient': '864.2236', 'aut_centralizer_order': 4, 'aut_label': '36.t1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '24.14', 'aut_weyl_index': 72, 'centralizer': '108.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.k1.a1', '18.a1.a1'], 'contains': ['72.e1.a1', '72.j1.a1', '72.k1.a1', '108.i1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [5543, -1, 7822, -1, 4878, -1, 3020, -1], 'generators': [1, 438, 12, 48], 'label': '864.2236.36.t1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1.a1', 'old_label': '36.t1.a1', 'projective_image': '432.523', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.t1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 111526760
    {'ambient': '864.2236', 'aut_centralizer_order': 4, 'aut_label': '36.u1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '24.14', 'aut_weyl_index': 72, 'centralizer': '108.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.j1.a1', '18.c1.a1'], 'contains': ['72.f1.a1', '72.l1.a1', '72.m1.a1', '108.h1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [6657, -1, 7130, -1, 3605, -1, 2678, -1], 'generators': [1, 6, 12, 288], 'label': '864.2236.36.u1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.c1.a1', 'old_label': '36.u1.a1', 'projective_image': '432.523', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.u1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 111526761
    {'ambient': '864.2236', 'aut_centralizer_order': 4, 'aut_label': '36.v1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '24.14', 'aut_weyl_index': 72, 'centralizer': '108.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.k1.a1', '18.c1.a1'], 'contains': ['72.f1.a1', '72.m1.a1', '72.n1.a1', '108.i1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [8124, -1, 8453, -1, 2268, -1, 1479, -1], 'generators': [1, 438, 12, 288], 'label': '864.2236.36.v1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.c1.a1', 'old_label': '36.v1.a1', 'projective_image': '432.523', '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': '6.1'}
  • id: 111526762
    {'ambient': '864.2236', 'aut_centralizer_order': 2, 'aut_label': '36.w1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '24.14', 'aut_weyl_index': 72, 'centralizer': '216.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['9.c1.a1', '12.l1.a1'], 'contains': ['72.g1.a1', '72.o1.a1', '72.p1.a1', '108.h1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [3066, -1, 3698, -1, 7840, -1, 6998, -1], 'generators': [1, 6, 12, 8], 'label': '864.2236.36.w1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.w1.a1', 'old_label': '36.w1.a1', 'projective_image': '432.523', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.w1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 111526763
    {'ambient': '864.2236', 'aut_centralizer_order': 12, 'aut_label': '36.x1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '8.5', 'aut_weyl_index': 216, 'centralizer': '72.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.m1.a1', '18.i1.a1'], 'contains': ['72.q1.a1', '72.t1.a1', '72.v1.b1', '108.j1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [1612, -1, 2607, -1, 7233, -1, 7301, -1], 'generators': [511, 516, 48, 432], 'label': '864.2236.36.x1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '36.x1.a1', 'projective_image': '864.2236', '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': '8.5'}
  • id: 111526764
    {'ambient': '864.2236', 'aut_centralizer_order': 12, 'aut_label': '36.x1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '8.5', 'aut_weyl_index': 216, 'centralizer': '72.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.m1.b1', '18.i1.a1'], 'contains': ['72.q1.a1', '72.t1.b1', '72.v1.a1', '108.j1.b1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [1612, -1, 2463, -1, 7233, -1, 7149, -1], 'generators': [7, 516, 48, 432], 'label': '864.2236.36.x1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '36.x1.b1', 'projective_image': '864.2236', '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': '8.5'}
  • id: 111526765
    {'ambient': '864.2236', 'aut_centralizer_order': 12, 'aut_label': '36.y1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '24.14', 'aut_weyl_index': 72, 'centralizer': '72.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.m1.a1', '18.j1.a1'], 'contains': ['72.r1.a1', '72.u1.a1', '72.w1.b1', '108.j1.a1'], 'core': '864.a1.a1', 'coset_action_label': '36T1337', 'count': 3, 'diagramx': [3782, -1, 4610, -1, 5525, -1, 5484, -1], 'generators': [511, 516, 432, 288], 'label': '864.2236.36.y1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '36.y1.a1', 'projective_image': '864.2236', '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': '24.14'}
  • id: 111526766
    {'ambient': '864.2236', 'aut_centralizer_order': 12, 'aut_label': '36.y1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '24.14', 'aut_weyl_index': 72, 'centralizer': '72.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.m1.b1', '18.j1.a1'], 'contains': ['72.r1.a1', '72.u1.b1', '72.w1.a1', '108.j1.b1'], 'core': '864.a1.a1', 'coset_action_label': '36T1337', 'count': 3, 'diagramx': [3782, -1, 4379, -1, 5525, -1, 5340, -1], 'generators': [7, 516, 432, 288], 'label': '864.2236.36.y1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '36.y1.b1', 'projective_image': '864.2236', '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': '24.14'}
  • id: 111526767
    {'ambient': '864.2236', 'aut_centralizer_order': 12, 'aut_label': '36.z1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '8.5', 'aut_weyl_index': 216, 'centralizer': '72.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.n1.a1', '12.o1.a1', '12.p1.a1', '18.i1.a1'], 'contains': ['72.a1.a1', '72.t1.a1', '72.v1.a1', '108.k1.a1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [1308, -1, 1578, -1, 7407, -1, 8272, -1], 'generators': [19, 504, 48, 432], 'label': '864.2236.36.z1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '36.z1.a1', 'projective_image': '864.2236', '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': '8.5'}
  • id: 111526768
    {'ambient': '864.2236', 'aut_centralizer_order': 12, 'aut_label': '36.z1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '8.5', 'aut_weyl_index': 216, 'centralizer': '72.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.n1.b1', '12.o1.b1', '12.p1.b1', '18.i1.a1'], 'contains': ['72.a1.a1', '72.t1.b1', '72.v1.b1', '108.k1.b1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [1308, -1, 1917, -1, 7407, -1, 8121, -1], 'generators': [7, 504, 48, 432], 'label': '864.2236.36.z1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '36.z1.b1', 'projective_image': '864.2236', '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': '8.5'}
  • id: 111526769
    {'ambient': '864.2236', 'aut_centralizer_order': 2, 'aut_label': '6.b1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '864.4000', 'aut_weyl_index': 2, 'centralizer': '432.a1.a1', 'complements': ['144.l1.b1', '144.n1.b1', '144.l1.a1', '144.n1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1', '3.b1.a1'], 'contains': ['12.b1.a1', '18.n1.a1', '18.r1.a1', '24.k1.a1'], 'core': '6.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3714, 8548, 3088, 1299, 8026, 8920, 6486, 6821], 'generators': [1, 432, 504, 12, 8, 48], 'label': '864.2236.6.b1.a1', 'mobius_quo': 0, 'mobius_sub': 3, 'normal_closure': '6.b1.a1', 'normal_contained_in': ['2.c1.a1'], 'normal_contains': ['12.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '6.b1.a1', 'projective_image': '432.523', 'quotient_action_image': '6.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '6.b1.a1', 'subgroup_fusion': None, 'weyl_group': '432.523'}
  • id: 111526770
    {'ambient': '864.2236', 'aut_centralizer_order': 12, 'aut_label': '36.ba1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '24.14', 'aut_weyl_index': 72, 'centralizer': '72.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.n1.a1', '18.j1.a1'], 'contains': ['72.u1.a1', '72.w1.a1', '72.x1.a1', '108.k1.a1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3530, -1, 3481, -1, 6399, -1, 6545, -1], 'generators': [19, 504, 432, 288], 'label': '864.2236.36.ba1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '36.ba1.a1', 'projective_image': '864.2236', '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': '24.14'}
  • id: 111526771
    {'ambient': '864.2236', 'aut_centralizer_order': 12, 'aut_label': '36.ba1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '24.14', 'aut_weyl_index': 72, 'centralizer': '72.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.n1.b1', '18.j1.a1'], 'contains': ['72.u1.b1', '72.w1.b1', '72.x1.a1', '108.k1.b1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3530, -1, 3578, -1, 6399, -1, 6443, -1], 'generators': [7, 504, 432, 288], 'label': '864.2236.36.ba1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '36.ba1.b1', 'projective_image': '864.2236', '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': '24.14'}
  • id: 111526772
    {'ambient': '864.2236', 'aut_centralizer_order': 12, 'aut_label': '36.bb1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '24.12', 'aut_weyl_index': 72, 'centralizer': '72.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.o1.a1', '18.k1.a1'], 'contains': ['72.y1.a1', '108.k1.a1', '144.m1.a1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [1483, -1, 1729, -1, 8850, -1, 8662, -1], 'generators': [19, 8, 504, 432], 'label': '864.2236.36.bb1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '36.bb1.a1', 'projective_image': '864.2236', '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': '24.12'}
  • id: 111526773
    {'ambient': '864.2236', 'aut_centralizer_order': 12, 'aut_label': '36.bb1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '24.12', 'aut_weyl_index': 72, 'centralizer': '72.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.o1.b1', '18.k1.a1'], 'contains': ['72.y1.a1', '108.k1.b1', '144.m1.b1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [1483, -1, 1806, -1, 8850, -1, 8583, -1], 'generators': [7, 8, 504, 432], 'label': '864.2236.36.bb1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '36.bb1.b1', 'projective_image': '864.2236', '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': '24.12'}
  • id: 111526774
    {'ambient': '864.2236', 'aut_centralizer_order': 6, 'aut_label': '36.bc1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '24.12', 'aut_weyl_index': 72, 'centralizer': '144.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.p1.a1', '18.l1.a1'], 'contains': ['72.z1.a1', '108.k1.a1', '144.n1.a1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [54, -1, 29, -1, 9965, -1, 9970, -1], 'generators': [19, 680, 504, 432], 'label': '864.2236.36.bc1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.i1.a1', 'old_label': '36.bc1.a1', 'projective_image': '864.2236', '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': '24.12'}
  • id: 111526775
    {'ambient': '864.2236', 'aut_centralizer_order': 6, 'aut_label': '36.bc1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '24.12', 'aut_weyl_index': 72, 'centralizer': '144.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.p1.b1', '18.l1.a1'], 'contains': ['72.z1.a1', '108.k1.b1', '144.n1.b1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [54, -1, 170, -1, 9965, -1, 9655, -1], 'generators': [7, 680, 504, 432], 'label': '864.2236.36.bc1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.i1.a1', 'old_label': '36.bc1.b1', 'projective_image': '864.2236', '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': '24.12'}
  • id: 111526776
    {'ambient': '864.2236', 'aut_centralizer_order': 144, 'aut_label': '48.a1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '12.4', 'aut_weyl_index': 144, 'centralizer': '12.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '24.a1.a1', '24.d1.a1', '24.e1.a1', '24.h1.a1', '24.i1.a1'], 'contains': ['96.a1.a1', '144.a1.a1', '144.b1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4838, 2295, 5796, 8257, 5104, 2262, 4107, 7813], 'generators': [12, 288, 48], 'label': '864.2236.48.a1.a1', 'mobius_quo': 0, 'mobius_sub': 24, 'normal_closure': '48.a1.a1', 'normal_contained_in': ['12.a1.a1', '24.a1.a1'], 'normal_contains': ['96.a1.a1', '144.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '48.a1.a1', 'projective_image': '432.523', 'quotient_action_image': '12.4', 'quotient_action_kernel': '4.2', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '48.a1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 111526777
    {'ambient': '864.2236', 'aut_centralizer_order': 36, 'aut_label': '48.b1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '12.4', 'aut_weyl_index': 144, 'centralizer': '48.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.b1.a1', '16.a1.a1', '24.f1.a1', '24.j1.a1', '24.k1.a1'], 'contains': ['96.b1.a1', '144.a1.a1', '144.c1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [1984, -1, 2214, -1, 8161, -1, 7567, -1], 'generators': [12, 8, 48], 'label': '864.2236.48.b1.a1', 'mobius_quo': None, 'mobius_sub': 6, 'normal_closure': '12.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1.a1', 'old_label': '48.b1.a1', 'projective_image': '432.523', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.b1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 111526778
    {'ambient': '864.2236', 'aut_centralizer_order': 36, 'aut_label': '48.c1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '6.1', 'aut_weyl_index': 288, 'centralizer': '48.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.i1.a1', '16.a1.a1', '24.g1.a1'], 'contains': ['96.c1.a1', '144.a1.a1', '144.d1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [1075, -1, 1205, -1, 9052, -1, 8888, -1], 'generators': [12, 584, 48], 'label': '864.2236.48.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.b1.a1', 'old_label': '48.c1.a1', 'projective_image': '432.523', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.c1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 111526779
    {'ambient': '864.2236', 'aut_centralizer_order': 144, 'aut_label': '48.d1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '4.2', 'aut_weyl_index': 432, 'centralizer': '12.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.b1.a1', '24.d1.a1', '24.l1.a1', '24.m1.a1', '24.m1.b1', '24.n1.a1', '24.n1.b1'], 'contains': ['96.a1.a1', '144.e1.a1', '144.f1.a1', '144.g1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3113, -1, 4082, -1, 6167, -1, 6018, -1], 'generators': [504, 288, 48], 'label': '864.2236.48.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '48.d1.a1', 'projective_image': '864.2236', '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': '4.2'}
  • id: 111526780
    {'ambient': '864.2236', 'aut_centralizer_order': 2, 'aut_label': '6.c1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '288.1040', 'aut_weyl_index': 6, 'centralizer': '216.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1.a1'], 'contains': ['12.c1.a1', '12.d1.a1', '12.f1.a1', '12.j1.a1', '12.k1.a1', '18.a1.a1', '18.c1.a1'], 'core': '24.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6666, -1, 7444, -1, 4176, -1, 3362, -1], 'generators': [1, 48, 288, 6, 432, 12], 'label': '864.2236.6.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '6.c1.a1', 'projective_image': '432.523', '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': '72.46'}
  • id: 111526781
    {'ambient': '864.2236', 'aut_centralizer_order': 144, 'aut_label': '48.e1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '4.2', 'aut_weyl_index': 432, 'centralizer': '12.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.d1.a1', '24.l1.a1', '24.p1.a1', '24.q1.a1'], 'contains': ['96.a1.a1', '144.h1.a1', '144.i1.a1', '144.j1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7696, -1, 6340, -1, 3954, -1, 3645, -1], 'generators': [516, 288, 48], 'label': '864.2236.48.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '48.e1.a1', 'projective_image': '864.2236', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.e1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 111526782
    {'ambient': '864.2236', 'aut_centralizer_order': 12, 'aut_label': '48.f1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '12.4', 'aut_weyl_index': 144, 'centralizer': '72.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.b1.a1', '24.e1.a1', '24.m1.a1', '24.p1.a1'], 'contains': ['96.a1.a1', '144.k1.a1', '144.l1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [4440, -1, 5572, -1, 6776, -1, 5618, -1], 'generators': [19, 48, 288], 'label': '864.2236.48.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.c1.a1', 'old_label': '48.f1.a1', 'projective_image': '864.2236', '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': '12.4'}
  • id: 111526783
    {'ambient': '864.2236', 'aut_centralizer_order': 12, 'aut_label': '48.f1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '12.4', 'aut_weyl_index': 144, 'centralizer': '72.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.b1.b1', '24.e1.a1', '24.m1.b1', '24.p1.a1'], 'contains': ['96.a1.a1', '144.k1.b1', '144.l1.b1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [4440, -1, 5268, -1, 6776, -1, 5387, -1], 'generators': [7, 48, 288], 'label': '864.2236.48.f1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.c1.a1', 'old_label': '48.f1.b1', 'projective_image': '864.2236', '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': '12.4'}
  • id: 111526784
    {'ambient': '864.2236', 'aut_centralizer_order': 6, 'aut_label': '48.g1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '12.4', 'aut_weyl_index': 144, 'centralizer': '144.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.o1.a1', '16.b1.a1', '24.f1.a1'], 'contains': ['96.b1.a1', '144.k1.a1', '144.m1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [862, -1, 821, -1, 8473, -1, 8543, -1], 'generators': [19, 48, 8], 'label': '864.2236.48.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.l1.a1', 'old_label': '48.g1.a1', 'projective_image': '864.2236', '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': '12.4'}
  • id: 111526785
    {'ambient': '864.2236', 'aut_centralizer_order': 6, 'aut_label': '48.g1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '12.4', 'aut_weyl_index': 144, 'centralizer': '144.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.o1.b1', '16.b1.b1', '24.f1.a1'], 'contains': ['96.b1.a1', '144.k1.b1', '144.m1.b1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [862, -1, 1349, -1, 8473, -1, 8392, -1], 'generators': [7, 48, 8], 'label': '864.2236.48.g1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.l1.a1', 'old_label': '48.g1.b1', 'projective_image': '864.2236', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.g1.b1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 111526786
    {'ambient': '864.2236', 'aut_centralizer_order': 6, 'aut_label': '48.h1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '6.1', 'aut_weyl_index': 288, 'centralizer': '144.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.p1.a1', '16.b1.a1', '24.g1.a1'], 'contains': ['96.c1.a1', '144.k1.a1', '144.n1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [325, -1, 333, -1, 9224, -1, 9188, -1], 'generators': [19, 48, 680], 'label': '864.2236.48.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.g1.a1', 'old_label': '48.h1.a1', 'projective_image': '864.2236', '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': '6.1'}
  • id: 111526787
    {'ambient': '864.2236', 'aut_centralizer_order': 6, 'aut_label': '48.h1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '6.1', 'aut_weyl_index': 288, 'centralizer': '144.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.p1.b1', '16.b1.b1', '24.g1.a1'], 'contains': ['96.c1.a1', '144.k1.b1', '144.n1.b1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [325, -1, 597, -1, 9224, -1, 9039, -1], 'generators': [7, 48, 680], 'label': '864.2236.48.h1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.g1.a1', 'old_label': '48.h1.b1', 'projective_image': '864.2236', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.h1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 111526788
    {'ambient': '864.2236', 'aut_centralizer_order': 8, 'aut_label': '54.a1', 'aut_quo_index': None, 'aut_stab_index': 27, 'aut_weyl_group': '8.5', 'aut_weyl_index': 216, 'centralizer': '54.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.a1.a1', '18.c1.a1', '27.a1.a1'], 'contains': ['108.b1.a1', '108.c1.a1', '108.e1.a1', '108.h1.a1', '108.i1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [5846, -1, 8100, -1, 3220, -1, 2841, -1], 'generators': [1, 6, 432], 'label': '864.2236.54.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1.a1', 'old_label': '54.a1.a1', 'projective_image': '432.523', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '54.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 111526789
    {'ambient': '864.2236', 'aut_centralizer_order': 4, 'aut_label': '54.b1', 'aut_quo_index': None, 'aut_stab_index': 27, 'aut_weyl_group': '16.14', 'aut_weyl_index': 108, 'centralizer': '108.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.b1.a1', '18.d1.a1', '27.a1.a1'], 'contains': ['108.b1.a1', '108.f1.a1', '108.g1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [7433, -1, 8684, -1, 1327, -1, 1802, -1], 'generators': [505, 510], 'label': '864.2236.54.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1.a1', 'old_label': '54.b1.a1', 'projective_image': '432.523', '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': '4.2'}
  • id: 111526790
    {'ambient': '864.2236', 'aut_centralizer_order': 8, 'aut_label': '54.c1', 'aut_quo_index': None, 'aut_stab_index': 27, 'aut_weyl_group': '8.5', 'aut_weyl_index': 216, 'centralizer': '54.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.e1.a1', '18.g1.a1', '27.a1.a1'], 'contains': ['108.c1.a1', '108.d1.a1', '108.f1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [7080, -1, 9349, -1, 1801, -1, 1911, -1], 'generators': [505, 6], 'label': '864.2236.54.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1.a1', 'old_label': '54.c1.a1', 'projective_image': '432.523', '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': '2.1'}
  • id: 111526791
    {'ambient': '864.2236', 'aut_centralizer_order': 2, 'aut_label': '6.d1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '288.1040', 'aut_weyl_index': 6, 'centralizer': '216.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1.a1'], 'contains': ['12.c1.a1', '12.g1.a1', '12.h1.a1', '18.b1.a1', '18.d1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8057, -1, 8181, -1, 2664, -1, 1887, -1], 'generators': [505, 48, 288, 510, 444, 432], 'label': '864.2236.6.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '6.d1.a1', 'projective_image': '432.523', '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': '72.46'}
  • id: 111526792
    {'ambient': '864.2236', 'aut_centralizer_order': 4, 'aut_label': '54.d1', 'aut_quo_index': None, 'aut_stab_index': 27, 'aut_weyl_group': '16.14', 'aut_weyl_index': 108, 'centralizer': '108.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.f1.a1', '18.h1.a1', '27.a1.a1'], 'contains': ['108.d1.a1', '108.e1.a1', '108.g1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [6974, -1, 7480, -1, 2124, -1, 2192, -1], 'generators': [1, 510], 'label': '864.2236.54.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1.a1', 'old_label': '54.d1.a1', 'projective_image': '432.523', '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': '4.2'}
  • id: 111526793
    {'ambient': '864.2236', 'aut_centralizer_order': 24, 'aut_label': '54.e1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '8.5', 'aut_weyl_index': 216, 'centralizer': '36.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.i1.a1', '18.j1.a1', '18.k1.a1', '18.l1.a1', '27.a1.a1'], 'contains': ['108.a1.a1', '108.b1.a1', '108.d1.a1', '108.j1.a1', '108.j1.b1', '108.k1.a1', '108.k1.b1'], 'core': '108.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [2547, -1, 2534, -1, 5870, -1, 6847, -1], 'generators': [7, 12, 504], 'label': '864.2236.54.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '54.e1.a1', 'projective_image': '432.523', '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': '4.2'}
  • id: 111526794
    {'ambient': '864.2236', 'aut_centralizer_order': 16, 'aut_label': '54.f1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '12.4', 'aut_weyl_index': 144, 'centralizer': '54.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.m1.a1', '18.o1.a1', '18.q1.a1', '27.a1.a1'], 'contains': ['108.a1.a1', '108.c1.a1', '108.g1.a1'], 'core': '108.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [4677, -1, 7692, -1, 2878, -1, 2331, -1], 'generators': [6, 504, 432], 'label': '864.2236.54.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1.a1', 'old_label': '54.f1.a1', 'projective_image': '432.523', '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': '6.1'}
  • id: 111526795
    {'ambient': '864.2236', 'aut_centralizer_order': 24, 'aut_label': '54.g1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '8.5', 'aut_weyl_index': 216, 'centralizer': '36.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.n1.a1', '18.p1.a1', '18.r1.a1', '27.a1.a1'], 'contains': ['108.a1.a1', '108.e1.a1', '108.f1.a1'], 'core': '108.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [5540, -1, 6529, -1, 3049, -1, 4445, -1], 'generators': [1, 504], 'label': '864.2236.54.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1.a1', 'old_label': '54.g1.a1', 'projective_image': '432.523', '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': '4.2'}
  • id: 111526796
    {'ambient': '864.2236', 'aut_centralizer_order': 144, 'aut_label': '72.a1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '12.4', 'aut_weyl_index': 144, 'centralizer': '12.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['24.b1.a1', '24.c1.a1', '24.o1.a1', '36.a1.a1', '36.z1.a1', '36.z1.b1'], 'contains': ['144.e1.a1', '216.a1.a1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1286, 5937, 1504, 3240, 7325, 4641, 7902, 4573], 'generators': [504, 432, 48], 'label': '864.2236.72.a1.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '72.a1.a1', 'normal_contained_in': ['24.b1.a1', '24.c1.a1', '36.a1.a1'], 'normal_contains': ['216.a1.a1', '288.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '72.a1.a1', 'projective_image': '864.2236', 'quotient_action_image': '12.4', 'quotient_action_kernel': '6.2', 'quotient_action_kernel_order': 6, 'quotient_fusion': None, 'short_label': '72.a1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 111526797
    {'ambient': '864.2236', 'aut_centralizer_order': 288, 'aut_label': '72.b1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '2.1', 'aut_weyl_index': 864, 'centralizer': '6.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.d1.a1', '36.a1.a1', '36.b1.a1', '36.d1.a1', '36.e1.a1', '36.f1.a1', '36.g1.a1', '36.h1.a1'], 'contains': ['144.a1.a1', '144.e1.a1', '144.h1.a1', '216.b1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6257, -1, 6277, -1, 4758, -1, 3956, -1], 'generators': [12, 504, 48], 'label': '864.2236.72.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '72.b1.a1', 'projective_image': '432.523', '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': '2.1'}
  • id: 111526798
    {'ambient': '864.2236', 'aut_centralizer_order': 288, 'aut_label': '72.c1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '2.1', 'aut_weyl_index': 864, 'centralizer': '6.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.d1.a1', '36.c1.a1', '36.i1.a1', '36.k1.a1', '36.l1.a1', '36.m1.a1', '36.n1.a1', '36.p1.a1'], 'contains': ['144.b1.a1', '144.f1.a1', '144.i1.a1', '216.b1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8883, -1, 7543, -1, 2573, -1, 2944, -1], 'generators': [12, 432, 288], 'label': '864.2236.72.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '72.c1.a1', 'projective_image': '432.523', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.c1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 111526799
    {'ambient': '864.2236', 'aut_centralizer_order': 144, 'aut_label': '72.d1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '2.1', 'aut_weyl_index': 864, 'centralizer': '12.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.d1.a1', '36.j1.a1', '36.o1.a1', '36.p1.a1'], 'contains': ['144.b1.a1', '144.g1.a1', '144.j1.a1', '216.b1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [8333, -1, 7687, -1, 2918, -1, 3192, -1], 'generators': [12, 504, 288], 'label': '864.2236.72.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.a1', 'old_label': '72.d1.a1', 'projective_image': '432.523', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.d1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 111526800
    {'ambient': '864.2236', 'aut_centralizer_order': 24, 'aut_label': '72.e1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '4.2', 'aut_weyl_index': 432, 'centralizer': '36.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.e1.a1', '24.f1.a1', '24.g1.a1', '36.b1.a1', '36.s1.a1', '36.t1.a1'], 'contains': ['144.a1.a1', '144.k1.a1', '144.k1.b1', '216.c1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [4727, -1, 5233, -1, 6604, -1, 5769, -1], 'generators': [7, 12, 48], 'label': '864.2236.72.e1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1.a1', 'old_label': '72.e1.a1', 'projective_image': '432.523', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.e1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 111526801
    {'ambient': '864.2236', 'aut_centralizer_order': 24, 'aut_label': '72.f1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '12.4', 'aut_weyl_index': 144, 'centralizer': '36.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.e1.a1', '36.c1.a1', '36.u1.a1', '36.v1.a1'], 'contains': ['144.b1.a1', '144.l1.a1', '144.l1.b1', '216.c1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [6478, -1, 7050, -1, 4522, -1, 3840, -1], 'generators': [7, 12, 288], 'label': '864.2236.72.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.c1.a1', 'old_label': '72.f1.a1', 'projective_image': '432.523', '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': '6.1'}
  • id: 111526802
    {'ambient': '864.2236', 'aut_centralizer_order': 2, 'aut_label': '6.e1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '288.1040', 'aut_weyl_index': 6, 'centralizer': '216.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1.a1'], 'contains': ['12.d1.a1', '12.e1.a1', '12.g1.a1', '18.e1.a1', '18.g1.a1'], 'core': '24.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7379, -1, 8664, -1, 3154, -1, 2251, -1], 'generators': [505, 48, 288, 6, 444, 432], 'label': '864.2236.6.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '6.e1.a1', 'projective_image': '432.523', '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': '72.46'}
  • id: 111526803
    {'ambient': '864.2236', 'aut_centralizer_order': 12, 'aut_label': '72.g1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '12.4', 'aut_weyl_index': 144, 'centralizer': '72.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.k1.a1', '24.f1.a1', '36.w1.a1'], 'contains': ['144.c1.a1', '144.m1.a1', '144.m1.b1', '216.c1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [2134, -1, 2142, -1, 8029, -1, 8113, -1], 'generators': [7, 12, 8], 'label': '864.2236.72.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.l1.a1', 'old_label': '72.g1.a1', 'projective_image': '432.523', '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': '6.1'}
  • id: 111526804
    {'ambient': '864.2236', 'aut_centralizer_order': 6, 'aut_label': '72.h1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '12.4', 'aut_weyl_index': 144, 'centralizer': '144.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.l1.a1', '24.g1.a1'], 'contains': ['144.d1.a1', '144.n1.a1', '144.n1.b1', '216.c1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [550, -1, 684, -1, 9404, -1, 9346, -1], 'generators': [7, 12, 680], 'label': '864.2236.72.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.g1.a1', 'old_label': '72.h1.a1', 'projective_image': '432.523', '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': '6.1'}
  • id: 111526805
    {'ambient': '864.2236', 'aut_centralizer_order': 48, 'aut_label': '72.i1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '12.4', 'aut_weyl_index': 144, 'centralizer': '18.k1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.a1.a1', '24.j1.a1', '36.d1.a1', '36.s1.a1'], 'contains': ['144.a1.a1', '216.d1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3955, -1, 4923, -1, 5352, -1, 4475, -1], 'generators': [6, 12, 48], 'label': '864.2236.72.i1.a1', 'mobius_quo': None, 'mobius_sub': 12, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '72.i1.a1', 'projective_image': '432.523', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.i1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 111526806
    {'ambient': '864.2236', 'aut_centralizer_order': 24, 'aut_label': '72.j1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '12.4', 'aut_weyl_index': 144, 'centralizer': '36.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.h1.a1', '24.k1.a1', '36.f1.a1', '36.s1.a1', '36.t1.a1'], 'contains': ['144.a1.a1', '216.e1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [4340, -1, 5072, -1, 5469, -1, 4728, -1], 'generators': [1, 12, 48], 'label': '864.2236.72.j1.a1', 'mobius_quo': None, 'mobius_sub': 6, 'normal_closure': '6.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.c1.a1', 'old_label': '72.j1.a1', 'projective_image': '432.523', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.j1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 111526807
    {'ambient': '864.2236', 'aut_centralizer_order': 16, 'aut_label': '72.k1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '12.4', 'aut_weyl_index': 144, 'centralizer': '54.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.i1.a1', '36.d1.a1', '36.h1.a1', '36.t1.a1'], 'contains': ['144.a1.a1', '216.f1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [7198, -1, 8432, -1, 3464, -1, 2671, -1], 'generators': [510, 12, 48], 'label': '864.2236.72.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '72.k1.a1', 'projective_image': '432.523', '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': '6.1'}
  • id: 111526808
    {'ambient': '864.2236', 'aut_centralizer_order': 16, 'aut_label': '72.l1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '12.4', 'aut_weyl_index': 144, 'centralizer': '54.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.a1.a1', '36.i1.a1', '36.j1.a1', '36.u1.a1'], 'contains': ['144.b1.a1', '216.d1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [7949, -1, 9519, -1, 3063, -1, 2569, -1], 'generators': [6, 12, 288], 'label': '864.2236.72.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1.a1', 'old_label': '72.l1.a1', 'projective_image': '432.523', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.l1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 111526809
    {'ambient': '864.2236', 'aut_centralizer_order': 24, 'aut_label': '72.m1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '4.2', 'aut_weyl_index': 432, 'centralizer': '36.l1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.h1.a1', '36.l1.a1', '36.u1.a1', '36.v1.a1'], 'contains': ['144.b1.a1', '216.e1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [8061, -1, 7174, -1, 3350, -1, 3068, -1], 'generators': [1, 288, 12], 'label': '864.2236.72.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.c1.a1', 'old_label': '72.m1.a1', 'projective_image': '432.523', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.m1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 111526810
    {'ambient': '864.2236', 'aut_centralizer_order': 16, 'aut_label': '72.n1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '12.4', 'aut_weyl_index': 144, 'centralizer': '54.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.i1.a1', '36.i1.a1', '36.o1.a1', '36.v1.a1'], 'contains': ['144.b1.a1', '216.f1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [8526, -1, 8994, -1, 1794, -1, 1424, -1], 'generators': [438, 12, 288], 'label': '864.2236.72.n1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1.a1', 'old_label': '72.n1.a1', 'projective_image': '432.523', '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': '6.1'}
  • id: 111526811
    {'ambient': '864.2236', 'aut_centralizer_order': 8, 'aut_label': '72.n2', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '12.4', 'aut_weyl_index': 144, 'centralizer': '108.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.i1.a1', '36.j1.a1', '36.n1.a1', '36.o1.a1'], 'contains': ['144.b1.a1', '216.f1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [8743, -1, 9103, -1, 1677, -1, 1215, -1], 'generators': [510, 12, 288], 'label': '864.2236.72.n2.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.o1.a1', 'old_label': '72.n2.a1', 'projective_image': '432.523', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.n2.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 111526812
    {'ambient': '864.2236', 'aut_centralizer_order': 12, 'aut_label': '72.o1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '4.2', 'aut_weyl_index': 432, 'centralizer': '72.o1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.q1.a1', '24.j1.a1', '36.w1.a1'], 'contains': ['144.c1.a1', '216.d1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [2903, -1, 4293, -1, 7729, -1, 5893, -1], 'generators': [6, 8, 12], 'label': '864.2236.72.o1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.w1.a1', 'old_label': '72.o1.a1', 'projective_image': '432.523', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.o1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 111526813
    {'ambient': '864.2236', 'aut_centralizer_order': 2, 'aut_label': '6.f1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '288.1040', 'aut_weyl_index': 6, 'centralizer': '216.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1.a1'], 'contains': ['12.e1.a1', '12.f1.a1', '12.h1.a1', '18.f1.a1', '18.h1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7135, -1, 7202, -1, 3470, -1, 2930, -1], 'generators': [1, 48, 288, 510, 12, 432], 'label': '864.2236.6.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '6.f1.a1', 'projective_image': '432.523', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.f1.a1', 'subgroup_fusion': None, 'weyl_group': '72.46'}
  • id: 111526814
    {'ambient': '864.2236', 'aut_centralizer_order': 4, 'aut_label': '72.p1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '12.4', 'aut_weyl_index': 144, 'centralizer': '216.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['18.r1.a1', '24.k1.a1', '36.w1.a1'], 'contains': ['144.c1.a1', '216.e1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [3291, -1, 3257, -1, 7877, -1, 7398, -1], 'generators': [1, 12, 8], 'label': '864.2236.72.p1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '36.w1.a1', 'old_label': '72.p1.a1', 'projective_image': '432.523', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.p1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 111526815
    {'ambient': '864.2236', 'aut_centralizer_order': 144, 'aut_label': '72.q1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '4.2', 'aut_weyl_index': 432, 'centralizer': '12.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.l1.a1', '36.a1.a1', '36.x1.a1', '36.x1.b1'], 'contains': ['144.e1.a1', '144.h1.a1', '216.g1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [2355, -1, 3377, -1, 6340, -1, 6615, -1], 'generators': [444, 504, 48], 'label': '864.2236.72.q1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '72.q1.a1', 'projective_image': '864.2236', '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': '4.2'}
  • id: 111526816
    {'ambient': '864.2236', 'aut_centralizer_order': 144, 'aut_label': '72.r1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '4.2', 'aut_weyl_index': 432, 'centralizer': '12.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.l1.a1', '36.p1.a1', '36.y1.a1', '36.y1.b1'], 'contains': ['144.f1.a1', '144.j1.a1', '216.g1.a1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4141, -1, 4751, -1, 4390, -1, 5157, -1], 'generators': [516, 432, 288], 'label': '864.2236.72.r1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '72.r1.a1', 'projective_image': '864.2236', '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': '4.2'}
  • id: 111526817
    {'ambient': '864.2236', 'aut_centralizer_order': 144, 'aut_label': '72.s1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '2.1', 'aut_weyl_index': 864, 'centralizer': '12.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.l1.a1', '36.p1.a1'], 'contains': ['144.g1.a1', '144.i1.a1', '144.j1.a1', '216.g1.a1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [5381, -1, 5377, -1, 3781, -1, 4855, -1], 'generators': [444, 504, 288], 'label': '864.2236.72.s1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.a1', 'old_label': '72.s1.a1', 'projective_image': '864.2236', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.s1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 111526818
    {'ambient': '864.2236', 'aut_centralizer_order': 24, 'aut_label': '72.t1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '4.2', 'aut_weyl_index': 432, 'centralizer': '36.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.m1.a1', '36.b1.a1', '36.x1.a1', '36.z1.a1'], 'contains': ['144.e1.a1', '144.k1.a1', '216.h1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [1961, -1, 3680, -1, 7061, -1, 7272, -1], 'generators': [19, 432, 48], 'label': '864.2236.72.t1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '72.t1.a1', 'projective_image': '864.2236', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.t1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 111526819
    {'ambient': '864.2236', 'aut_centralizer_order': 24, 'aut_label': '72.t1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '4.2', 'aut_weyl_index': 432, 'centralizer': '36.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.m1.b1', '36.b1.a1', '36.x1.b1', '36.z1.b1'], 'contains': ['144.e1.a1', '144.k1.b1', '216.h1.b1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [1961, -1, 2883, -1, 7061, -1, 6926, -1], 'generators': [7, 432, 48], 'label': '864.2236.72.t1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '72.t1.b1', 'projective_image': '864.2236', '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': '4.2'}
  • id: 111526820
    {'ambient': '864.2236', 'aut_centralizer_order': 24, 'aut_label': '72.u1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '12.4', 'aut_weyl_index': 144, 'centralizer': '36.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.m1.a1', '36.c1.a1', '36.y1.a1', '36.ba1.a1'], 'contains': ['144.f1.a1', '144.l1.a1', '216.h1.a1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3855, -1, 4511, -1, 6035, -1, 5503, -1], 'generators': [19, 432, 288], 'label': '864.2236.72.u1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '72.u1.a1', 'projective_image': '864.2236', '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': '12.4'}
  • id: 111526821
    {'ambient': '864.2236', 'aut_centralizer_order': 24, 'aut_label': '72.u1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '12.4', 'aut_weyl_index': 144, 'centralizer': '36.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.m1.b1', '36.c1.a1', '36.y1.b1', '36.ba1.b1'], 'contains': ['144.f1.a1', '144.l1.b1', '216.h1.b1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3855, -1, 4031, -1, 6035, -1, 5272, -1], 'generators': [7, 432, 288], 'label': '864.2236.72.u1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '72.u1.b1', 'projective_image': '864.2236', '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': '12.4'}
  • id: 111526822
    {'ambient': '864.2236', 'aut_centralizer_order': 24, 'aut_label': '72.v1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '4.2', 'aut_weyl_index': 432, 'centralizer': '36.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.n1.a1', '36.e1.a1', '36.x1.b1', '36.z1.a1'], 'contains': ['144.e1.a1', '216.i1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [1824, -1, 2725, -1, 6918, -1, 7050, -1], 'generators': [523, 48, 432], 'label': '864.2236.72.v1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '72.v1.a1', 'projective_image': '864.2236', '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': '4.2'}
  • id: 111526823
    {'ambient': '864.2236', 'aut_centralizer_order': 24, 'aut_label': '72.v1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '4.2', 'aut_weyl_index': 432, 'centralizer': '36.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.n1.b1', '36.e1.a1', '36.x1.a1', '36.z1.b1'], 'contains': ['144.e1.a1', '216.i1.b1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [1824, -1, 3162, -1, 6918, -1, 7148, -1], 'generators': [511, 48, 432], 'label': '864.2236.72.v1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '72.v1.b1', 'projective_image': '864.2236', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.v1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 111526824
    {'ambient': '864.2236', 'aut_centralizer_order': 12, 'aut_label': '6.g1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '48.51', 'aut_weyl_index': 36, 'centralizer': '72.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '3.a1.a1'], 'contains': ['12.a1.a1', '12.c1.a1', '12.e1.a1', '12.m1.a1', '12.m1.b1', '12.n1.a1', '12.n1.b1', '18.i1.a1', '18.j1.a1'], 'core': '12.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4944, -1, 4188, -1, 5690, -1, 5835, -1], 'generators': [7, 288, 432, 12, 504, 48], 'label': '864.2236.6.g1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '6.g1.a1', 'projective_image': '432.523', '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': '24.14'}
  • id: 111526825
    {'ambient': '864.2236', 'aut_centralizer_order': 24, 'aut_label': '72.w1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '12.4', 'aut_weyl_index': 144, 'centralizer': '36.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.n1.a1', '36.k1.a1', '36.y1.b1', '36.ba1.a1'], 'contains': ['144.f1.a1', '216.i1.a1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3700, -1, 3944, -1, 5758, -1, 6144, -1], 'generators': [523, 432, 288], 'label': '864.2236.72.w1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '72.w1.a1', 'projective_image': '864.2236', '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': '12.4'}
  • id: 111526826
    {'ambient': '864.2236', 'aut_centralizer_order': 24, 'aut_label': '72.w1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '12.4', 'aut_weyl_index': 144, 'centralizer': '36.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.n1.b1', '36.k1.a1', '36.y1.a1', '36.ba1.b1'], 'contains': ['144.f1.a1', '216.i1.b1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3700, -1, 4118, -1, 5758, -1, 6246, -1], 'generators': [511, 432, 288], 'label': '864.2236.72.w1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '72.w1.b1', 'projective_image': '864.2236', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.w1.b1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 111526827
    {'ambient': '864.2236', 'aut_centralizer_order': 144, 'aut_label': '72.x1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '4.2', 'aut_weyl_index': 432, 'centralizer': '12.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.b1.a1', '36.p1.a1', '36.ba1.a1', '36.ba1.b1'], 'contains': ['144.f1.a1', '144.g1.a1', '216.a1.a1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3554, -1, 3824, -1, 5903, -1, 6373, -1], 'generators': [504, 432, 288], 'label': '864.2236.72.x1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '72.x1.a1', 'projective_image': '864.2236', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '72.x1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 111526828
    {'ambient': '864.2236', 'aut_centralizer_order': 24, 'aut_label': '72.y1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '24.12', 'aut_weyl_index': 72, 'centralizer': '72.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.c1.a1', '36.q1.a1', '36.bb1.a1', '36.bb1.b1'], 'contains': ['216.a1.a1', '288.c1.a1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [1459, -1, 1625, -1, 8293, -1, 8235, -1], 'generators': [8, 504, 432], 'label': '864.2236.72.y1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '72.y1.a1', 'projective_image': '864.2236', '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': '24.12'}
  • id: 111526829
    {'ambient': '864.2236', 'aut_centralizer_order': 12, 'aut_label': '72.z1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '24.12', 'aut_weyl_index': 72, 'centralizer': '144.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.o1.a1', '36.r1.a1', '36.bc1.a1', '36.bc1.b1'], 'contains': ['216.a1.a1', '288.d1.a1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [33, -1, 30, -1, 9613, -1, 9581, -1], 'generators': [584, 504, 432], 'label': '864.2236.72.z1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.i1.a1', 'old_label': '72.z1.a1', 'projective_image': '864.2236', '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': '24.12'}
  • id: 111526830
    {'ambient': '864.2236', 'aut_centralizer_order': 24, 'aut_label': '72.ba1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '4.2', 'aut_weyl_index': 432, 'centralizer': '36.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.p1.a1', '36.b1.a1'], 'contains': ['144.h1.a1', '144.k1.a1', '144.k1.b1', '216.j1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [5102, -1, 6133, -1, 5614, -1, 5006, -1], 'generators': [7, 444, 48], 'label': '864.2236.72.ba1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1.a1', 'old_label': '72.ba1.a1', 'projective_image': '864.2236', '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': '2.1'}
  • id: 111526831
    {'ambient': '864.2236', 'aut_centralizer_order': 24, 'aut_label': '72.bb1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '12.4', 'aut_weyl_index': 144, 'centralizer': '36.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.p1.a1', '36.c1.a1'], 'contains': ['144.i1.a1', '144.l1.a1', '144.l1.b1', '216.j1.a1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [6612, -1, 6507, -1, 4086, -1, 3760, -1], 'generators': [7, 444, 288], 'label': '864.2236.72.bb1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.c1.a1', 'old_label': '72.bb1.a1', 'projective_image': '864.2236', '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': '6.1'}
  • id: 111526832
    {'ambient': '864.2236', 'aut_centralizer_order': 24, 'aut_label': '72.bc1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '12.4', 'aut_weyl_index': 144, 'centralizer': '36.k1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.q1.a1', '36.g1.a1'], 'contains': ['144.h1.a1', '216.k1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [9232, -1, 9795, -1, 1560, -1, 1113, -1], 'generators': [505, 444, 48], 'label': '864.2236.72.bc1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.e1.a1', 'old_label': '72.bc1.a1', 'projective_image': '864.2236', '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': '6.1'}
  • id: 111526833
    {'ambient': '864.2236', 'aut_centralizer_order': 24, 'aut_label': '72.bd1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '4.2', 'aut_weyl_index': 432, 'centralizer': '36.m1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.q1.a1', '36.m1.a1'], 'contains': ['144.i1.a1', '216.k1.a1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [9359, -1, 9945, -1, 874, -1, 612, -1], 'generators': [505, 288, 444], 'label': '864.2236.72.bd1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.g1.a1', 'old_label': '72.bd1.a1', 'projective_image': '864.2236', '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': '2.1'}
  • id: 111526834
    {'ambient': '864.2236', 'aut_centralizer_order': 144, 'aut_label': '96.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '12.4', 'aut_weyl_index': 144, 'centralizer': '12.a1.a1', 'complements': ['9.c1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['32.a1.a1', '48.a1.a1', '48.d1.a1', '48.e1.a1', '48.f1.a1', '48.f1.b1'], 'contains': ['288.a1.a1', '288.b1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4452, 3411, 5617, 7533, 6047, 3452, 5618, 5741], 'generators': [288, 48], 'label': '864.2236.96.a1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '96.a1.a1', 'normal_contained_in': ['24.b1.a1', '48.a1.a1'], 'normal_contains': ['288.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '96.a1.a1', 'projective_image': '864.2236', 'quotient_action_image': '12.4', 'quotient_action_kernel': '8.5', 'quotient_action_kernel_order': 8, 'quotient_fusion': None, 'short_label': '96.a1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 111526835
    {'ambient': '864.2236', 'aut_centralizer_order': 6, 'aut_label': '6.h1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '96.226', 'aut_weyl_index': 18, 'centralizer': '144.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '3.b1.a1'], 'contains': ['12.b1.a1', '12.o1.a1', '12.o1.b1', '18.i1.a1', '18.k1.a1', '24.f1.a1'], 'core': '12.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [2131, -1, 2477, -1, 8245, -1, 7841, -1], 'generators': [7, 432, 504, 12, 48, 8], 'label': '864.2236.6.h1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '6.h1.a1', 'projective_image': '432.523', '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': '48.48'}
  • id: 111526836
    {'ambient': '864.2236', 'aut_centralizer_order': 36, 'aut_label': '96.b1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '12.4', 'aut_weyl_index': 144, 'centralizer': '48.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.c1.a1', '32.a1.a1', '48.b1.a1', '48.g1.a1', '48.g1.b1'], 'contains': ['288.a1.a1', '288.c1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [849, -1, 1148, -1, 8335, -1, 8392, -1], 'generators': [8, 48], 'label': '864.2236.96.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1.a1', 'old_label': '96.b1.a1', 'projective_image': '864.2236', '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': '12.4'}
  • id: 111526837
    {'ambient': '864.2236', 'aut_centralizer_order': 36, 'aut_label': '96.c1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '6.1', 'aut_weyl_index': 288, 'centralizer': '48.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.o1.a1', '32.a1.a1', '48.c1.a1', '48.h1.a1', '48.h1.b1'], 'contains': ['288.a1.a1', '288.d1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [434, -1, 472, -1, 9052, -1, 8991, -1], 'generators': [584, 48], 'label': '864.2236.96.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.b1.a1', 'old_label': '96.c1.a1', 'projective_image': '864.2236', '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': '6.1'}
  • id: 111526838
    {'ambient': '864.2236', 'aut_centralizer_order': 288, 'aut_label': '108.a1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '6.1', 'aut_weyl_index': 288, 'centralizer': '6.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['36.a1.a1', '36.p1.a1', '36.q1.a1', '36.r1.a1', '54.e1.a1', '54.f1.a1', '54.g1.a1'], 'contains': ['216.a1.a1', '216.b1.a1', '216.g1.a1'], 'core': '108.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2710, 7947, 3724, 4310, 5242, 6650, 6494, 6193], 'generators': [12, 504, 432], 'label': '864.2236.108.a1.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '108.a1.a1', 'normal_contained_in': ['36.a1.a1'], 'normal_contains': ['216.a1.a1', '432.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '108.a1.a1', 'projective_image': '432.523', 'quotient_action_image': '6.1', 'quotient_action_kernel': '18.4', 'quotient_action_kernel_order': 18, 'quotient_fusion': None, 'short_label': '108.a1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 111526839
    {'ambient': '864.2236', 'aut_centralizer_order': 48, 'aut_label': '108.b1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '4.2', 'aut_weyl_index': 432, 'centralizer': '18.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.b1.a1', '36.c1.a1', '54.a1.a1', '54.b1.a1', '54.e1.a1'], 'contains': ['216.b1.a1', '216.c1.a1', '216.h1.a1', '216.h1.b1', '216.j1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [5103, -1, 7445, -1, 4620, -1, 4228, -1], 'generators': [7, 12, 432], 'label': '864.2236.108.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '108.b1.a1', 'projective_image': '432.523', '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': '2.1'}
  • id: 111526840
    {'ambient': '864.2236', 'aut_centralizer_order': 32, 'aut_label': '108.c1', 'aut_quo_index': None, 'aut_stab_index': 27, 'aut_weyl_group': '2.1', 'aut_weyl_index': 864, 'centralizer': '27.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.d1.a1', '36.i1.a1', '36.j1.a1', '54.a1.a1', '54.c1.a1', '54.f1.a1'], 'contains': ['216.b1.a1', '216.d1.a1', '216.f1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [6707, -1, 8857, -1, 2746, -1, 2387, -1], 'generators': [6, 504], 'label': '864.2236.108.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1.a1', 'old_label': '108.c1.a1', 'projective_image': '432.523', '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': '1.1'}
  • id: 111526841
    {'ambient': '864.2236', 'aut_centralizer_order': 48, 'aut_label': '108.d1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '4.2', 'aut_weyl_index': 432, 'centralizer': '18.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.e1.a1', '36.k1.a1', '54.c1.a1', '54.d1.a1', '54.e1.a1'], 'contains': ['216.b1.a1', '216.i1.a1', '216.i1.b1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [6966, -1, 5587, -1, 4218, -1, 4349, -1], 'generators': [511, 12], 'label': '864.2236.108.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '108.d1.a1', 'projective_image': '432.523', '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': '2.1'}
  • id: 111526842
    {'ambient': '864.2236', 'aut_centralizer_order': 48, 'aut_label': '108.e1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '4.2', 'aut_weyl_index': 432, 'centralizer': '18.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.f1.a1', '36.l1.a1', '54.a1.a1', '54.d1.a1', '54.g1.a1'], 'contains': ['216.b1.a1', '216.e1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [5939, -1, 7091, -1, 3208, -1, 3494, -1], 'generators': [1, 432], 'label': '864.2236.108.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1.a1', 'old_label': '108.e1.a1', 'projective_image': '432.523', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.e1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 111526843
    {'ambient': '864.2236', 'aut_centralizer_order': 48, 'aut_label': '108.f1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '4.2', 'aut_weyl_index': 432, 'centralizer': '18.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.g1.a1', '36.m1.a1', '54.b1.a1', '54.c1.a1', '54.g1.a1'], 'contains': ['216.b1.a1', '216.k1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [7340, -1, 9384, -1, 1939, -1, 1802, -1], 'generators': [505, 432], 'label': '864.2236.108.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1.a1', 'old_label': '108.f1.a1', 'projective_image': '432.523', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.f1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 111526844
    {'ambient': '864.2236', 'aut_centralizer_order': 16, 'aut_label': '108.g1', 'aut_quo_index': None, 'aut_stab_index': 27, 'aut_weyl_group': '4.2', 'aut_weyl_index': 432, 'centralizer': '54.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.h1.a1', '36.n1.a1', '36.o1.a1', '54.b1.a1', '54.d1.a1', '54.f1.a1'], 'contains': ['216.b1.a1', '216.f1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [7572, -1, 8352, -1, 2262, -1, 2114, -1], 'generators': [438, 504], 'label': '864.2236.108.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1.a1', 'old_label': '108.g1.a1', 'projective_image': '432.523', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.g1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 111526845
    {'ambient': '864.2236', 'aut_centralizer_order': 8, 'aut_label': '108.h1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '4.2', 'aut_weyl_index': 432, 'centralizer': '54.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.s1.a1', '36.u1.a1', '36.w1.a1', '54.a1.a1'], 'contains': ['216.c1.a1', '216.d1.a1', '216.e1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 54, 'diagramx': [4691, -1, 5282, -1, 4931, -1, 4602, -1], 'generators': [1, 6], 'label': '864.2236.108.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.a1.a1', 'old_label': '108.h1.a1', 'projective_image': '432.523', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.h1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 111526846
    {'ambient': '864.2236', 'aut_centralizer_order': 6, 'aut_label': '6.i1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '48.48', 'aut_weyl_index': 36, 'centralizer': '144.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1'], 'contains': ['12.i1.a1', '12.p1.a1', '12.p1.b1', '18.i1.a1', '18.l1.a1', '24.g1.a1'], 'core': '36.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [931, -1, 1162, -1, 9386, -1, 9346, -1], 'generators': [7, 432, 504, 12, 48, 680], 'label': '864.2236.6.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.i1.a1', 'old_label': '6.i1.a1', 'projective_image': '432.523', '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': '24.12'}
  • id: 111526847
    {'ambient': '864.2236', 'aut_centralizer_order': 8, 'aut_label': '108.i1', 'aut_quo_index': None, 'aut_stab_index': 54, 'aut_weyl_group': '4.2', 'aut_weyl_index': 432, 'centralizer': '54.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.t1.a1', '36.v1.a1', '54.a1.a1'], 'contains': ['216.c1.a1', '216.e1.a1', '216.f1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 54, 'diagramx': [6104, -1, 8209, -1, 3609, -1, 3343, -1], 'generators': [1, 438], 'label': '864.2236.108.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '54.a1.a1', 'old_label': '108.i1.a1', 'projective_image': '432.523', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.i1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 111526848
    {'ambient': '864.2236', 'aut_centralizer_order': 24, 'aut_label': '108.j1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '4.2', 'aut_weyl_index': 432, 'centralizer': '36.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.x1.a1', '36.y1.a1', '54.e1.a1'], 'contains': ['216.g1.a1', '216.h1.a1', '216.i1.b1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [1945, -1, 2945, -1, 6472, -1, 6810, -1], 'generators': [511, 516], 'label': '864.2236.108.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '108.j1.a1', 'projective_image': '864.2236', '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': '4.2'}
  • id: 111526849
    {'ambient': '864.2236', 'aut_centralizer_order': 24, 'aut_label': '108.j1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '4.2', 'aut_weyl_index': 432, 'centralizer': '36.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.x1.b1', '36.y1.b1', '54.e1.a1'], 'contains': ['216.g1.a1', '216.h1.b1', '216.i1.a1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [1945, -1, 2708, -1, 6472, -1, 6730, -1], 'generators': [7, 516], 'label': '864.2236.108.j1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '108.j1.b1', 'projective_image': '864.2236', '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': '4.2'}
  • id: 111526850
    {'ambient': '864.2236', 'aut_centralizer_order': 24, 'aut_label': '108.k1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '4.2', 'aut_weyl_index': 432, 'centralizer': '36.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.z1.a1', '36.ba1.a1', '36.bb1.a1', '36.bc1.a1', '54.e1.a1'], 'contains': ['216.a1.a1', '216.h1.a1', '216.i1.a1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [1576, -1, 2026, -1, 7193, -1, 7762, -1], 'generators': [19, 504], 'label': '864.2236.108.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '108.k1.a1', 'projective_image': '864.2236', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.k1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 111526851
    {'ambient': '864.2236', 'aut_centralizer_order': 24, 'aut_label': '108.k1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '4.2', 'aut_weyl_index': 432, 'centralizer': '36.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.z1.b1', '36.ba1.b1', '36.bb1.b1', '36.bc1.b1', '54.e1.a1'], 'contains': ['216.a1.a1', '216.h1.b1', '216.i1.b1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [1576, -1, 2142, -1, 7193, -1, 7682, -1], 'generators': [7, 504], 'label': '864.2236.108.k1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '108.k1.b1', 'projective_image': '864.2236', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '108.k1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 111526852
    {'ambient': '864.2236', 'aut_centralizer_order': 864, 'aut_label': '144.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 864, 'centralizer': '2.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['48.a1.a1', '48.b1.a1', '48.c1.a1', '72.b1.a1', '72.e1.a1', '72.i1.a1', '72.j1.a1', '72.k1.a1'], 'contains': ['288.a1.a1', '432.a1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4224, 5284, 4950, 6201, 5700, 5078, 5362, 7008], 'generators': [12, 48], 'label': '864.2236.144.a1.a1', 'mobius_quo': 1, 'mobius_sub': -72, 'normal_closure': '144.a1.a1', 'normal_contained_in': ['36.a1.a1', '48.a1.a1'], 'normal_contains': ['288.a1.a1', '432.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '144.a1.a1', 'projective_image': '432.523', 'quotient_action_image': '2.1', 'quotient_action_kernel': '72.43', 'quotient_action_kernel_order': 72, 'quotient_fusion': None, 'short_label': '144.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 111526853
    {'ambient': '864.2236', 'aut_centralizer_order': 288, 'aut_label': '144.b1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '2.1', 'aut_weyl_index': 864, 'centralizer': '6.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.a1.a1', '72.c1.a1', '72.d1.a1', '72.f1.a1', '72.l1.a1', '72.m1.a1', '72.n1.a1', '72.n2.a1'], 'contains': ['288.b1.a1', '432.a1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8282, -1, 7897, -1, 3873, -1, 3130, -1], 'generators': [12, 288], 'label': '864.2236.144.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '144.b1.a1', 'projective_image': '432.523', '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': '2.1'}
  • id: 111526854
    {'ambient': '864.2236', 'aut_centralizer_order': 72, 'aut_label': '144.c1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '2.1', 'aut_weyl_index': 864, 'centralizer': '24.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.q1.a1', '48.b1.a1', '72.g1.a1', '72.o1.a1', '72.p1.a1'], 'contains': ['288.c1.a1', '432.a1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [2826, -1, 2565, -1, 7959, -1, 7470, -1], 'generators': [12, 8], 'label': '864.2236.144.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.l1.a1', 'old_label': '144.c1.a1', 'projective_image': '432.523', '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': '2.1'}
  • id: 111526855
    {'ambient': '864.2236', 'aut_centralizer_order': 36, 'aut_label': '144.d1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '2.1', 'aut_weyl_index': 864, 'centralizer': '48.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.r1.a1', '48.c1.a1', '72.h1.a1'], 'contains': ['288.d1.a1', '432.a1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [709, -1, 684, -1, 9149, -1, 9076, -1], 'generators': [12, 584], 'label': '864.2236.144.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.g1.a1', 'old_label': '144.d1.a1', 'projective_image': '432.523', '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': '2.1'}
  • id: 111526856
    {'ambient': '864.2236', 'aut_centralizer_order': 288, 'aut_label': '144.e1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '2.1', 'aut_weyl_index': 864, 'centralizer': '6.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.d1.a1', '72.a1.a1', '72.b1.a1', '72.q1.a1', '72.t1.a1', '72.t1.b1', '72.v1.a1', '72.v1.b1'], 'contains': ['288.a1.a1', '432.b1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [2201, -1, 3220, -1, 6340, -1, 6926, -1], 'generators': [504, 48], 'label': '864.2236.144.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '72.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '144.e1.a1', 'projective_image': '864.2236', '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': '2.1'}
  • id: 111526857
    {'ambient': '864.2236', 'aut_centralizer_order': 6, 'aut_label': '2.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '288.1028', 'aut_weyl_index': 6, 'centralizer': '144.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1', '4.b1.a1', '4.b1.b1', '6.g1.a1', '6.h1.a1', '6.i1.a1', '8.b1.a1'], 'core': '2.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1991, 5061, 2096, 5279, 8450, 5078, 8146, 2810], 'generators': [7, 504, 48, 12, 432, 8, 288], 'label': '864.2236.2.a1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.a1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.a1.a1', '4.b1.a1', '4.b1.b1'], 'normalizer': '1.a1.a1', 'old_label': '2.a1.a1', 'projective_image': '432.523', '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': '144.183'}
  • id: 111526858
    {'ambient': '864.2236', 'aut_centralizer_order': 12, 'aut_label': '6.j1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '48.51', 'aut_weyl_index': 36, 'centralizer': '72.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1', '3.a1.a1'], 'contains': ['12.a1.a1', '12.f1.a1', '12.g1.a1', '18.n1.a1', '18.p1.a1'], 'core': '12.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6915, -1, 5066, -1, 3917, -1, 3588, -1], 'generators': [1, 48, 432, 504, 288, 12], 'label': '864.2236.6.j1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '6.j1.a1', 'projective_image': '432.523', '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': '24.14'}
  • id: 111526859
    {'ambient': '864.2236', 'aut_centralizer_order': 288, 'aut_label': '144.f1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '2.1', 'aut_weyl_index': 864, 'centralizer': '6.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.d1.a1', '72.c1.a1', '72.r1.a1', '72.u1.a1', '72.u1.b1', '72.w1.a1', '72.w1.b1', '72.x1.a1'], 'contains': ['288.b1.a1', '432.b1.a1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3846, -1, 4215, -1, 5309, -1, 5861, -1], 'generators': [432, 288], 'label': '864.2236.144.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '144.f1.a1', 'projective_image': '864.2236', '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': '2.1'}
  • id: 111526860
    {'ambient': '864.2236', 'aut_centralizer_order': 144, 'aut_label': '144.g1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '2.1', 'aut_weyl_index': 864, 'centralizer': '12.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.d1.a1', '72.d1.a1', '72.s1.a1', '72.x1.a1'], 'contains': ['288.b1.a1', '432.b1.a1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [4518, -1, 4764, -1, 5022, -1, 5442, -1], 'generators': [504, 288], 'label': '864.2236.144.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.a1', 'old_label': '144.g1.a1', 'projective_image': '864.2236', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.g1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 111526861
    {'ambient': '864.2236', 'aut_centralizer_order': 288, 'aut_label': '144.h1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '2.1', 'aut_weyl_index': 864, 'centralizer': '6.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.e1.a1', '72.b1.a1', '72.q1.a1', '72.ba1.a1', '72.bc1.a1'], 'contains': ['288.a1.a1', '432.c1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6283, -1, 6081, -1, 5218, -1, 4920, -1], 'generators': [516, 48], 'label': '864.2236.144.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '36.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '144.h1.a1', 'projective_image': '864.2236', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.h1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 111526862
    {'ambient': '864.2236', 'aut_centralizer_order': 288, 'aut_label': '144.i1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '2.1', 'aut_weyl_index': 864, 'centralizer': '6.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.e1.a1', '72.c1.a1', '72.s1.a1', '72.bb1.a1', '72.bd1.a1'], 'contains': ['288.b1.a1', '432.c1.a1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8098, -1, 6697, -1, 3781, -1, 3760, -1], 'generators': [444, 288], 'label': '864.2236.144.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '144.i1.a1', 'projective_image': '864.2236', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.i1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 111526863
    {'ambient': '864.2236', 'aut_centralizer_order': 144, 'aut_label': '144.j1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '2.1', 'aut_weyl_index': 864, 'centralizer': '12.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.e1.a1', '72.d1.a1', '72.r1.a1', '72.s1.a1'], 'contains': ['288.b1.a1', '432.c1.a1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [7771, -1, 5692, -1, 4354, -1, 4840, -1], 'generators': [516, 288], 'label': '864.2236.144.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.a1', 'old_label': '144.j1.a1', 'projective_image': '864.2236', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.j1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 111526864
    {'ambient': '864.2236', 'aut_centralizer_order': 24, 'aut_label': '144.k1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '2.1', 'aut_weyl_index': 864, 'centralizer': '36.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.f1.a1', '48.g1.a1', '48.h1.a1', '72.e1.a1', '72.t1.a1', '72.ba1.a1'], 'contains': ['288.a1.a1', '432.d1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [3545, -1, 4687, -1, 6690, -1, 7006, -1], 'generators': [19, 48], 'label': '864.2236.144.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1.a1', 'old_label': '144.k1.a1', 'projective_image': '864.2236', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '144.k1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 111526865
    {'ambient': '864.2236', 'aut_centralizer_order': 24, 'aut_label': '144.k1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '2.1', 'aut_weyl_index': 864, 'centralizer': '36.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.f1.b1', '48.g1.b1', '48.h1.b1', '72.e1.a1', '72.t1.b1', '72.ba1.a1'], 'contains': ['288.a1.a1', '432.d1.b1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [3545, -1, 4046, -1, 6690, -1, 6846, -1], 'generators': [7, 48], 'label': '864.2236.144.k1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1.a1', 'old_label': '144.k1.b1', 'projective_image': '864.2236', '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': '2.1'}
  • id: 111526866
    {'ambient': '864.2236', 'aut_centralizer_order': 24, 'aut_label': '144.l1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '6.1', 'aut_weyl_index': 288, 'centralizer': '36.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.f1.a1', '72.f1.a1', '72.u1.a1', '72.bb1.a1'], 'contains': ['288.b1.a1', '432.d1.a1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [5383, -1, 6160, -1, 5505, -1, 5282, -1], 'generators': [19, 288], 'label': '864.2236.144.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.c1.a1', 'old_label': '144.l1.a1', 'projective_image': '864.2236', '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': '6.1'}
  • id: 111526867
    {'ambient': '864.2236', 'aut_centralizer_order': 24, 'aut_label': '144.l1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '6.1', 'aut_weyl_index': 288, 'centralizer': '36.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.f1.b1', '72.f1.a1', '72.u1.b1', '72.bb1.a1'], 'contains': ['288.b1.a1', '432.d1.b1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [5383, -1, 5881, -1, 5505, -1, 5202, -1], 'generators': [7, 288], 'label': '864.2236.144.l1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.c1.a1', 'old_label': '144.l1.b1', 'projective_image': '864.2236', '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': '6.1'}
  • id: 111526868
    {'ambient': '864.2236', 'aut_centralizer_order': 12, 'aut_label': '144.m1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '6.1', 'aut_weyl_index': 288, 'centralizer': '72.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.bb1.a1', '48.g1.a1', '72.g1.a1'], 'contains': ['288.c1.a1', '432.d1.a1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [1537, -1, 1206, -1, 8167, -1, 8266, -1], 'generators': [19, 8], 'label': '864.2236.144.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.l1.a1', 'old_label': '144.m1.a1', 'projective_image': '864.2236', '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': '6.1'}
  • id: 111526869
    {'ambient': '864.2236', 'aut_centralizer_order': 2, 'aut_label': '6.k1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '288.1028', 'aut_weyl_index': 6, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '3.b1.a1'], 'contains': ['12.b1.a1', '18.m1.a1', '18.q1.a1', '24.j1.a1'], 'core': '12.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [2923, -1, 4838, -1, 7303, -1, 5529, -1], 'generators': [6, 48, 432, 8, 12, 504], 'label': '864.2236.6.k1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '6.k1.a1', 'projective_image': '432.523', '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': '144.183'}
  • id: 111526870
    {'ambient': '864.2236', 'aut_centralizer_order': 12, 'aut_label': '144.m1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '6.1', 'aut_weyl_index': 288, 'centralizer': '72.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.bb1.b1', '48.g1.b1', '72.g1.a1'], 'contains': ['288.c1.a1', '432.d1.b1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [1537, -1, 1419, -1, 8167, -1, 8144, -1], 'generators': [7, 8], 'label': '864.2236.144.m1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.l1.a1', 'old_label': '144.m1.b1', 'projective_image': '864.2236', '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': '6.1'}
  • id: 111526871
    {'ambient': '864.2236', 'aut_centralizer_order': 6, 'aut_label': '144.n1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '6.1', 'aut_weyl_index': 288, 'centralizer': '144.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.bc1.a1', '48.h1.a1', '72.h1.a1'], 'contains': ['288.d1.a1', '432.d1.a1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [501, -1, 212, -1, 9241, -1, 9236, -1], 'generators': [19, 680], 'label': '864.2236.144.n1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.g1.a1', 'old_label': '144.n1.a1', 'projective_image': '864.2236', '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': '6.1'}
  • id: 111526872
    {'ambient': '864.2236', 'aut_centralizer_order': 6, 'aut_label': '144.n1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '6.1', 'aut_weyl_index': 288, 'centralizer': '144.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['36.bc1.b1', '48.h1.b1', '72.h1.a1'], 'contains': ['288.d1.a1', '432.d1.b1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [501, -1, 535, -1, 9241, -1, 9156, -1], 'generators': [7, 680], 'label': '864.2236.144.n1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.g1.a1', 'old_label': '144.n1.b1', 'projective_image': '864.2236', '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': '6.1'}
  • id: 111526873
    {'ambient': '864.2236', 'aut_centralizer_order': 288, 'aut_label': '216.a1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '6.1', 'aut_weyl_index': 288, 'centralizer': '6.a1.a1', 'complements': ['4.c1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['72.a1.a1', '72.x1.a1', '72.y1.a1', '72.z1.a1', '108.a1.a1', '108.k1.a1', '108.k1.b1'], 'contains': ['432.b1.a1'], 'core': '216.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1466, 7294, 2501, 3339, 7193, 6650, 7722, 4419], 'generators': [504, 432], 'label': '864.2236.216.a1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '216.a1.a1', 'normal_contained_in': ['72.a1.a1', '108.a1.a1'], 'normal_contains': ['864.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '216.a1.a1', 'projective_image': '864.2236', 'quotient_action_image': '6.1', 'quotient_action_kernel': '36.7', 'quotient_action_kernel_order': 36, 'quotient_fusion': None, 'short_label': '216.a1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
  • id: 111526874
    {'ambient': '864.2236', 'aut_centralizer_order': 576, 'aut_label': '216.b1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '1.1', 'aut_weyl_index': 1728, 'centralizer': '3.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.b1.a1', '72.c1.a1', '72.d1.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.c1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6824, -1, 7091, -1, 4218, -1, 3956, -1], 'generators': [12, 504], 'label': '864.2236.216.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '108.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '216.b1.a1', 'projective_image': '432.523', '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': '1.1'}
  • id: 111526875
    {'ambient': '864.2236', 'aut_centralizer_order': 48, 'aut_label': '216.c1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '2.1', 'aut_weyl_index': 864, 'centralizer': '18.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.e1.a1', '72.f1.a1', '72.g1.a1', '72.h1.a1', '108.b1.a1', '108.h1.a1', '108.i1.a1'], 'contains': ['432.a1.a1', '432.d1.a1', '432.d1.b1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [4663, -1, 5133, -1, 5602, -1, 5527, -1], 'generators': [7, 12], 'label': '864.2236.216.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1.a1', 'old_label': '216.c1.a1', 'projective_image': '432.523', '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': '1.1'}
  • id: 111526876
    {'ambient': '864.2236', 'aut_centralizer_order': 96, 'aut_label': '216.d1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '2.1', 'aut_weyl_index': 864, 'centralizer': '9.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.i1.a1', '72.l1.a1', '72.o1.a1', '108.c1.a1', '108.h1.a1'], 'contains': ['432.a1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [4757, -1, 5265, -1, 4840, -1, 4499, -1], 'generators': [6], 'label': '864.2236.216.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1.a1', 'old_label': '216.d1.a1', 'projective_image': '432.523', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.d1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 111526877
    {'ambient': '864.2236', 'aut_centralizer_order': 48, 'aut_label': '216.e1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '2.1', 'aut_weyl_index': 864, 'centralizer': '18.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.j1.a1', '72.m1.a1', '72.p1.a1', '108.e1.a1', '108.h1.a1', '108.i1.a1'], 'contains': ['432.a1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [4863, -1, 5415, -1, 4931, -1, 4602, -1], 'generators': [1], 'label': '864.2236.216.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.c1.a1', 'old_label': '216.e1.a1', 'projective_image': '432.523', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.e1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 111526878
    {'ambient': '864.2236', 'aut_centralizer_order': 32, 'aut_label': '216.f1', 'aut_quo_index': None, 'aut_stab_index': 27, 'aut_weyl_group': '2.1', 'aut_weyl_index': 864, 'centralizer': '27.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.k1.a1', '72.n1.a1', '72.n2.a1', '108.c1.a1', '108.g1.a1', '108.i1.a1'], 'contains': ['432.a1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [7019, -1, 8444, -1, 2746, -1, 2387, -1], 'generators': [510], 'label': '864.2236.216.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1.a1', 'old_label': '216.f1.a1', 'projective_image': '432.523', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.f1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 111526879
    {'ambient': '864.2236', 'aut_centralizer_order': 288, 'aut_label': '216.g1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '2.1', 'aut_weyl_index': 864, 'centralizer': '6.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.q1.a1', '72.r1.a1', '72.s1.a1', '108.a1.a1', '108.j1.a1', '108.j1.b1'], 'contains': ['432.b1.a1', '432.c1.a1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3437, -1, 3517, -1, 5407, -1, 6418, -1], 'generators': [444, 504], 'label': '864.2236.216.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '108.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '216.g1.a1', 'projective_image': '864.2236', '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': '2.1'}
  • id: 111526880
    {'ambient': '864.2236', 'aut_centralizer_order': 12, 'aut_label': '8.a1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '144.183', 'aut_weyl_index': 12, 'centralizer': '144.a1.a1', 'complements': ['108.h1.a1', '108.i1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '4.b1.a1', '4.b1.b1'], 'contains': ['24.b1.a1', '24.c1.a1', '24.o1.a1', '32.a1.a1'], 'core': '8.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [707, 5404, 818, 5279, 9025, 4655, 8800, 3592], 'generators': [8, 432, 288, 48, 504], 'label': '864.2236.8.a1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': ['4.a1.a1', '4.b1.a1', '4.b1.b1'], 'normal_contains': ['24.b1.a1', '24.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.a1.a1', 'projective_image': '864.2236', 'quotient_action_image': '4.2', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '8.a1.a1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 111526881
    {'ambient': '864.2236', 'aut_centralizer_order': 48, 'aut_label': '216.h1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '2.1', 'aut_weyl_index': 864, 'centralizer': '18.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.t1.a1', '72.u1.a1', '108.b1.a1', '108.j1.a1', '108.k1.a1'], 'contains': ['432.b1.a1', '432.d1.a1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [3291, -1, 3787, -1, 6242, -1, 6760, -1], 'generators': [19, 432], 'label': '864.2236.216.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '216.h1.a1', 'projective_image': '864.2236', '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': '2.1'}
  • id: 111526882
    {'ambient': '864.2236', 'aut_centralizer_order': 48, 'aut_label': '216.h1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '2.1', 'aut_weyl_index': 864, 'centralizer': '18.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.t1.b1', '72.u1.b1', '108.b1.a1', '108.j1.b1', '108.k1.b1'], 'contains': ['432.b1.a1', '432.d1.b1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [3291, -1, 3004, -1, 6242, -1, 6509, -1], 'generators': [7, 432], 'label': '864.2236.216.h1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '216.h1.b1', 'projective_image': '864.2236', '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': '2.1'}
  • id: 111526883
    {'ambient': '864.2236', 'aut_centralizer_order': 48, 'aut_label': '216.i1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '2.1', 'aut_weyl_index': 864, 'centralizer': '18.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.v1.a1', '72.w1.a1', '108.d1.a1', '108.j1.b1', '108.k1.a1'], 'contains': ['432.b1.a1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [2177, -1, 3085, -1, 6144, -1, 6595, -1], 'generators': [523], 'label': '864.2236.216.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '216.i1.a1', 'projective_image': '864.2236', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.i1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 111526884
    {'ambient': '864.2236', 'aut_centralizer_order': 48, 'aut_label': '216.i1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '2.1', 'aut_weyl_index': 864, 'centralizer': '18.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.v1.b1', '72.w1.b1', '108.d1.a1', '108.j1.a1', '108.k1.b1'], 'contains': ['432.b1.a1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [2177, -1, 3162, -1, 6144, -1, 6675, -1], 'generators': [511], 'label': '864.2236.216.i1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '216.i1.b1', 'projective_image': '864.2236', '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': '2.1'}
  • id: 111526885
    {'ambient': '864.2236', 'aut_centralizer_order': 48, 'aut_label': '216.j1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '2.1', 'aut_weyl_index': 864, 'centralizer': '18.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.ba1.a1', '72.bb1.a1', '108.b1.a1'], 'contains': ['432.c1.a1', '432.d1.a1', '432.d1.b1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [5196, -1, 6315, -1, 5120, -1, 5006, -1], 'generators': [7, 444], 'label': '864.2236.216.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1.a1', 'old_label': '216.j1.a1', 'projective_image': '864.2236', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '216.j1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 111526886
    {'ambient': '864.2236', 'aut_centralizer_order': 48, 'aut_label': '216.k1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '2.1', 'aut_weyl_index': 864, 'centralizer': '18.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.bc1.a1', '72.bd1.a1', '108.f1.a1'], 'contains': ['432.c1.a1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [8550, -1, 9656, -1, 1749, -1, 1484, -1], 'generators': [505], 'label': '864.2236.216.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.g1.a1', 'old_label': '216.k1.a1', 'projective_image': '864.2236', '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': '1.1'}
  • id: 111526887
    {'ambient': '864.2236', 'aut_centralizer_order': 864, 'aut_label': '288.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 864, 'centralizer': '2.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['96.a1.a1', '96.b1.a1', '96.c1.a1', '144.a1.a1', '144.e1.a1', '144.h1.a1', '144.k1.a1', '144.k1.b1'], 'contains': ['864.a1.a1'], 'core': '288.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3611, 4494, 4456, 6037, 6336, 4586, 6846, 5675], 'generators': [48], 'label': '864.2236.288.a1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '288.a1.a1', 'normal_contained_in': ['72.a1.a1', '96.a1.a1', '144.a1.a1'], 'normal_contains': ['864.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '288.a1.a1', 'projective_image': '864.2236', 'quotient_action_image': '2.1', 'quotient_action_kernel': '144.189', 'quotient_action_kernel_order': 144, 'quotient_fusion': None, 'short_label': '288.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 111526888
    {'ambient': '864.2236', 'aut_centralizer_order': 288, 'aut_label': '288.b1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '2.1', 'aut_weyl_index': 864, 'centralizer': '6.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.a1.a1', '144.b1.a1', '144.f1.a1', '144.g1.a1', '144.i1.a1', '144.j1.a1', '144.l1.a1', '144.l1.b1'], 'contains': ['864.a1.a1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5383, -1, 5760, -1, 5261, -1, 5282, -1], 'generators': [288], 'label': '864.2236.288.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '96.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '288.b1.a1', 'projective_image': '864.2236', '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': '2.1'}
  • id: 111526889
    {'ambient': '864.2236', 'aut_centralizer_order': 72, 'aut_label': '288.c1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '2.1', 'aut_weyl_index': 864, 'centralizer': '24.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.y1.a1', '96.b1.a1', '144.c1.a1', '144.m1.a1', '144.m1.b1'], 'contains': ['864.a1.a1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [1539, -1, 1385, -1, 8097, -1, 8175, -1], 'generators': [8], 'label': '864.2236.288.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.l1.a1', 'old_label': '288.c1.a1', 'projective_image': '864.2236', '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': '2.1'}
  • id: 111526890
    {'ambient': '864.2236', 'aut_centralizer_order': 36, 'aut_label': '288.d1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '2.1', 'aut_weyl_index': 864, 'centralizer': '48.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['72.z1.a1', '96.c1.a1', '144.d1.a1', '144.n1.a1', '144.n1.b1'], 'contains': ['864.a1.a1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [568, -1, 504, -1, 9149, -1, 9116, -1], 'generators': [584], 'label': '864.2236.288.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.g1.a1', 'old_label': '288.d1.a1', 'projective_image': '864.2236', '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': '2.1'}
  • id: 111526891
    {'ambient': '864.2236', 'aut_centralizer_order': 6, 'aut_label': '8.b1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '72.46', 'aut_weyl_index': 24, 'centralizer': '144.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '4.c1.a1'], 'contains': ['16.a1.a1', '16.b1.a1', '16.b1.b1', '24.e1.a1', '24.f1.a1', '24.g1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [1809, -1, 1915, -1, 8615, -1, 8292, -1], 'generators': [7, 48, 12, 8, 288], 'label': '864.2236.8.b1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1.a1', 'old_label': '8.b1.a1', 'projective_image': '432.523', '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': '36.10'}
  • id: 111526892
    {'ambient': '864.2236', 'aut_centralizer_order': 1728, 'aut_label': '432.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '1.1', 'aut_weyl_index': 1728, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['144.a1.a1', '144.b1.a1', '144.c1.a1', '144.d1.a1', '216.b1.a1', '216.c1.a1', '216.d1.a1', '216.e1.a1', '216.f1.a1'], 'contains': ['864.a1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4732, 6074, 5176, 4687, 5478, 5694, 5081, 6468], 'generators': [12], 'label': '864.2236.432.a1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '432.a1.a1', 'normal_contained_in': ['108.a1.a1', '144.a1.a1'], 'normal_contains': ['864.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '432.a1.a1', 'projective_image': '432.523', 'quotient_action_image': '1.1', 'quotient_action_kernel': '432.523', 'quotient_action_kernel_order': 432, 'quotient_fusion': None, 'short_label': '432.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 111526893
    {'ambient': '864.2236', 'aut_centralizer_order': 576, 'aut_label': '432.b1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '1.1', 'aut_weyl_index': 1728, 'centralizer': '3.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.e1.a1', '144.f1.a1', '144.g1.a1', '216.a1.a1', '216.b1.a1', '216.g1.a1', '216.h1.a1', '216.h1.b1', '216.i1.a1', '216.i1.b1'], 'contains': ['864.a1.a1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3405, -1, 3260, -1, 6144, -1, 6532, -1], 'generators': [504], 'label': '864.2236.432.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '216.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '432.b1.a1', 'projective_image': '864.2236', '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': '1.1'}
  • id: 111526894
    {'ambient': '864.2236', 'aut_centralizer_order': 576, 'aut_label': '432.c1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '1.1', 'aut_weyl_index': 1728, 'centralizer': '3.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.h1.a1', '144.i1.a1', '144.j1.a1', '216.b1.a1', '216.g1.a1', '216.j1.a1', '216.k1.a1'], 'contains': ['864.a1.a1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6786, -1, 6205, -1, 4756, -1, 4880, -1], 'generators': [516], 'label': '864.2236.432.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '108.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '432.c1.a1', 'projective_image': '864.2236', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '432.c1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 111526895
    {'ambient': '864.2236', 'aut_centralizer_order': 48, 'aut_label': '432.d1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '1.1', 'aut_weyl_index': 1728, 'centralizer': '18.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.k1.a1', '144.l1.a1', '144.m1.a1', '144.n1.a1', '216.c1.a1', '216.h1.a1', '216.j1.a1'], 'contains': ['864.a1.a1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [3545, -1, 4565, -1, 6238, -1, 6737, -1], 'generators': [19], 'label': '864.2236.432.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1.a1', 'old_label': '432.d1.a1', 'projective_image': '864.2236', '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': '1.1'}
  • id: 111526896
    {'ambient': '864.2236', 'aut_centralizer_order': 48, 'aut_label': '432.d1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '1.1', 'aut_weyl_index': 1728, 'centralizer': '18.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['144.k1.b1', '144.l1.b1', '144.m1.b1', '144.n1.b1', '216.c1.a1', '216.h1.b1', '216.j1.a1'], 'contains': ['864.a1.a1'], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [3545, -1, 4236, -1, 6238, -1, 6612, -1], 'generators': [7], 'label': '864.2236.432.d1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '18.a1.a1', 'old_label': '432.d1.b1', 'projective_image': '864.2236', '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': '1.1'}
  • id: 111526897
    {'ambient': '864.2236', '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': ['1.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['288.a1.a1', '288.b1.a1', '288.c1.a1', '288.d1.a1', '432.a1.a1', '432.b1.a1', '432.c1.a1', '432.d1.a1', '432.d1.b1'], 'contains': [], 'core': '864.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3577, 6074, 4456, 4687, 6190, 5694, 6612, 5675], 'generators': [], 'label': '864.2236.864.a1.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '864.a1.a1', 'normal_contained_in': ['216.a1.a1', '288.a1.a1', '432.a1.a1'], 'normal_contains': [], 'normalizer': '1.a1.a1', 'old_label': '864.a1.a1', 'projective_image': '864.2236', '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': '1.1'}
  • id: 111526898
    {'ambient': '864.2236', 'aut_centralizer_order': 2, 'aut_label': '8.c1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '216.102', 'aut_weyl_index': 8, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '4.c1.a1'], 'contains': ['16.a1.a1', '24.a1.a1', '24.j1.a1'], 'core': '24.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [3148, -1, 4445, -1, 7188, -1, 5663, -1], 'generators': [6, 48, 8, 12, 288], 'label': '864.2236.8.c1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1.a1', 'old_label': '8.c1.a1', 'projective_image': '432.523', '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': '108.17'}
  • id: 111526899
    {'ambient': '864.2236', 'aut_centralizer_order': 2, 'aut_label': '8.d1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '216.102', 'aut_weyl_index': 8, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.c1.a1', '4.c1.a1'], 'contains': ['16.a1.a1', '24.h1.a1', '24.k1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [3526, -1, 3231, -1, 7850, -1, 6520, -1], 'generators': [1, 48, 288, 12, 8], 'label': '864.2236.8.d1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1.a1', 'old_label': '8.d1.a1', 'projective_image': '432.523', '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': '108.17'}
  • id: 111526900
    {'ambient': '864.2236', 'aut_centralizer_order': 2, 'aut_label': '9.a1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '96.230', 'aut_weyl_index': 18, 'centralizer': '216.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1.a1', '3.b1.a1'], 'contains': ['18.a1.a1', '18.b1.a1', '18.e1.a1', '18.f1.a1', '18.i1.a1', '18.m1.a1', '18.n1.a1', '27.a1.a1'], 'core': '36.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [5462, -1, 7297, -1, 4536, -1, 3792, -1], 'generators': [1, 48, 432, 6, 504, 12], 'label': '864.2236.9.a1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '9.a1.a1', 'projective_image': '432.523', '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': '24.14'}
  • id: 111526901
    {'ambient': '864.2236', 'aut_centralizer_order': 2, 'aut_label': '9.b1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '96.230', 'aut_weyl_index': 18, 'centralizer': '216.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1.a1'], 'contains': ['18.c1.a1', '18.d1.a1', '18.g1.a1', '18.h1.a1', '18.j1.a1', '18.o1.a1', '18.p1.a1', '27.a1.a1'], 'core': '108.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [8782, -1, 8433, -1, 2392, -1, 2454, -1], 'generators': [1, 288, 432, 6, 504, 12], 'label': '864.2236.9.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1.a1', 'old_label': '9.b1.a1', 'projective_image': '432.523', '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': '24.14'}
  • id: 111526902
    {'ambient': '864.2236', 'aut_centralizer_order': 2, 'aut_label': '9.c1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '96.226', 'aut_weyl_index': 18, 'centralizer': '216.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.b1.a1'], 'contains': ['18.k1.a1', '18.q1.a1', '18.r1.a1', '27.a1.a1', '36.w1.a1'], 'core': '108.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [3474, -1, 3650, -1, 7780, -1, 6064, -1], 'generators': [1, 432, 504, 6, 12, 8], 'label': '864.2236.9.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1.a1', 'old_label': '9.c1.a1', 'projective_image': '432.523', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '9.c1.a1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 111526903
    {'ambient': '864.2236', 'aut_centralizer_order': 144, 'aut_label': '12.a1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '12.4', 'aut_weyl_index': 144, 'centralizer': '12.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '6.a1.a1', '6.g1.a1', '6.j1.a1'], 'contains': ['24.b1.a1', '24.d1.a1', '24.l1.a1', '36.a1.a1', '36.p1.a1'], 'core': '12.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4847, 3720, 4613, 6908, 5690, 2809, 5303, 6568], 'generators': [12, 48, 504, 432, 288], 'label': '864.2236.12.a1.a1', 'mobius_quo': 0, 'mobius_sub': -6, 'normal_closure': '12.a1.a1', 'normal_contained_in': ['4.a1.a1', '6.a1.a1'], 'normal_contains': ['24.b1.a1', '36.a1.a1', '48.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '12.a1.a1', 'projective_image': '432.523', 'quotient_action_image': '12.4', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '12.a1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 111526904
    {'ambient': '864.2236', 'aut_centralizer_order': 2, 'aut_label': '2.b1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '864.4000', 'aut_weyl_index': 2, 'centralizer': '432.a1.a1', 'complements': ['432.d1.b1', '432.d1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1', '6.a1.a1', '6.k1.a1', '8.c1.a1'], 'core': '2.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3049, 1675, 4731, 8520, 7303, 2385, 5663, 6667], 'generators': [6, 288, 432, 8, 48, 12, 504], 'label': '864.2236.2.b1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.b1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.a1.a1', '6.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.b1.a1', 'projective_image': '432.523', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.b1.a1', 'subgroup_fusion': None, 'weyl_group': '432.523'}
  • id: 111526905
    {'ambient': '864.2236', 'aut_centralizer_order': 12, 'aut_label': '12.b1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '144.183', 'aut_weyl_index': 12, 'centralizer': '144.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '6.b1.a1', '6.h1.a1', '6.k1.a1'], 'contains': ['24.c1.a1', '36.a1.a1', '36.q1.a1', '48.b1.a1'], 'core': '12.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2356, 7759, 2860, 3240, 8363, 6541, 7712, 4959], 'generators': [12, 432, 8, 48, 504], 'label': '864.2236.12.b1.a1', 'mobius_quo': 0, 'mobius_sub': -6, 'normal_closure': '12.b1.a1', 'normal_contained_in': ['4.a1.a1', '6.b1.a1'], 'normal_contains': ['24.c1.a1', '36.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '12.b1.a1', 'projective_image': '432.523', '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': '144.183'}
  • id: 111526906
    {'ambient': '864.2236', 'aut_centralizer_order': 12, 'aut_label': '12.c1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '48.51', 'aut_weyl_index': 36, 'centralizer': '72.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.c1.a1', '6.d1.a1', '6.g1.a1'], 'contains': ['24.d1.a1', '24.e1.a1', '24.m1.a1', '24.m1.b1', '24.p1.a1', '36.b1.a1', '36.c1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6100, -1, 6482, -1, 5456, -1, 4440, -1], 'generators': [7, 288, 12, 432, 48], 'label': '864.2236.12.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.c1.a1', 'projective_image': '432.523', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.c1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 111526907
    {'ambient': '864.2236', 'aut_centralizer_order': 8, 'aut_label': '12.d1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '72.46', 'aut_weyl_index': 24, 'centralizer': '108.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.a1.a1', '6.c1.a1', '6.e1.a1'], 'contains': ['24.a1.a1', '24.d1.a1', '24.i1.a1', '36.d1.a1', '36.i1.a1', '36.j1.a1'], 'core': '24.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6737, -1, 8101, -1, 2897, -1, 2233, -1], 'generators': [6, 48, 504, 12, 288], 'label': '864.2236.12.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.d1.a1', 'projective_image': '432.523', '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': '36.10'}
  • id: 111526908
    {'ambient': '864.2236', 'aut_centralizer_order': 12, 'aut_label': '12.e1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '48.51', 'aut_weyl_index': 36, 'centralizer': '72.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.e1.a1', '6.f1.a1', '6.g1.a1'], 'contains': ['24.d1.a1', '24.n1.a1', '24.n1.b1', '36.e1.a1', '36.k1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7255, -1, 5094, -1, 4412, -1, 4649, -1], 'generators': [511, 288, 12, 48, 432], 'label': '864.2236.12.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.e1.a1', 'projective_image': '432.523', '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': '24.14'}
  • id: 111526909
    {'ambient': '864.2236', 'aut_centralizer_order': 12, 'aut_label': '12.f1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '48.51', 'aut_weyl_index': 36, 'centralizer': '72.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.c1.a1', '6.f1.a1', '6.j1.a1'], 'contains': ['24.d1.a1', '24.h1.a1', '36.f1.a1', '36.l1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6956, -1, 6282, -1, 3625, -1, 3344, -1], 'generators': [1, 48, 432, 288, 12], 'label': '864.2236.12.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.f1.a1', 'projective_image': '432.523', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.f1.a1', 'subgroup_fusion': None, 'weyl_group': '24.14'}
  • id: 111526910
    {'ambient': '864.2236', 'aut_centralizer_order': 12, 'aut_label': '12.g1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '48.51', 'aut_weyl_index': 36, 'centralizer': '72.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.d1.a1', '6.e1.a1', '6.j1.a1'], 'contains': ['24.d1.a1', '24.q1.a1', '36.g1.a1', '36.m1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8013, -1, 8849, -1, 1572, -1, 1228, -1], 'generators': [505, 48, 432, 288, 444], 'label': '864.2236.12.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.g1.a1', 'projective_image': '432.523', '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': '24.14'}
  • id: 111526911
    {'ambient': '864.2236', 'aut_centralizer_order': 8, 'aut_label': '12.h1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '72.46', 'aut_weyl_index': 24, 'centralizer': '108.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.a1.a1', '6.d1.a1', '6.f1.a1'], 'contains': ['24.d1.a1', '24.i1.a1', '36.h1.a1', '36.n1.a1', '36.o1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7751, -1, 7822, -1, 2153, -1, 1714, -1], 'generators': [438, 48, 504, 12, 288], 'label': '864.2236.12.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.h1.a1', 'projective_image': '432.523', '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': '36.10'}
  • id: 111526912
    {'ambient': '864.2236', 'aut_centralizer_order': 12, 'aut_label': '12.i1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '72.43', 'aut_weyl_index': 24, 'centralizer': '144.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '6.i1.a1'], 'contains': ['24.o1.a1', '36.a1.a1', '36.r1.a1', '48.c1.a1'], 'core': '36.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [999, -1, 1162, -1, 9331, -1, 9250, -1], 'generators': [12, 432, 584, 48, 504], 'label': '864.2236.12.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '12.i1.a1', 'projective_image': '432.523', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.i1.a1', 'subgroup_fusion': None, 'weyl_group': '72.43'}
  • id: 111526913
    {'ambient': '864.2236', 'aut_centralizer_order': 2, 'aut_label': '12.j1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '144.192', 'aut_weyl_index': 12, 'centralizer': '216.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.c1.a1', '6.c1.a1'], 'contains': ['24.a1.a1', '24.e1.a1', '24.h1.a1', '36.s1.a1', '36.u1.a1'], 'core': '24.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [4390, -1, 5479, -1, 5218, -1, 4231, -1], 'generators': [1, 48, 6, 12, 288], 'label': '864.2236.12.j1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.c1.a1', 'old_label': '12.j1.a1', 'projective_image': '432.523', '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': '36.10'}
  • id: 111526914
    {'ambient': '864.2236', 'aut_centralizer_order': 2, 'aut_label': '12.k1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '144.192', 'aut_weyl_index': 12, 'centralizer': '216.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.c1.a1'], 'contains': ['24.e1.a1', '24.h1.a1', '24.i1.a1', '36.t1.a1', '36.v1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [6330, -1, 7516, -1, 3988, -1, 2872, -1], 'generators': [1, 48, 438, 12, 288], 'label': '864.2236.12.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.c1.a1', 'old_label': '12.k1.a1', 'projective_image': '432.523', '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': '36.10'}
  • id: 111526915
    {'ambient': '864.2236', 'aut_centralizer_order': 2, 'aut_label': '2.c1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '864.4000', 'aut_weyl_index': 2, 'centralizer': '432.a1.a1', 'complements': ['432.d1.b1', '432.d1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1', '6.b1.a1', '6.j1.a1', '8.d1.a1'], 'core': '2.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3683, 8531, 3202, 1958, 7891, 7840, 6486, 5036], 'generators': [1, 504, 48, 288, 432, 12, 8], 'label': '864.2236.2.c1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.c1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.a1.a1', '6.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.c1.a1', 'projective_image': '432.523', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.c1.a1', 'subgroup_fusion': None, 'weyl_group': '432.523'}
  • id: 111526916
    {'ambient': '864.2236', 'aut_centralizer_order': 1, 'aut_label': '12.l1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '144.192', 'aut_weyl_index': 12, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.b1.a1', '4.c1.a1'], 'contains': ['24.f1.a1', '24.j1.a1', '24.k1.a1', '36.s1.a1', '36.w1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [3261, -1, 3368, -1, 7605, -1, 6348, -1], 'generators': [1, 48, 6, 12, 8], 'label': '864.2236.12.l1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.l1.a1', 'old_label': '12.l1.a1', 'projective_image': '432.523', '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': '36.10'}
  • id: 111526917
    {'ambient': '864.2236', 'aut_centralizer_order': 12, 'aut_label': '12.m1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '24.14', 'aut_weyl_index': 72, 'centralizer': '72.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.g1.a1'], 'contains': ['24.l1.a1', '24.m1.a1', '24.n1.b1', '36.x1.a1', '36.y1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3742, -1, 4282, -1, 6229, -1, 6020, -1], 'generators': [511, 288, 516, 48, 432], 'label': '864.2236.12.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.m1.a1', 'projective_image': '864.2236', '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': '24.14'}
  • id: 111526918
    {'ambient': '864.2236', 'aut_centralizer_order': 12, 'aut_label': '12.m1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '24.14', 'aut_weyl_index': 72, 'centralizer': '72.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.g1.a1'], 'contains': ['24.l1.a1', '24.m1.b1', '24.n1.a1', '36.x1.b1', '36.y1.b1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3742, -1, 3977, -1, 6229, -1, 5835, -1], 'generators': [7, 288, 516, 48, 432], 'label': '864.2236.12.m1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.m1.b1', 'projective_image': '864.2236', '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': '24.14'}
  • id: 111526919
    {'ambient': '864.2236', 'aut_centralizer_order': 12, 'aut_label': '12.n1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '24.14', 'aut_weyl_index': 72, 'centralizer': '72.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '6.g1.a1'], 'contains': ['24.b1.a1', '24.m1.a1', '24.n1.a1', '36.z1.a1', '36.ba1.a1'], 'core': '24.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [2586, -1, 2643, -1, 6955, -1, 6878, -1], 'generators': [19, 288, 504, 48, 432], 'label': '864.2236.12.n1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.n1.a1', 'projective_image': '864.2236', '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': '24.14'}
  • id: 111526920
    {'ambient': '864.2236', 'aut_centralizer_order': 12, 'aut_label': '12.n1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '24.14', 'aut_weyl_index': 72, 'centralizer': '72.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1.b1', '6.g1.a1'], 'contains': ['24.b1.a1', '24.m1.b1', '24.n1.b1', '36.z1.b1', '36.ba1.b1'], 'core': '24.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [2586, -1, 3112, -1, 6955, -1, 6693, -1], 'generators': [7, 288, 504, 48, 432], 'label': '864.2236.12.n1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.n1.b1', 'projective_image': '864.2236', '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': '24.14'}
  • id: 111526921
    {'ambient': '864.2236', 'aut_centralizer_order': 6, 'aut_label': '12.o1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '48.48', 'aut_weyl_index': 36, 'centralizer': '144.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '6.h1.a1'], 'contains': ['24.c1.a1', '36.z1.a1', '36.bb1.a1', '48.g1.a1'], 'core': '24.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [1447, -1, 1470, -1, 8868, -1, 8662, -1], 'generators': [19, 432, 48, 8, 504], 'label': '864.2236.12.o1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '12.o1.a1', 'projective_image': '864.2236', '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': '48.48'}
  • id: 111526922
    {'ambient': '864.2236', 'aut_centralizer_order': 6, 'aut_label': '12.o1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '48.48', 'aut_weyl_index': 36, 'centralizer': '144.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1.b1', '6.h1.a1'], 'contains': ['24.c1.a1', '36.z1.b1', '36.bb1.b1', '48.g1.b1'], 'core': '24.c1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [1447, -1, 1697, -1, 8868, -1, 8512, -1], 'generators': [7, 432, 48, 8, 504], 'label': '864.2236.12.o1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '12.o1.b1', 'projective_image': '864.2236', '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': '48.48'}
  • id: 111526923
    {'ambient': '864.2236', 'aut_centralizer_order': 6, 'aut_label': '12.p1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '24.12', 'aut_weyl_index': 72, 'centralizer': '144.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '6.i1.a1'], 'contains': ['24.o1.a1', '36.z1.a1', '36.bc1.a1', '48.h1.a1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [206, -1, 190, -1, 9582, -1, 9762, -1], 'generators': [19, 432, 48, 680, 504], 'label': '864.2236.12.p1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.i1.a1', 'old_label': '12.p1.a1', 'projective_image': '864.2236', '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': '24.12'}
  • id: 111526924
    {'ambient': '864.2236', 'aut_centralizer_order': 6, 'aut_label': '12.p1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '24.12', 'aut_weyl_index': 72, 'centralizer': '144.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1.b1', '6.i1.a1'], 'contains': ['24.o1.a1', '36.z1.b1', '36.bc1.b1', '48.h1.b1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [206, -1, 646, -1, 9582, -1, 9442, -1], 'generators': [7, 432, 48, 680, 504], 'label': '864.2236.12.p1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.i1.a1', 'old_label': '12.p1.b1', 'projective_image': '864.2236', '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': '24.12'}
  • id: 111526925
    {'ambient': '864.2236', 'aut_centralizer_order': 12, 'aut_label': '16.a1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '36.10', 'aut_weyl_index': 48, 'centralizer': '144.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '8.b1.a1', '8.c1.a1', '8.d1.a1'], 'contains': ['32.a1.a1', '48.a1.a1', '48.b1.a1', '48.c1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [1711, -1, 2017, -1, 8681, -1, 7938, -1], 'generators': [12, 8, 288, 48], 'label': '864.2236.16.a1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1.a1', 'old_label': '16.a1.a1', 'projective_image': '432.523', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.a1.a1', 'subgroup_fusion': None, 'weyl_group': '36.10'}
  • id: 111526926
    {'ambient': '864.2236', 'aut_centralizer_order': 2, 'aut_label': '3.a1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '288.1040', 'aut_weyl_index': 6, 'centralizer': '216.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['6.a1.a1', '6.c1.a1', '6.d1.a1', '6.e1.a1', '6.f1.a1', '6.g1.a1', '6.j1.a1', '9.a1.a1', '9.b1.a1'], 'core': '6.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6740, -1, 7345, -1, 3798, -1, 3238, -1], 'generators': [1, 288, 432, 6, 48, 504, 12], 'label': '864.2236.3.a1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '3.a1.a1', 'projective_image': '432.523', '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': '72.46'}
  • id: 111526927
    {'ambient': '864.2236', 'aut_centralizer_order': 6, 'aut_label': '16.b1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '36.10', 'aut_weyl_index': 48, 'centralizer': '144.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '8.b1.a1'], 'contains': ['32.a1.a1', '48.f1.a1', '48.g1.a1', '48.h1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [545, -1, 777, -1, 9188, -1, 9124, -1], 'generators': [19, 8, 288, 48], 'label': '864.2236.16.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1.a1', 'old_label': '16.b1.a1', 'projective_image': '864.2236', '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': '36.10'}
  • id: 111526928
    {'ambient': '864.2236', 'aut_centralizer_order': 6, 'aut_label': '16.b1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '36.10', 'aut_weyl_index': 48, 'centralizer': '144.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1.b1', '8.b1.a1'], 'contains': ['32.a1.a1', '48.f1.b1', '48.g1.b1', '48.h1.b1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [545, -1, 1374, -1, 9188, -1, 9000, -1], 'generators': [7, 8, 288, 48], 'label': '864.2236.16.b1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1.a1', 'old_label': '16.b1.b1', 'projective_image': '864.2236', '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': '36.10'}
  • id: 111526929
    {'ambient': '864.2236', 'aut_centralizer_order': 4, 'aut_label': '18.a1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '48.51', 'aut_weyl_index': 36, 'centralizer': '108.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.c1.a1', '9.a1.a1'], 'contains': ['36.b1.a1', '36.d1.a1', '36.f1.a1', '36.s1.a1', '36.t1.a1', '54.a1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [6014, -1, 7367, -1, 4993, -1, 4035, -1], 'generators': [1, 48, 6, 432, 12], 'label': '864.2236.18.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '18.a1.a1', 'projective_image': '432.523', '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': '12.4'}
  • id: 111526930
    {'ambient': '864.2236', 'aut_centralizer_order': 2, 'aut_label': '18.b1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '96.230', 'aut_weyl_index': 18, 'centralizer': '216.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.d1.a1', '9.a1.a1'], 'contains': ['36.b1.a1', '36.g1.a1', '36.h1.a1', '54.b1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [7016, -1, 8251, -1, 3074, -1, 3015, -1], 'generators': [505, 48, 510, 444, 432], 'label': '864.2236.18.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '18.b1.a1', 'projective_image': '432.523', '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': '24.14'}
  • id: 111526931
    {'ambient': '864.2236', 'aut_centralizer_order': 4, 'aut_label': '18.c1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '48.51', 'aut_weyl_index': 36, 'centralizer': '108.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.c1.a1', '9.b1.a1'], 'contains': ['36.c1.a1', '36.i1.a1', '36.l1.a1', '36.u1.a1', '36.v1.a1', '54.a1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [8134, -1, 8491, -1, 2644, -1, 2454, -1], 'generators': [1, 288, 6, 432, 12], 'label': '864.2236.18.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1.a1', 'old_label': '18.c1.a1', 'projective_image': '432.523', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.c1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 111526932
    {'ambient': '864.2236', 'aut_centralizer_order': 2, 'aut_label': '18.d1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '96.230', 'aut_weyl_index': 18, 'centralizer': '216.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.d1.a1', '9.b1.a1'], 'contains': ['36.c1.a1', '36.m1.a1', '36.n1.a1', '54.b1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [9327, -1, 9185, -1, 1195, -1, 1372, -1], 'generators': [505, 288, 510, 444, 432], 'label': '864.2236.18.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1.a1', 'old_label': '18.d1.a1', 'projective_image': '432.523', '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': '24.14'}
  • id: 111526933
    {'ambient': '864.2236', 'aut_centralizer_order': 4, 'aut_label': '18.e1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '48.51', 'aut_weyl_index': 36, 'centralizer': '108.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.e1.a1', '9.a1.a1'], 'contains': ['36.d1.a1', '36.e1.a1', '36.g1.a1', '54.c1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [6812, -1, 8769, -1, 3413, -1, 3159, -1], 'generators': [505, 48, 6, 444, 432], 'label': '864.2236.18.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '18.e1.a1', 'projective_image': '432.523', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.e1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 111526934
    {'ambient': '864.2236', 'aut_centralizer_order': 2, 'aut_label': '18.f1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '96.230', 'aut_weyl_index': 18, 'centralizer': '216.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.f1.a1', '9.a1.a1'], 'contains': ['36.e1.a1', '36.f1.a1', '36.h1.a1', '54.d1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [6637, -1, 6524, -1, 3807, -1, 3655, -1], 'generators': [1, 48, 510, 12, 432], 'label': '864.2236.18.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '18.f1.a1', 'projective_image': '432.523', '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': '24.14'}
  • id: 111526935
    {'ambient': '864.2236', 'aut_centralizer_order': 4, 'aut_label': '18.g1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '48.51', 'aut_weyl_index': 36, 'centralizer': '108.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.e1.a1', '9.b1.a1'], 'contains': ['36.i1.a1', '36.k1.a1', '36.m1.a1', '54.c1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [8963, -1, 9546, -1, 1360, -1, 1517, -1], 'generators': [505, 288, 6, 444, 432], 'label': '864.2236.18.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1.a1', 'old_label': '18.g1.a1', 'projective_image': '432.523', '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': '12.4'}
  • id: 111526936
    {'ambient': '864.2236', 'aut_centralizer_order': 2, 'aut_label': '18.h1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '96.230', 'aut_weyl_index': 18, 'centralizer': '216.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.f1.a1', '9.b1.a1'], 'contains': ['36.k1.a1', '36.l1.a1', '36.n1.a1', '54.d1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [9122, -1, 7793, -1, 1737, -1, 2078, -1], 'generators': [1, 288, 510, 12, 432], 'label': '864.2236.18.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1.a1', 'old_label': '18.h1.a1', 'projective_image': '432.523', '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': '24.14'}
  • id: 111526937
    {'ambient': '864.2236', 'aut_centralizer_order': 1, 'aut_label': '3.b1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '576.8659', 'aut_weyl_index': 3, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['6.b1.a1', '6.h1.a1', '6.k1.a1', '9.a1.a1', '9.c1.a1', '12.l1.a1'], 'core': '6.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3368, -1, 3518, -1, 7670, -1, 6161, -1], 'generators': [1, 504, 48, 6, 432, 12, 8], 'label': '864.2236.3.b1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '3.b1.a1', 'projective_image': '432.523', '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': '144.183'}
  • id: 111526938
    {'ambient': '864.2236', 'aut_centralizer_order': 12, 'aut_label': '18.i1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '16.14', 'aut_weyl_index': 108, 'centralizer': '72.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.g1.a1', '6.h1.a1', '6.i1.a1', '9.a1.a1'], 'contains': ['36.a1.a1', '36.b1.a1', '36.e1.a1', '36.x1.a1', '36.x1.b1', '36.z1.a1', '36.z1.b1', '54.e1.a1'], 'core': '36.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [2371, -1, 2590, -1, 6592, -1, 7114, -1], 'generators': [7, 432, 12, 504, 48], 'label': '864.2236.18.i1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '18.i1.a1', 'projective_image': '432.523', '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': '8.5'}
  • id: 111526939
    {'ambient': '864.2236', 'aut_centralizer_order': 12, 'aut_label': '18.j1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '48.51', 'aut_weyl_index': 36, 'centralizer': '72.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.g1.a1', '9.b1.a1'], 'contains': ['36.c1.a1', '36.k1.a1', '36.p1.a1', '36.y1.a1', '36.y1.b1', '36.ba1.a1', '36.ba1.b1', '54.e1.a1'], 'core': '108.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6417, -1, 4830, -1, 4200, -1, 5123, -1], 'generators': [7, 288, 12, 504, 432], 'label': '864.2236.18.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '18.j1.a1', 'projective_image': '432.523', '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': '24.14'}
  • id: 111526940
    {'ambient': '864.2236', 'aut_centralizer_order': 12, 'aut_label': '18.k1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '48.48', 'aut_weyl_index': 36, 'centralizer': '72.i1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.h1.a1', '9.c1.a1'], 'contains': ['36.q1.a1', '36.bb1.a1', '36.bb1.b1', '54.e1.a1', '72.g1.a1'], 'core': '108.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [2911, -1, 2983, -1, 8191, -1, 7862, -1], 'generators': [7, 432, 12, 8, 504], 'label': '864.2236.18.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '18.k1.a1', 'projective_image': '432.523', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '18.k1.a1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
  • id: 111526941
    {'ambient': '864.2236', 'aut_centralizer_order': 6, 'aut_label': '18.l1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '48.48', 'aut_weyl_index': 36, 'centralizer': '144.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.i1.a1'], 'contains': ['36.r1.a1', '36.bc1.a1', '36.bc1.b1', '54.e1.a1', '72.h1.a1'], 'core': '108.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [661, -1, 418, -1, 9834, -1, 9606, -1], 'generators': [7, 432, 12, 680, 504], 'label': '864.2236.18.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.i1.a1', 'old_label': '18.l1.a1', 'projective_image': '432.523', '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': '24.12'}
  • id: 111526942
    {'ambient': '864.2236', 'aut_centralizer_order': 8, 'aut_label': '18.m1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '72.46', 'aut_weyl_index': 24, 'centralizer': '108.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.a1.a1', '6.k1.a1', '9.a1.a1'], 'contains': ['36.a1.a1', '36.d1.a1', '36.h1.a1', '54.f1.a1'], 'core': '36.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4944, -1, 7129, -1, 4638, -1, 3826, -1], 'generators': [6, 48, 504, 432, 12], 'label': '864.2236.18.m1.a1', 'mobius_quo': None, 'mobius_sub': -3, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.b1.a1', 'old_label': '18.m1.a1', 'projective_image': '432.523', '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': '36.10'}
  • id: 111526943
    {'ambient': '864.2236', 'aut_centralizer_order': 12, 'aut_label': '18.n1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '48.51', 'aut_weyl_index': 36, 'centralizer': '72.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1.a1', '6.j1.a1', '9.a1.a1'], 'contains': ['36.a1.a1', '36.f1.a1', '36.g1.a1', '54.g1.a1'], 'core': '36.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5704, -1, 5046, -1, 4816, -1, 4794, -1], 'generators': [1, 48, 504, 12, 432], 'label': '864.2236.18.n1.a1', 'mobius_quo': None, 'mobius_sub': -3, 'normal_closure': '6.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '18.n1.a1', 'projective_image': '432.523', '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': '24.14'}
  • id: 111526944
    {'ambient': '864.2236', 'aut_centralizer_order': 8, 'aut_label': '18.o1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '24.14', 'aut_weyl_index': 72, 'centralizer': '108.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.a1.a1', '9.b1.a1'], 'contains': ['36.i1.a1', '36.j1.a1', '36.n1.a1', '36.o1.a1', '36.p1.a1', '54.f1.a1'], 'core': '108.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [8377, -1, 8958, -1, 1914, -1, 1923, -1], 'generators': [6, 288, 504, 432, 12], 'label': '864.2236.18.o1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1.a1', 'old_label': '18.o1.a1', 'projective_image': '432.523', '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': '12.4'}
  • id: 111526945
    {'ambient': '864.2236', 'aut_centralizer_order': 12, 'aut_label': '18.p1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '16.14', 'aut_weyl_index': 108, 'centralizer': '72.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.j1.a1', '9.b1.a1'], 'contains': ['36.l1.a1', '36.m1.a1', '36.p1.a1', '54.g1.a1'], 'core': '108.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [8746, -1, 7565, -1, 2392, -1, 2675, -1], 'generators': [1, 432, 504, 288, 12], 'label': '864.2236.18.p1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1.a1', 'old_label': '18.p1.a1', 'projective_image': '432.523', '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': '8.5'}
  • id: 111526946
    {'ambient': '864.2236', 'aut_centralizer_order': 4, 'aut_label': '18.q1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '48.48', 'aut_weyl_index': 36, 'centralizer': '216.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.k1.a1', '9.c1.a1'], 'contains': ['36.q1.a1', '54.f1.a1', '72.o1.a1'], 'core': '108.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [3170, -1, 4630, -1, 7413, -1, 5508, -1], 'generators': [6, 432, 8, 12, 504], 'label': '864.2236.18.q1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1.a1', 'old_label': '18.q1.a1', 'projective_image': '432.523', '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': '24.12'}
  • id: 111526947
    {'ambient': '864.2236', 'aut_centralizer_order': 4, 'aut_label': '18.r1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '48.48', 'aut_weyl_index': 36, 'centralizer': '216.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1.a1', '9.c1.a1'], 'contains': ['36.q1.a1', '54.g1.a1', '72.p1.a1'], 'core': '108.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [4031, -1, 3289, -1, 8048, -1, 6205, -1], 'generators': [1, 432, 12, 8, 504], 'label': '864.2236.18.r1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.c1.a1', 'old_label': '18.r1.a1', 'projective_image': '432.523', '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': '24.12'}
  • id: 111526948
    {'ambient': '864.2236', 'aut_centralizer_order': 12, 'aut_label': '4.a1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '144.183', 'aut_weyl_index': 12, 'centralizer': '144.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '2.b1.a1', '2.c1.a1'], 'contains': ['8.a1.a1', '12.a1.a1', '12.b1.a1', '12.i1.a1', '16.a1.a1'], 'core': '4.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1991, 6607, 2606, 5279, 8450, 6432, 8021, 4815], 'generators': [12, 432, 504, 8, 288, 48], 'label': '864.2236.4.a1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.a1.a1', 'normal_contained_in': ['2.a1.a1', '2.b1.a1', '2.c1.a1'], 'normal_contains': ['8.a1.a1', '12.a1.a1', '12.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.a1.a1', 'projective_image': '432.523', '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': '144.183'}
  • id: 111526949
    {'ambient': '864.2236', 'aut_centralizer_order': 8, 'aut_label': '24.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '216.102', 'aut_weyl_index': 8, 'centralizer': '108.a1.a1', 'complements': ['36.bb1.b1', '36.bc1.b1', '36.bb1.a1', '36.bc1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['8.c1.a1', '12.d1.a1', '12.j1.a1'], 'contains': ['48.a1.a1', '72.i1.a1', '72.l1.a1'], 'core': '24.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4390, 1452, 5442, 8701, 4488, 1306, 3810, 8804], 'generators': [6, 12, 288, 48], 'label': '864.2236.24.a1.a1', 'mobius_quo': 0, 'mobius_sub': -12, 'normal_closure': '24.a1.a1', 'normal_contained_in': ['6.a1.a1'], 'normal_contains': ['48.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '24.a1.a1', 'projective_image': '432.523', 'quotient_action_image': '6.1', 'quotient_action_kernel': '4.2', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '24.a1.a1', 'subgroup_fusion': None, 'weyl_group': '108.17'}
  • id: 111526950
    {'ambient': '864.2236', 'aut_centralizer_order': 144, 'aut_label': '24.b1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '12.4', 'aut_weyl_index': 144, 'centralizer': '12.a1.a1', 'complements': ['36.w1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '12.a1.a1', '12.n1.a1', '12.n1.b1'], 'contains': ['48.d1.a1', '72.a1.a1', '72.x1.a1'], 'core': '24.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2218, 3789, 2182, 5773, 7094, 3165, 7591, 5014], 'generators': [504, 432, 288, 48], 'label': '864.2236.24.b1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '24.b1.a1', 'normal_contained_in': ['8.a1.a1', '12.a1.a1'], 'normal_contains': ['72.a1.a1', '96.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '24.b1.a1', 'projective_image': '864.2236', 'quotient_action_image': '12.4', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '24.b1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 111526951
    {'ambient': '864.2236', 'aut_centralizer_order': 12, 'aut_label': '24.c1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '144.183', 'aut_weyl_index': 12, 'centralizer': '144.a1.a1', 'complements': ['36.u1.a1', '36.v1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '12.b1.a1', '12.o1.a1', '12.o1.b1'], 'contains': ['72.a1.a1', '72.y1.a1', '96.b1.a1'], 'core': '24.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1365, 6315, 1110, 3240, 8982, 4655, 8777, 3813], 'generators': [8, 48, 504, 432], 'label': '864.2236.24.c1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '24.c1.a1', 'normal_contained_in': ['8.a1.a1', '12.b1.a1'], 'normal_contains': ['72.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '24.c1.a1', 'projective_image': '864.2236', 'quotient_action_image': '12.4', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '24.c1.a1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 111526952
    {'ambient': '864.2236', 'aut_centralizer_order': 144, 'aut_label': '24.d1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '4.2', 'aut_weyl_index': 432, 'centralizer': '12.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.a1.a1', '12.c1.a1', '12.d1.a1', '12.e1.a1', '12.f1.a1', '12.g1.a1', '12.h1.a1'], 'contains': ['48.a1.a1', '48.d1.a1', '48.e1.a1', '72.b1.a1', '72.c1.a1', '72.d1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7584, -1, 6780, -1, 3941, -1, 3158, -1], 'generators': [12, 504, 288, 48], 'label': '864.2236.24.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '24.d1.a1', 'projective_image': '432.523', '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': '4.2'}
  • id: 111526953
    {'ambient': '864.2236', 'aut_centralizer_order': 12, 'aut_label': '24.e1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '24.14', 'aut_weyl_index': 72, 'centralizer': '72.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.b1.a1', '12.c1.a1', '12.j1.a1', '12.k1.a1'], 'contains': ['48.a1.a1', '48.f1.a1', '48.f1.b1', '72.e1.a1', '72.f1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [4931, -1, 5978, -1, 6255, -1, 4583, -1], 'generators': [7, 12, 48, 288], 'label': '864.2236.24.e1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.c1.a1', 'old_label': '24.e1.a1', 'projective_image': '432.523', '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': '12.4'}
  • id: 111526954
    {'ambient': '864.2236', 'aut_centralizer_order': 6, 'aut_label': '24.f1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '24.14', 'aut_weyl_index': 72, 'centralizer': '144.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.h1.a1', '8.b1.a1', '12.l1.a1'], 'contains': ['48.b1.a1', '48.g1.a1', '48.g1.b1', '72.e1.a1', '72.g1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [1991, -1, 1905, -1, 8473, -1, 8467, -1], 'generators': [7, 12, 48, 8], 'label': '864.2236.24.f1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.l1.a1', 'old_label': '24.f1.a1', 'projective_image': '432.523', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.f1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 111526955
    {'ambient': '864.2236', 'aut_centralizer_order': 6, 'aut_label': '24.g1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '12.4', 'aut_weyl_index': 144, 'centralizer': '144.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.i1.a1', '8.b1.a1'], 'contains': ['48.c1.a1', '48.h1.a1', '48.h1.b1', '72.e1.a1', '72.h1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [920, -1, 1294, -1, 9442, -1, 9346, -1], 'generators': [7, 12, 48, 680], 'label': '864.2236.24.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.g1.a1', 'old_label': '24.g1.a1', 'projective_image': '432.523', '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': '6.1'}
  • id: 111526956
    {'ambient': '864.2236', 'aut_centralizer_order': 12, 'aut_label': '24.h1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '24.14', 'aut_weyl_index': 72, 'centralizer': '72.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.d1.a1', '12.f1.a1', '12.j1.a1', '12.k1.a1'], 'contains': ['48.a1.a1', '72.j1.a1', '72.m1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [4700, -1, 5590, -1, 4666, -1, 3470, -1], 'generators': [1, 288, 12, 48], 'label': '864.2236.24.h1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.c1.a1', 'old_label': '24.h1.a1', 'projective_image': '432.523', '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': '12.4'}
  • id: 111526957
    {'ambient': '864.2236', 'aut_centralizer_order': 8, 'aut_label': '24.i1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '72.46', 'aut_weyl_index': 24, 'centralizer': '108.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.d1.a1', '12.h1.a1', '12.k1.a1'], 'contains': ['48.a1.a1', '72.k1.a1', '72.n1.a1', '72.n2.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7372, -1, 7982, -1, 1677, -1, 1160, -1], 'generators': [510, 12, 288, 48], 'label': '864.2236.24.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '24.i1.a1', 'projective_image': '432.523', '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': '36.10'}
  • id: 111526958
    {'ambient': '864.2236', 'aut_centralizer_order': 6, 'aut_label': '24.j1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '24.14', 'aut_weyl_index': 72, 'centralizer': '144.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.k1.a1', '8.c1.a1', '12.l1.a1'], 'contains': ['48.b1.a1', '72.i1.a1', '72.o1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [2696, -1, 4172, -1, 7600, -1, 5628, -1], 'generators': [6, 8, 12, 48], 'label': '864.2236.24.j1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.l1.a1', 'old_label': '24.j1.a1', 'projective_image': '432.523', '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': '12.4'}
  • id: 111526959
    {'ambient': '864.2236', 'aut_centralizer_order': 6, 'aut_label': '4.b1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '144.183', 'aut_weyl_index': 12, 'centralizer': '144.a1.a1', 'complements': ['216.d1.a1', '216.f1.a1', '216.e1.a1', '216.k1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1'], 'contains': ['8.a1.a1', '12.n1.a1', '12.o1.a1', '12.p1.a1', '16.b1.a1'], 'core': '4.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [906, 3480, 915, 8273, 8946, 3944, 8777, 871], 'generators': [19, 432, 504, 8, 288, 48], 'label': '864.2236.4.b1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': ['2.a1.a1'], 'normal_contains': ['8.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.b1.a1', 'projective_image': '864.2236', 'quotient_action_image': '2.1', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '4.b1.a1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 111526960
    {'ambient': '864.2236', 'aut_centralizer_order': 2, 'aut_label': '24.k1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '216.102', 'aut_weyl_index': 8, 'centralizer': '432.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1.a1', '8.d1.a1', '12.l1.a1'], 'contains': ['48.b1.a1', '72.j1.a1', '72.p1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [3435, -1, 2804, -1, 7997, -1, 7483, -1], 'generators': [1, 12, 8, 48], 'label': '864.2236.24.k1.a1', 'mobius_quo': None, 'mobius_sub': -3, 'normal_closure': '6.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1.a1', 'old_label': '24.k1.a1', 'projective_image': '432.523', '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': '108.17'}
  • id: 111526961
    {'ambient': '864.2236', 'aut_centralizer_order': 144, 'aut_label': '24.l1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '4.2', 'aut_weyl_index': 432, 'centralizer': '12.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.a1.a1', '12.m1.a1', '12.m1.b1'], 'contains': ['48.d1.a1', '48.e1.a1', '72.q1.a1', '72.r1.a1', '72.s1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4085, -1, 4383, -1, 5035, -1, 5243, -1], 'generators': [444, 504, 288, 48], 'label': '864.2236.24.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '24.l1.a1', 'projective_image': '864.2236', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.l1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 111526962
    {'ambient': '864.2236', 'aut_centralizer_order': 12, 'aut_label': '24.m1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '24.14', 'aut_weyl_index': 72, 'centralizer': '72.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.c1.a1', '12.m1.a1', '12.n1.a1'], 'contains': ['48.d1.a1', '48.f1.a1', '72.t1.a1', '72.u1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3586, -1, 4537, -1, 6955, -1, 5946, -1], 'generators': [19, 432, 48, 288], 'label': '864.2236.24.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '24.m1.a1', 'projective_image': '864.2236', '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': '24.14'}
  • id: 111526963
    {'ambient': '864.2236', 'aut_centralizer_order': 12, 'aut_label': '24.m1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '24.14', 'aut_weyl_index': 72, 'centralizer': '72.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.c1.a1', '12.m1.b1', '12.n1.b1'], 'contains': ['48.d1.a1', '48.f1.b1', '72.t1.b1', '72.u1.b1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3586, -1, 3797, -1, 6955, -1, 5796, -1], 'generators': [7, 432, 48, 288], 'label': '864.2236.24.m1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '24.m1.b1', 'projective_image': '864.2236', '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': '24.14'}
  • id: 111526964
    {'ambient': '864.2236', 'aut_centralizer_order': 12, 'aut_label': '24.n1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '24.14', 'aut_weyl_index': 72, 'centralizer': '72.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.e1.a1', '12.m1.b1', '12.n1.a1'], 'contains': ['48.d1.a1', '72.v1.a1', '72.w1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3264, -1, 3638, -1, 6564, -1, 6113, -1], 'generators': [523, 48, 432, 288], 'label': '864.2236.24.n1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '24.n1.a1', 'projective_image': '864.2236', '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': '24.14'}
  • id: 111526965
    {'ambient': '864.2236', 'aut_centralizer_order': 12, 'aut_label': '24.n1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '24.14', 'aut_weyl_index': 72, 'centralizer': '72.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.e1.a1', '12.m1.a1', '12.n1.b1'], 'contains': ['48.d1.a1', '72.v1.b1', '72.w1.b1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3264, -1, 3957, -1, 6564, -1, 6299, -1], 'generators': [511, 48, 432, 288], 'label': '864.2236.24.n1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '24.n1.b1', 'projective_image': '864.2236', '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': '24.14'}
  • id: 111526966
    {'ambient': '864.2236', 'aut_centralizer_order': 12, 'aut_label': '24.o1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '72.43', 'aut_weyl_index': 24, 'centralizer': '144.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '12.i1.a1', '12.p1.a1', '12.p1.b1'], 'contains': ['72.a1.a1', '72.z1.a1', '96.c1.a1'], 'core': '72.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [224, -1, 158, -1, 9613, -1, 9770, -1], 'generators': [584, 48, 504, 432], 'label': '864.2236.24.o1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '24.o1.a1', 'projective_image': '864.2236', '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': '72.43'}
  • id: 111526967
    {'ambient': '864.2236', 'aut_centralizer_order': 12, 'aut_label': '24.p1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '24.14', 'aut_weyl_index': 72, 'centralizer': '72.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.c1.a1'], 'contains': ['48.e1.a1', '48.f1.a1', '48.f1.b1', '72.ba1.a1', '72.bb1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [6072, -1, 6301, -1, 5173, -1, 3948, -1], 'generators': [7, 444, 48, 288], 'label': '864.2236.24.p1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.c1.a1', 'old_label': '24.p1.a1', 'projective_image': '864.2236', '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': '12.4'}
  • id: 111526968
    {'ambient': '864.2236', 'aut_centralizer_order': 12, 'aut_label': '24.q1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '24.14', 'aut_weyl_index': 72, 'centralizer': '72.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.g1.a1'], 'contains': ['48.e1.a1', '72.bc1.a1', '72.bd1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [9967, -1, 9971, -1, 301, -1, 83, -1], 'generators': [505, 288, 444, 48], 'label': '864.2236.24.q1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.e1.a1', 'old_label': '24.q1.a1', 'projective_image': '864.2236', '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': '12.4'}
  • id: 111526969
    {'ambient': '864.2236', 'aut_centralizer_order': 4, 'aut_label': '27.a1', 'aut_quo_index': None, 'aut_stab_index': 27, 'aut_weyl_group': '16.14', 'aut_weyl_index': 108, 'centralizer': '108.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['9.a1.a1', '9.b1.a1', '9.c1.a1'], 'contains': ['54.a1.a1', '54.b1.a1', '54.c1.a1', '54.d1.a1', '54.e1.a1', '54.f1.a1', '54.g1.a1'], 'core': '108.a1.a1', 'coset_action_label': None, 'count': 27, 'diagramx': [5321, -1, 7436, -1, 3220, -1, 3513, -1], 'generators': [1, 6, 504], 'label': '864.2236.27.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '27.a1.a1', 'old_label': '27.a1.a1', 'projective_image': '432.523', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '27.a1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 111526970
    {'ambient': '864.2236', 'aut_centralizer_order': 6, 'aut_label': '4.b1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '144.183', 'aut_weyl_index': 12, 'centralizer': '144.a1.a1', 'complements': ['216.d1.a1', '216.f1.a1', '216.e1.a1', '216.k1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1'], 'contains': ['8.a1.a1', '12.n1.b1', '12.o1.b1', '12.p1.b1', '16.b1.b1'], 'core': '4.b1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [906, 3480, 1424, 2286, 8946, 3944, 8558, 2810], 'generators': [7, 432, 504, 8, 288, 48], 'label': '864.2236.4.b1.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '4.b1.b1', 'normal_contained_in': ['2.a1.a1'], 'normal_contains': ['8.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.b1.b1', 'projective_image': '864.2236', 'quotient_action_image': '2.1', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '4.b1.b1', 'subgroup_fusion': None, 'weyl_group': '144.183'}
  • id: 111526971
    {'ambient': '864.2236', 'aut_centralizer_order': 12, 'aut_label': '32.a1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '36.10', 'aut_weyl_index': 48, 'centralizer': '144.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '16.a1.a1', '16.b1.a1', '16.b1.b1'], 'contains': ['96.a1.a1', '96.b1.a1', '96.c1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [458, -1, 853, -1, 8800, -1, 8772, -1], 'generators': [8, 288], 'label': '864.2236.32.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1.a1', 'old_label': '32.a1.a1', 'projective_image': '864.2236', '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': '36.10'}
  • id: 111526972
    {'ambient': '864.2236', 'aut_centralizer_order': 144, 'aut_label': '36.a1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '12.4', 'aut_weyl_index': 144, 'centralizer': '12.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['12.a1.a1', '12.b1.a1', '12.i1.a1', '18.i1.a1', '18.m1.a1', '18.n1.a1'], 'contains': ['72.a1.a1', '72.b1.a1', '72.q1.a1', '108.a1.a1'], 'core': '36.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2535, 7621, 3348, 5033, 6770, 6650, 6684, 6336], 'generators': [12, 504, 432, 48], 'label': '864.2236.36.a1.a1', 'mobius_quo': -1, 'mobius_sub': 18, 'normal_closure': '36.a1.a1', 'normal_contained_in': ['12.a1.a1', '12.b1.a1'], 'normal_contains': ['72.a1.a1', '108.a1.a1', '144.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '36.a1.a1', 'projective_image': '432.523', 'quotient_action_image': '12.4', 'quotient_action_kernel': '3.1', 'quotient_action_kernel_order': 3, 'quotient_fusion': None, 'short_label': '36.a1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 111526973
    {'ambient': '864.2236', 'aut_centralizer_order': 24, 'aut_label': '36.b1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '8.5', 'aut_weyl_index': 216, 'centralizer': '36.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.c1.a1', '18.a1.a1', '18.b1.a1', '18.i1.a1'], 'contains': ['72.b1.a1', '72.e1.a1', '72.t1.a1', '72.t1.b1', '72.ba1.a1', '108.b1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [5112, -1, 6569, -1, 5684, -1, 4745, -1], 'generators': [7, 12, 432, 48], 'label': '864.2236.36.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '36.b1.a1', 'projective_image': '432.523', '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': '4.2'}
  • id: 111526974
    {'ambient': '864.2236', 'aut_centralizer_order': 24, 'aut_label': '36.c1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '24.14', 'aut_weyl_index': 72, 'centralizer': '36.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.c1.a1', '18.c1.a1', '18.d1.a1', '18.j1.a1'], 'contains': ['72.c1.a1', '72.f1.a1', '72.u1.a1', '72.u1.b1', '72.bb1.a1', '108.b1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6882, -1, 6976, -1, 3790, -1, 3290, -1], 'generators': [7, 12, 432, 288], 'label': '864.2236.36.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '36.c1.a1', 'projective_image': '432.523', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '36.c1.a1', 'subgroup_fusion': None, 'weyl_group': '12.4'}
  • id: 111526975
    {'ambient': '864.2236', 'aut_centralizer_order': 16, 'aut_label': '36.d1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '12.4', 'aut_weyl_index': 144, 'centralizer': '54.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.d1.a1', '18.a1.a1', '18.e1.a1', '18.m1.a1'], 'contains': ['72.b1.a1', '72.i1.a1', '72.k1.a1', '108.c1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [6274, -1, 8255, -1, 4099, -1, 2511, -1], 'generators': [6, 504, 12, 48], 'label': '864.2236.36.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '36.d1.a1', 'projective_image': '432.523', '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': '6.1'}
  • id: 111526976
    {'ambient': '864.2236', 'aut_centralizer_order': 24, 'aut_label': '36.e1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '8.5', 'aut_weyl_index': 216, 'centralizer': '36.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.e1.a1', '18.e1.a1', '18.f1.a1', '18.i1.a1'], 'contains': ['72.b1.a1', '72.v1.a1', '72.v1.b1', '108.d1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [6475, -1, 5831, -1, 5363, -1, 4922, -1], 'generators': [511, 12, 48, 432], 'label': '864.2236.36.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '36.e1.a1', 'projective_image': '432.523', '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': '4.2'}
  • id: 111526977
    {'ambient': '864.2236', 'aut_centralizer_order': 24, 'aut_label': '36.f1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '24.14', 'aut_weyl_index': 72, 'centralizer': '36.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.f1.a1', '18.a1.a1', '18.f1.a1', '18.n1.a1'], 'contains': ['72.b1.a1', '72.j1.a1', '108.e1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6024, -1, 5577, -1, 4310, -1, 3655, -1], 'generators': [1, 432, 12, 48], 'label': '864.2236.36.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '36.f1.a1', 'projective_image': '432.523', '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': '12.4'}
  • id: 111526978
    {'ambient': '864.2236', 'aut_centralizer_order': 24, 'aut_label': '36.g1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '24.14', 'aut_weyl_index': 72, 'centralizer': '36.k1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.g1.a1', '18.b1.a1', '18.e1.a1', '18.n1.a1'], 'contains': ['72.b1.a1', '72.bc1.a1', '108.f1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7375, -1, 9206, -1, 1959, -1, 1646, -1], 'generators': [505, 432, 444, 48], 'label': '864.2236.36.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '36.g1.a1', 'projective_image': '432.523', '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': '12.4'}
  • id: 111526979
    {'ambient': '864.2236', 'aut_centralizer_order': 8, 'aut_label': '36.h1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '24.14', 'aut_weyl_index': 72, 'centralizer': '108.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.h1.a1', '18.b1.a1', '18.f1.a1', '18.m1.a1'], 'contains': ['72.b1.a1', '72.k1.a1', '108.g1.a1'], 'core': '144.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [7171, -1, 7999, -1, 2672, -1, 2048, -1], 'generators': [438, 504, 12, 48], 'label': '864.2236.36.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.a1.a1', 'old_label': '36.h1.a1', 'projective_image': '432.523', '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': '12.4'}
  • id: 111526980
    {'ambient': '864.2236', 'aut_centralizer_order': 16, 'aut_label': '36.i1', 'aut_quo_index': None, 'aut_stab_index': 9, 'aut_weyl_group': '12.4', 'aut_weyl_index': 144, 'centralizer': '54.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.d1.a1', '18.c1.a1', '18.g1.a1', '18.o1.a1'], 'contains': ['72.c1.a1', '72.l1.a1', '72.n1.a1', '108.c1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 9, 'diagramx': [8698, -1, 9462, -1, 937, -1, 1005, -1], 'generators': [6, 432, 12, 288], 'label': '864.2236.36.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '9.b1.a1', 'old_label': '36.i1.a1', 'projective_image': '432.523', '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': '6.1'}